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Questions
A 0.010 kg bullet traveling horizontally at 400 m/s passes completely through a 2.0 kg block initially at rest on a frictionless surface, exiting at 100 m/s in the same direction. What is the block's speed just after the bullet exits?
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A 0.020 kg dart is fired horizontally into a 1.98 kg block hanging from long strings. The dart embeds in the block, and the block-dart combination swings upward, rising a maximum height of 0.20 m. Use g = 10 m/s^2. What was the dart's speed just before impact?
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A 0.10 M solution of a weak acid HA has a pH of 3.00 at 25°C. What is the acid dissociation constant, Ka, for HA?
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A 0.10 M solution of a weak acid HA is diluted with water to 0.010 M at constant temperature. Which statement correctly describes the changes upon dilution?
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A 0.10 M solution of a weak monoprotic acid HA has a pH of 2.70 at 25^°C. What is the percent ionization of the acid?
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A 0.10 M solution of ammonia (NH_3, a weak base) is titrated with 0.10 M HCl. Which best describes the pH at the equivalence point at 25^°C?
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A 0.100 M stock solution of a colored dye has an absorbance of 0.80 at its λ_max in a 1.0 cm cuvette. A student pipets 25.0 mL of the stock into a 100.0 mL volumetric flask and dilutes to the mark. What absorbance is expected for the diluted solution in the s...
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A 0.15 kg ball is dropped from a height of 1.8 m onto a hard floor and rebounds to a height of 0.80 m. Use g = 10 m/s^2. What is the magnitude of the impulse the floor delivers to the ball during the bounce?
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A 0.20 kg ball is at rest when a force is applied, accelerating it to 10 m/s in 0.050 s. What is the magnitude of the impulse delivered to the ball?
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A 0.20 kg ball of clay moving at 10 m/s strikes and sticks to the end of a uniform thin rod of mass 1.0 kg and length 0.80 m that is pivoted at its other end and initially at rest. What is the angular velocity of the rod-clay system immediately after the coll...
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A 0.20 M solution of a weak monoprotic acid is 1.5% ionized at equilibrium. What is the approximate K_a of the acid?
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A 0.25 kg mass oscillates on a spring with a frequency of 2.0 Hz. What is the spring constant?
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A 0.40 kg ball moving horizontally at 5.0 m/s strikes a wall and rebounds along the same line at 3.0 m/s. The ball is in contact with the wall for 0.020 s. What is the magnitude of the average force the wall exerts on the ball?
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A 0.40 kg block is pressed against a horizontal spring (k = 500 N/m) that is compressed 0.20 m. When released, the block slides across a frictionless surface. What is the speed of the block after it leaves the spring?
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A 0.50 kg ball attached to a string travels in a circle of radius 2.0 m at a speed of 8.0 m/s. What is the magnitude of the ball's angular momentum about the center of the circle?
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A 0.50 kg ball is released from rest at a height of 20 m above the ground on a frictionless track. Use g = 10 m/s^2. What is the speed of the ball at ground level?
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A 0.50 kg ball on a string is swung in a vertical circle of radius 1.0 m. At the lowest point of the circle, the ball's speed is 4.0 m/s. Using g = 10 m/s^2, what is the tension in the string at that point?
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A 0.50 kg ball on the end of a lightweight rod swings in a circle of radius 2.0 m. Treating the ball as a point mass, what is its rotational inertia about the center of the circle?
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A 0.50 kg ball rests on a vertical spring (k = 250 N/m) that is compressed 0.20 m and then released, launching the ball upward. Use g = 10 m/s^2. What maximum height above its release position does the ball reach?
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A 0.50 kg ball traveling at 8.0 m/s to the right strikes a wall and bounces back at 6.0 m/s to the left. The ball is in contact with the wall for 0.020 s. What is the magnitude of the average force exerted by the wall on the ball?
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A 0.50 kg block is attached to a spring with spring constant 200 N/m on a frictionless horizontal surface. What is the period of oscillation?
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A 0.50 kg block oscillates on a spring with spring constant 200 N/m and amplitude 0.10 m. What is the block's speed when it is 0.060 m from equilibrium?
