PHY10101 Problem Bank

You are driving toward a traffic signal when it turns yellow. Your speed is the legal speed limit of 55 km/h; your best deceleration rate has magnitude 5.18 m/s². Your best reaction time to begin braking is 0.75 s. To avoid having the front of your car enter the intersection after the light turns red, should you brake to a stop or continue to move at 55 km/h if the distance to the intersection and the duration of the yellow light are (a) 40 m and 2.8 s and (b) 32 m and 1.8 s? Give an answer of brake, continue, either, or neither.

A person walks 3.1 km north, then 2.4 km west, and finally 5.2 km south. (a) Sketch the vector diagram that represents this motion. (b) How far and (c) in what direction would a bird fly in a straight line from the same starting point to the same final point?

A baseball leaves a pitcher's hand horizontally at a speed of 153 km/h. The distance to the batter is 18.3 m. Ignore air resistance. (a) How long does the ball take to travel the first half of that distance? (b) The second half? (c) How far does the ball fall during the first half? (d) During the second half? (e) Why are the answers to (c) and (d) different?

An Earth satellite moves in a circular orbit 750 km above Earth's surface with a period of 98.0 min. What are (a) its speed and (b) the magnitude of its centripetal acceleration? Use Earth's radius 6370 km.

A block of mass m = 5.00 kg is pulled along a horizontal frictionless floor by a cord that exerts a force of magnitude F = 12.0 N at an angle θ = 25.0° above the horizontal. (a) What is the magnitude of the block's acceleration? (b) The force magnitude F is slowly increased. What is its value just before the block is lifted completely off the floor? (c) What is the magnitude of the block's acceleration just before it is lifted off the floor?

A 15 kg sled on a horizontal table is attached to a 2.0 kg hanging sand box by a string of negligible mass passing over a pulley of negligible mass and friction. The coefficient of kinetic friction between the sled and table top is 0.040. Find (a) the acceleration of the sled and (b) the tension of the string.

A 5.0 kg block slides down a 30° incline. The coefficient of kinetic friction is 0.20. (a) Draw the free-body diagram. (b) Find the acceleration along the incline.

A puck of mass m = 1.50 kg slides in a circle of radius r = 25.0 cm on a frictionless table while attached to a hanging cylinder of mass M = 2.50 kg by means of a cord that extends through a hole in the table. What speed keeps the cylinder at rest?

A cave rescue team lifts an 80.0 kg injured spelunker vertically through three successive 12.0 m stages: (a) from rest to 5.00 m/s, (b) at constant speed 5.00 m/s, and (c) from 5.00 m/s back to rest. How much work is done on the rescuee by the lifting force during each stage?

A child is released from rest at the top of a frictionless water slide, 8.5 m above the bottom. Find the child's speed at the bottom.

A 2.0 kg package slides along a floor at 4.0 m/s. It reaches an initially relaxed spring along a frictionless path. While the spring is being compressed, a kinetic friction force of 15 N acts on the package. If the spring constant is 10000 N/m, by what distance is the spring compressed when the package momentarily stops?

A boy starts essentially from rest at the top of a frictionless hemispherical ice mound of radius 12.8 m. At what height above the center of the mound does he lose contact with the ice?

A paratrooper whose chute fails to open lands in snow; he is hurt slightly. Had he landed on bare ground, the stopping time would have been 10 times shorter and the collision lethal. Does the presence of the snow increase, decrease, or leave unchanged the values of (a) the paratrooper's change in momentum, (b) the impulse stopping the paratrooper, and (c) the force stopping the paratrooper?

A 2.0 kg cart moving at 4.0 m/s collides with a 3.0 kg cart initially at rest. The carts stick together. Find (a) their common speed and (b) the decrease in total kinetic energy.

A block of wood of mass 5.4 kg hangs from two long cords. A bullet of mass 9.5 g embeds in the block. The block and bullet then swing upward until their center of mass has risen 6.3 cm. Find the speed of the bullet just before the collision.

Two metal spheres hang from vertical cords and initially just touch. Sphere 1 has mass 30 g and is released from rest from a height 8.0 cm above its lowest point. It then makes a one-dimensional elastic collision with sphere 2, whose mass is 75 g and is initially at rest. Find the velocity of sphere 1 just after the collision.

A disk rotates about its central axis starting from rest with constant angular acceleration. At one time it is rotating at 10 rev/s; 60 revolutions later, its angular speed is 15 rev/s. Calculate (a) the angular acceleration, (b) the time required for those 60 revolutions, (c) the time required to reach 10 rev/s from rest, and (d) the number of revolutions made before reaching 10 rev/s.

A uniform disk of mass 2.5 kg and radius 20 cm is mounted on a fixed horizontal axle. A 1.2 kg block hangs from a massless cord wrapped around the rim. The cord does not slip and axle friction is negligible. Find (a) the acceleration of the block, (b) the angular acceleration of the disk, and (c) the tension in the cord.

A solid ball of radius 6.0 cm is initially rolling smoothly at 10 m/s along a horizontal floor. It then rolls smoothly up a ramp until it momentarily stops. What maximum height above the floor does it reach?

A student on a frictionless rotating stool has total rotational inertia 4.0 kg·m² and angular speed 2.0 rad/s. The student pulls the arms inward, reducing the rotational inertia to 2.0 kg·m². (a) Find the new angular speed. (b) Find the change in rotational kinetic energy. (c) Explain why kinetic energy can change while angular momentum is conserved.

A 0.500 kg block attached to a spring of constant 200 N/m executes simple harmonic motion with amplitude 0.100 m. Find (a) angular frequency, (b) period, (c) maximum speed, and (d) maximum acceleration.

For an ideal mass-spring oscillator of amplitude A, determine the fractions of the total mechanical energy that are (a) potential and (b) kinetic when x = A/2. (c) What fraction of the maximum speed is the speed at that position?

A simple pendulum has length 1.00 m. For small oscillations, find its period (a) on Earth, where g = 9.80 m/s², and (b) on the Moon, where g = 1.62 m/s².

A block of mass m = 1.8 kg rests on top of a block of mass M = 5.0 kg. The lower block is attached to a horizontal spring of constant k = 200 N/m and moves on a frictionless horizontal surface. The coefficient of static friction between the two blocks is 0.40. What amplitude of simple harmonic motion puts the upper block on the verge of slipping over the lower block?

A wave traveling along a string is described by y = (0.00327 m) sin[(72.1 rad/m)x − (2.72 rad/s)t]. Find (a) the amplitude, (b) wavelength, (c) period, (d) frequency, (e) wave speed, and (f) the displacement at x = 22.5 cm and t = 18.9 s.

What phase difference between two identical traveling waves, moving in the same direction along a stretched string, produces a combined wave with amplitude 0.852 times the amplitude of either individual wave? Express the answer in (a) degrees, (b) radians, and (c) wavelengths.

What are (a) the lowest frequency, (b) the second-lowest frequency, and (c) the third-lowest frequency for standing waves on a wire 10.0 m long, of mass 100 g, stretched under a tension of 250 N?

A tube 0.900 m long is closed at one end. A stretched wire 0.330 m long and of mass 9.60 g is fixed at both ends and oscillates in its fundamental mode. By resonance it drives the air column in the tube at the column's second-lowest harmonic frequency. Find (a