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A 1.0 kg ball moving at 10 m/s collides with a 3.0 kg ball at rest, and they stick together. What fraction of the initial kinetic energy is lost in the collision?
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A 1.0 kg block on a frictionless horizontal surface is attached to a spring with spring constant 100 N/m. The block is displaced and released. What is the period of the resulting oscillation?
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A 1.0 kg block starts from rest and slides 2.0 m down a frictionless incline angled at 30^° above the horizontal, then compresses a spring (k = 100 N/m) aligned with the incline. Use g = 10 m/s^2. What is the maximum compression of the spring?
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A 1.0 L buffer contains 0.50 mol of a weak acid HA (pK_a = 4.00) and 0.50 mol of NaA. After 0.10 mol of solid NaOH dissolves in the buffer (no volume change), what is the new pH?
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A 1.0 L flask is charged with 0.80 mol of NOBr, which decomposes by 2 NOBr(g) leftharpoons 2 NO(g) + Br_2(g). At equilibrium, [Br_2] = 0.10 M. What is K_c?
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A 1.20 g sample of a compound (molar mass 60.0 g/mol) is burned in a bomb calorimeter whose total heat capacity is 5.86 kJ/^°C. The temperature rises by 3.00 ^°C. What is the enthalpy of combustion per mole of the compound?
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A 10 kg block rests on a horizontal surface with μ_s = 0.60 and μ_k = 0.40. A horizontal force is applied to the block, increasing linearly from 0 N at t = 0 to 80 N at t = 8.0 s. Use g = 10 m/s^2. At what time does the block begin to move?
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A 10 kg box sits on a horizontal surface with a coefficient of static friction μ_s = 0.40 and a coefficient of kinetic friction μ_k = 0.30. A horizontal force is gradually increased from zero. What is the minimum applied force needed to start the box moving,...
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A 10 kg cannon sits on a frictionless surface and fires a 2.0 kg cannonball horizontally at 50 m/s relative to the ground. What is the total kinetic energy released by the explosion?
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A 10 kg crate, initially at rest, is pulled 6.0 m across a rough horizontal floor by a constant horizontal force of 50 N. Friction exerts a constant 20 N force on the crate. What is the crate's speed after the 6.0 m?
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A 10 kg sled is pulled across a horizontal snowy field by a rope making an angle of 37^° above the horizontal, with a tension of 40 N. The coefficient of kinetic friction is 0.25. Using g = 10 m/s^2, sin 37^° = 0.60, and cos 37^° = 0.80, what is the sled's ac...
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A 100.0 g block of iron (c = 0.450 J/(g·^°C)) at 100.0 ^°C is dropped into 100.0 g of water (c = 4.18 J/(g·^°C)) at 20.0 ^°C in an insulated container. What is the final temperature of the system?
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A 1000 kg car travels at 20 m/s and a 2000 kg truck travels at 10 m/s in the same direction. Which of the following correctly compares their momenta and kinetic energies?
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A 1200 kg car accelerates from rest to 30 m/s in 12 s on a level road. What is the average power delivered by the engine, assuming no friction or air resistance?
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A 1500 kg car traveling at 20 m/s brakes and comes to rest. What is the magnitude of the total work done by the braking force?
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A 2.0 kg ball initially moving at 5.0 m/s is acted upon by a net force that does +36 J of work on it. What is the ball's final speed?
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A 2.0 kg ball is released from rest at a height of 5.0 m above the ground on a frictionless track. At the bottom of the track (ground level), the ball enters a rough horizontal section with a coefficient of kinetic friction μ_k = 0.50. How far along the rough...
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A 2.0 kg ball moving at 6.0 m/s collides head-on with a 2.0 kg ball at rest. The collision is perfectly elastic. What are the velocities of the two balls after the collision?
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A 2.0 kg ball on a string moves in a horizontal circle of radius 0.50 m at a constant speed of 3.0 m/s. What is the magnitude of the centripetal acceleration?
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A 2.0 kg block is held against a vertical wall by a horizontal force F pressing it into the wall. The coefficient of static friction between the block and the wall is 0.50. Using g = 10 m/s^2, what is the minimum force F that prevents the block from sliding d...
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A 2.0 kg block is pressed against a spring (k = 800 N/m) compressed by 0.10 m on a horizontal floor. When released, the block slides across the floor, where the coefficient of kinetic friction is 0.20. Use g = 10 m/s^2. How far does the block slide after leav...
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A 2.0 kg block is pushed up a frictionless ramp of length 5.0 m, rising a vertical height of 3.0 m from the floor to a table. Use g = 10 m/s^2. How much work does gravity do on the block during this trip?
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A 2.0 kg block oscillates on a horizontal spring, reaching a maximum speed of 3.0 m/s as it passes through equilibrium. What is the elastic potential energy stored in the spring when the block is at its maximum displacement?
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A 2.0 kg bucket hangs from a light rope wrapped around a solid cylindrical pulley of mass 4.0 kg (I = (1)/(2)MR^2) that is free to rotate about its axle. When the bucket is released, what is its downward acceleration? Use g = 10 m/s^2. Assume the rope does no...
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A 2.0 kg cart moving at 6.0 m/s collides head-on and perfectly elastically with a 4.0 kg cart at rest. What is the velocity of the 2.0 kg cart immediately after the collision?
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A 2.0 kg cart moving right at 6.0 m/s collides head-on with a 4.0 kg cart moving left at 3.0 m/s. The carts stick together. What is their common velocity immediately after the collision?
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A 2.0 kg cart starts from rest on a frictionless track. A force-time graph shows the net force on the cart: a constant +6.0 N for the first 2.0 s, then a constant -2.0 N for the next 3.0 s. What is the cart's velocity at t = 5.0 s?
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A 2.0 kg lab cart on a level track speeds up uniformly from 3.0 m/s to 9.0 m/s in 2.0 s. What is the magnitude of the net force on the cart?
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A 2.0 kg solid sphere (I = (2)/(5)MR^2, R = 0.10 m) rolls without slipping at a translational speed of 3.0 m/s. What is the total kinetic energy of the sphere?
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A 20 kg crate is lowered 5.0 m at constant speed by a rope. Use g = 10 m/s^2. How much work does the rope's tension do on the crate during the descent?
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A 20 kg crate is pushed across a horizontal floor at constant velocity by a horizontal force. The coefficient of kinetic friction between the crate and floor is μ_k = 0.25. Use g = 10 m/s^2. What is the magnitude of the applied force?
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A 25.0 g sample of a metal at 100.0°C is placed into 50.0 g of water at 22.0°C. The final temperature of the system is 24.5°C. What is the specific heat capacity of the metal? (c_water = 4.18 J/(g·°C))
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A 25.0 mL sample of 0.100 M acetic acid (K_a = 1.8 × 10^-5) is titrated with 0.100 M NaOH. What is the pH after exactly 12.5 mL of the base has been added?
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A 25.0 mL sample of 0.200 M HBr is titrated with 0.100 M KOH. What volume of the KOH solution is required to reach the equivalence point?
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A 25.0 mL sample of acetic acid solution is titrated with 0.150 M NaOH, and 30.0 mL of the base is required to reach the equivalence point. Given the 1:1 reaction HC_2H_3O_2 + NaOH arrow NaC_2H_3O_2 + H_2O, what is the molarity of the acetic acid solution?
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A 3.0 kg block is pushed 5.0 m up a frictionless incline that makes a 30^° angle with the horizontal by a force parallel to the incline. Use g = 10 m/s^2. What is the work done by gravity on the block during this displacement?
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A 3.0 kg block on a frictionless horizontal table is connected by a light string over a frictionless, massless pulley to a 2.0 kg block hanging vertically. Using g = 10 m/s^2, what is the acceleration of the system when released?
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A 3.0 kg metal object with volume 5.0 × 10^-4 m^3 hangs from a string, fully submerged in water (ρ = 1000 kg/m^3, g = 10 m/s^2). What is the tension in the string?
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A 3.0 kg object experiences a net force of 12 N to the east. What is the acceleration of the object?
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A 3.0 kg object moves to the right at 4.0 m/s and a 1.0 kg object moves to the left at 8.0 m/s. What is the velocity of the center of mass of the system?
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A 3.0 kg object moving at 8.0 m/s to the right collides head-on with a 5.0 kg object moving at 4.0 m/s to the left. After the collision, the 3.0 kg object moves at 2.0 m/s to the left. What is the velocity of the 5.0 kg object after the collision?
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A 3000 kg railroad car moving at 2.0 m/s couples with an identical 3000 kg car at rest on a straight, level track. What is the speed of the joined cars immediately after coupling?
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A 4.0 kg block is on a rough incline at 30^° with μ_k = 0.20. The block is given a push and slides up the incline. Use g = 10 m/s^2, sin 30^° = 0.50, cos 30^° = 0.87. What is the magnitude of the block's acceleration while it slides up?
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A 4.0 kg block slides across a rough horizontal surface. Its speed decreases from 6.0 m/s to 2.0 m/s over a distance of 4.0 m. What is the magnitude of the friction force acting on the block?
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A 4.0 kg box and a 2.0 kg box sit side by side, touching, on a frictionless floor. A horizontal force of 18 N is applied to the 4.0 kg box, pushing both boxes forward together. What is the magnitude of the contact force that the 4.0 kg box exerts on the 2.0 k...
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A 4.0 kg box slides 3.0 m across a horizontal floor while a constant friction force of 8.0 N acts on it. How much work does friction do on the box? Use g = 10 m/s^2.
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A 4.0 kg cart moving at 3.0 m/s to the right collides with a 2.0 kg cart at rest. After the collision, the two carts stick together. What is their combined velocity after the collision?
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A 4.0 kg cart moving at 6.0 m/s collides with an 8.0 kg cart at rest, and the two stick together. How much kinetic energy is converted to other forms during the collision?
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A 4.92 g sample of a hydrate, MgSO_4 · xH_2O, is heated to constant mass, leaving 2.40 g of anhydrous MgSO_4 (molar mass 120.36 g/mol). What is the value of x? (Molar mass of H_2O = 18.02 g/mol)
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A 5.0 kg block on a frictionless incline angled at 37^° is connected by a light string over a frictionless pulley at the top of the incline to a 3.0 kg block hanging vertically. Using g = 10 m/s^2 and sin 37^° = 0.60, what is the acceleration of the system wh...
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A 5.0 kg block rests on a frictionless horizontal surface. Two horizontal forces act on the block: a 20 N force to the right and a 12 N force to the left. What is the magnitude and direction of the block's acceleration?
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A 5.0 kg block slides across a horizontal floor where the coefficient of kinetic friction is 0.40. Using g = 10 m/s^2, what is the magnitude of the kinetic friction force on the block?
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A 5.0 kg block slides down a frictionless incline that makes an angle of 37^° with the horizontal. Use g = 10 m/s^2, sin 37^° = 0.60, and cos 37^° = 0.80. What is the normal force on the block and its acceleration down the incline?
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A 5.0 kg block starts from rest and slides 4.0 m down a rough incline angled at 30^° with the horizontal. The coefficient of kinetic friction is μ_k = 0.30. Use g = 10 m/s^2, sin 30^° = 0.50, cos 30^° = 0.87. What is the speed of the block at the bottom?
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A 5.0 kg metal block has a density of 2500 kg/m^3. It is completely submerged in water (ρ_water = 1000 kg/m^3). What is the apparent weight of the block in water? Use g = 10 m/s^2.
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A 5.00 L container holds an unknown gas at 25°C and 760 mmHg. The gas has a mass of 8.80 g. What is the molar mass of the gas? (R = 0.0821 L·atm/(mol·K))
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A 50 kg ice skater at rest throws a 5.0 kg ball horizontally at 10 m/s. What is the skater's recoil speed? (Assume the ice is frictionless.)
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A 50 kg rider on a Ferris wheel moves in a vertical circle of radius 5.0 m at a constant speed of 5.0 m/s. Using g = 10 m/s^2, what normal force does the seat exert on the rider at the lowest point of the ride?
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A 50 kg sprinter accelerates from rest to 10 m/s in 5.0 s on level ground. What average power does the sprinter develop over this interval?
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A 50 kg student stands at the rim (radius 2.0 m) of a platform with rotational inertia 100 kg·m^2, and the system rotates at 1.0 rad/s. The student then walks to the center of the platform. What is the final angular speed? (Treat the student as a point mass.)
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A 50.0 g piece of copper cools from 95.0 ^°C to 25.0 ^°C. Given that the specific heat capacity of copper is 0.385 J/(g·^°C), how much heat does the copper release?
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A 6.0 kg object at rest on a frictionless surface explodes into two pieces. The 2.0 kg piece flies east at 9.0 m/s. What is the velocity of the 4.0 kg piece?
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A 6.0 kg toy boat floats at rest on a pond. Using g = 10 m/s^2, what is the buoyant force acting on the boat?
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A 60 kg person jumps from a ledge and lands on the ground, coming to rest. The person's velocity just before landing is 5.0 m/s downward. If the person bends their knees and takes 0.50 s to stop, what is the average net force on the person during landing?
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A 60 N force is applied to the end of a 0.30 m wrench at an angle of 30° to the wrench handle. What is the magnitude of the torque about the bolt at the other end of the handle?
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A 60 N sign hangs in equilibrium from cord A, which is attached to the ceiling and makes an angle of 37^° with the vertical. A second cord, B, pulls horizontally on the sign to hold it in this position. Using sin 37^° = 0.60 and cos 37^° = 0.80, what is the t...
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A 8.0 kg sled is pulled 12 m along a horizontal surface by a rope that makes an angle of 60^° with the horizontal. The tension in the rope is 40 N. How much work does the rope do on the sled?
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A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If two marbles are drawn at random without replacement, what is the probability that both marbles are red?
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A bakery's bread recipe uses flour and sugar in a ratio of 5 to 2 by the cup. If a batch uses 20 cups of flour, how many cups of sugar does it use?
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A ball attached to a string is whirled in a horizontal circle at constant speed on a frictionless table. At the instant the string suddenly breaks, which path does the ball follow?
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A ball is dropped from rest from a bridge and takes 3.0 s to reach the water below. Use g = 10 m/s^2 and ignore air resistance. How high is the bridge above the water?
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A ball is in projectile motion after being thrown at an angle above the horizontal. Ignoring air resistance, which statement correctly compares the ball's acceleration while rising, at the peak, and while falling?
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A ball is kicked from ground level at 20 m/s at an angle of 30^° above the horizontal. Use g = 10 m/s^2 and ignore air resistance. What is the maximum height reached by the ball?
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A ball is kicked from ground level, and its height in feet after t seconds is modeled by h(t) = -16t^2 + 64t. According to the model, after how many seconds does the ball return to the ground?
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A ball is launched horizontally from the edge of a table that is 1.25 m above the floor with an initial speed of 3.0 m/s. Assuming no air resistance and g = 10 m/s^2, how far from the base of the table does the ball land?
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A ball is launched straight up from the ground. It passes a point 40 m above the ground on the way up, and passes the same point again 2.0 s later on the way down. Using g = 10 m/s^2 and ignoring air resistance, what was the ball's launch speed?
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A ball is launched straight up from the ground. Its height, in feet, t seconds after launch is modeled by h(t) = -16t^2 + 48t. According to the model, how many seconds after launch does the ball return to the ground?
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A ball is launched upward from a height of 5 feet. Its height h, in feet, after t seconds is modeled by h(t) = -16t² + 64t + 5. What is the maximum height, in feet, reached by the ball?
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A ball is launched upward, and its height above the ground is modeled by h(t) = -16(t - 3)^2 + 150, where h(t) is the height in feet t seconds after launch. According to the model, how many seconds after launch does the ball reach its maximum height?
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A ball is thrown from ground level at 25 m/s at an angle of 37^° above the horizontal, directly toward a tall wall that is 40 m away. Using g = 10 m/s^2, sin 37^° = 0.60, and cos 37^° = 0.80, at what height above the ground does the ball strike the wall?
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A ball is thrown straight downward with an initial speed of 5.0 m/s from the roof of a building 60 m tall. Using g = 10 m/s^2 and ignoring air resistance, how long does the ball take to reach the ground?
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A ball is thrown straight up and momentarily reaches its highest point. Which of the following correctly describes the ball's velocity and acceleration at that instant? (Ignore air resistance.)
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A ball is thrown straight up with an initial speed of 20 m/s. Ignoring air resistance and using g = 10 m/s^2, what maximum height above its launch point does the ball reach?
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A ball is thrown straight upward with an initial speed of 20 m/s from the edge of a cliff that is 25 m above the ground. Use g = 10 m/s^2. How long after being thrown does the ball hit the ground below the cliff?
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A ball of mass 0.50 kg is attached to a string and swung in a vertical circle of radius 1.0 m. At the top of the circle, the speed of the ball is 4.0 m/s. Use g = 10 m/s^2. What is the tension in the string at the top of the circle?
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A ball on a string moves in a horizontal circle of fixed radius, and the string provides a centripetal force F. If the ball's speed is doubled while the radius stays the same, what centripetal force is now required?
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A ball rolls without slipping down a ramp. Friction acts on the ball the entire way, yet total mechanical energy is conserved. Why?
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A baseball of mass 0.15 kg is pitched at 40 m/s toward the batter. The batter hits the ball, and it leaves the bat at 50 m/s in the opposite direction. The bat is in contact with the ball for 0.0020 s. What is the magnitude of the average force exerted on the...
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A bicycle wheel rolls without slipping along level ground, and its center moves forward at 4.0 m/s. What is the speed of the point at the very top of the wheel, relative to the ground?
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A biochemist needs a buffer at pH = 3.50. Which weak acid (paired with its sodium salt) is the best choice?
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A block attached to a horizontal spring oscillates in simple harmonic motion between x = -A and x = +A. At the instant the block is at x = +A, which statement correctly describes the net force on the block?
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A block attached to a single spring oscillates on a frictionless surface with period T. A second, identical spring is then attached side by side with the first, so that both springs connect the block to the same wall. What is the new period?
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A block attached to a spring oscillates in simple harmonic motion with position given by x(t) = 0.20cos(4π t), where x is in meters and t is in seconds. What are the amplitude and period of the motion?
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A block attached to a spring oscillates with period T. The spring is then cut into two equal halves, and the same block is attached to one of the halves. What is the new period of oscillation?
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A block attached to a spring with spring constant 200 N/m oscillates with amplitude 0.10 m. What is the total mechanical energy of the oscillation?
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A block hangs at rest from a vertical spring, stretching it 0.25 m beyond its natural length. The block is then pulled down slightly and released. Using g = 10 m/s^2, what is the period of the resulting oscillation?
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A block is released from rest at a height of 5.0 m on a frictionless ramp. At the bottom, it slides onto a horizontal floor where the coefficient of kinetic friction is 0.25. Use g = 10 m/s^2. How far along the floor does the block slide before stopping?
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A block is released from rest at x = +A at time t = 0 and undergoes simple harmonic motion with period T. At what time does the block first reach x = +A/2?
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A block of mass m oscillates on a horizontal frictionless surface attached to a spring with spring constant k. If the mass is doubled to 2m while the spring constant remains the same, how does the period of oscillation change?
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A block on a horizontal spring oscillates in simple harmonic motion. At which position is the magnitude of the block's acceleration the greatest?
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A block on a spring completes 50 full oscillation cycles in 20 s. What is the period of the motion?
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A block on a spring oscillates with amplitude A and maximum speed v_max. If the block is instead released with amplitude 2A (same block, same spring), what is its new maximum speed?
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A block on a spring oscillates with amplitude A. At the equilibrium position, which statement correctly describes the energy of the system?
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A block on a spring oscillates with frequency f. The spring is replaced by one with four times the spring constant, keeping the same block. What is the new oscillation frequency?
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A block oscillates horizontally on a frictionless track, attached to a spring. The entire apparatus is moved from Earth to the Moon, where the gravitational field strength is about one-sixth as large. How does the period of oscillation change?
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A block oscillates in simple harmonic motion with amplitude 0.05 m and angular frequency 10 rad/s. What is the maximum magnitude of its acceleration?
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A block oscillates in simple harmonic motion with amplitude A. What total distance does the block travel during one complete period?
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A block oscillates in simple harmonic motion with frequency f. At what frequency does the block's kinetic energy oscillate between its maximum value and zero?
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A block oscillates on a spring with amplitude A and total mechanical energy E. When the block is at displacement x = A/2, what is its kinetic energy?
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A block oscillates on a spring with amplitude A. At what displacement from equilibrium is the kinetic energy equal to the potential energy?
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A block oscillating in SHM has a position described by x(t) = Acos(ω t). Which of the following correctly describes the velocity as a function of time?
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A block oscillating on a spring is momentarily at its maximum displacement from equilibrium. Which statement correctly describes its velocity and acceleration at that instant?
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A block slides down a frictionless ramp while a solid sphere rolls without slipping down an identical ramp, both released from rest at the same height. Which statement correctly compares their speeds at the bottom?
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A block's position during simple harmonic motion is described by x(t) = Asin(ω t). Which statement correctly describes the block at t = 0?
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A boat can move at 5.0 m/s relative to the water. The captain wants to travel straight across an 80 m wide river whose current flows at 3.0 m/s, so she angles the boat upstream to cancel the drift. How long does the crossing take?
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A boat can travel at 5.0 m/s in still water. It attempts to cross a river that is 60 m wide and has a current flowing at 3.0 m/s from left to right. If the boat points directly across the river (perpendicular to the bank), how far downstream from its starting...
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A book rests on a horizontal table. Which of the following correctly describes the forces acting on the book and why it remains in equilibrium?
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A botanist transplanted 18 tomato seedlings into a garden and measured each seedling's height weekly. A scatterplot of height versus time has line of best fit y = 1.8w + 6.2, where w is the number of weeks after transplanting and y is the predicted height in...
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A bowling ball (I = (2)/(5)MR^2) rolls without slipping and reaches the bottom of a hill with a total kinetic energy of 70 J. It then rolls up a second hill. Assuming it continues to roll without slipping, to what maximum height does it rise? The ball has mas...
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A buffer contains 0.050 M of a weak acid HA (K_a = 1.0 × 10^-5) and 0.50 M of its conjugate base A^-. What is the pH of the buffer?
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A buffer contains 0.20 M HF and 0.40 M NaF. Given K_a(HF) = 6.3 × 10^-4 (pK_a = 3.20), what is the pH of this buffer?
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A buffer is prepared with 0.50 M NH₃ and 0.25 M NH₄Cl. What is the pH of this buffer? (Kb for NH₃ = 1.8 × 10⁻⁵)
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A buffer solution contains 0.40 mol CH₃COOH and 0.40 mol CH₃COO⁻ in 1.0 L. If 0.050 mol HCl is added (assume no volume change), what is the new pH? (Ka = 1.8 × 10⁻⁵, pKa = 4.74)
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A bus trip is modeled by d(t) = 240 - 60t, where d(t) is the distance, in miles, remaining to the destination t hours after departure. What is the best interpretation of the number 60 in this context?
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A car accelerates forward on dry pavement, and its drive wheels roll without slipping. What is the friction force exerted by the road on the drive wheels?
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A car accelerates from rest, and its wheels of radius 0.25 m roll without slipping. When the car's acceleration is 2.0 m/s^2, what is the angular acceleration of each wheel?
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A car doubles its speed from v to 2v. By what factor does the minimum braking distance increase, assuming the same constant braking force in both cases?
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A car drives over the crest of a hill that forms a vertical circular arc of radius 40 m. Using g = 10 m/s^2, what is the maximum speed at which the car can cross the crest without its wheels leaving the road?
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A car of mass 1000 kg rounds a flat (unbanked) curve of radius 50 m at constant speed. The coefficient of static friction between the tires and road is μ_s = 0.40. Use g = 10 m/s^2. What is the maximum speed at which the car can make the turn without sliding?
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A car purchased for $25,000 depreciates in value by 15% each year. Which expression represents the value of the car, in dollars, after 3 years?
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A car purchased for 24,000 dollars loses 15% of its value each year. To the nearest dollar, what is the car's value 2 years after purchase?
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A car starts from rest and accelerates uniformly at 2 m/s^2 for 10 s. It then travels at constant velocity for another 10 s. What is the total distance traveled by the car during the entire 20 s?
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A car traveled 342 miles using 9.5 gallons of gasoline. At this rate, how many miles does the car travel per gallon?
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A car travels 240 miles using 8 gallons of fuel. At this same rate, how many gallons of fuel would be needed to travel 420 miles?
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A car travels along a level highway at a constant 30 m/s while its engine delivers 60 kW of power to the wheels. What is the total magnitude of the resistive forces (air drag plus rolling resistance) acting on the car?
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A car's antilock braking system prevents the wheels from locking and skidding during hard braking. In terms of friction, why does keeping the tires rolling (not skidding) produce a shorter stopping distance?
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A car's engine delivers constant power to the wheels as the car speeds up along a level road. When the car's speed doubles from v to 2v, what happens to the propulsive force the engine applies through the wheels?
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A carpenter has exactly 60 hours available this week to build chairs and tables. Each chair takes 5 hours to build and each table takes 2 hours to build, so the combinations that use all 60 hours satisfy 5x + 2y = 60, where x is the number of chairs and y is...
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A cart on a frictionless track collides with a spring bumper attached to a force sensor. Students run trials at several initial speeds. For each trial they record the impulse J (from the area under the sensor's force-time graph) and the cart's velocity change...
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A cart on a spring track undergoes oscillations in which its acceleration is related to its position by a = -(25 s^-2) x. What is the period of the motion?
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A cart's velocity-time graph shows the velocity increasing linearly from 0 to +12 m/s between t = 0 and t = 3.0 s, then decreasing linearly back to 0 between t = 3.0 s and t = 6.0 s. What is the cart's total displacement over the 6.0 s?
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A catalyst is added to a gas-phase reaction mixture that has already reached equilibrium at constant temperature. Which statement correctly describes the effect of the catalyst?
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A catalyst is added to a reaction mixture at constant temperature. Which of the following quantities remains unchanged?
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A catapult launches a projectile from level ground at speed v and angle θ, achieving a horizontal range R. If the launch speed is doubled to 2v while the angle stays the same (air resistance negligible), what is the new range?
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A ceiling fan with rotational inertia 1.5 kg·m^2 is spinning at 30 rad/s when it is switched off. A constant friction torque brings it to rest in 5.0 s. What is the magnitude of the friction torque?
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A chemist needs a buffer with pH = 5.00 using a weak acid HA with K_a = 1.0 × 10^-4 (pK_a = 4.00). What ratio ([A^-])/([HA]) is required?
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A chemist needs to separate a homogeneous mixture of two miscible liquids, one boiling at 56°C and the other at 118°C. Distillation is chosen. Distillation separates these liquids based on differences in which property?
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A chemist transfers 25.0 mL of a 2.00 M stock solution into a volumetric flask and adds water until the total volume is 500.0 mL. What is the concentration of the diluted solution?
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A child runs and jumps onto the rim of a rotating merry-go-round, gripping the rail and rotating with it. During this landing, which quantity of the child + merry-go-round system is conserved?
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A chromium-plating bath contains Cr^3+(aq). What mass of chromium metal (molar mass 52.00 g/mol) is deposited when a current of 10.0 A flows for 1930 s? (F = 96,485 C/mol)
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A circle has a radius of 10 inches. What is the area, in square inches, of a sector of the circle with a central angle measuring 72°?
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A circle has a radius of 6 meters. An arc of the circle has a length of 5π meters. What is the measure, in degrees, of the central angle that intercepts this arc?
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A circle has a radius of 6. What is the area of a sector of this circle with a central angle of 60°?
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A circle has a radius of 9 centimeters. What is the length, in centimeters, of the arc intercepted by a central angle measuring 120°?
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A city's population is 5,000 and increases by 20% each year. Which expression gives the population m months after the population was 5,000?
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A colored solution in a 1.00 cm cuvette has an absorbance of 0.60 at its wavelength of maximum absorption, where the molar absorptivity is ε = 120 M^-1cm^-1. What is the molar concentration of the absorbing species?
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A community theater sold 12 tickets for a total of 81 dollars. Adult tickets cost 8 dollars each and child tickets cost 5 dollars each. How many adult tickets were sold?
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A company's quarterly sales are shown below. Quarter 1: $120,000 Quarter 2: $150,000 Quarter 3: $180,000 Quarter 4: $210,000 Quarter 3 sales represent what fraction of the total annual sales?
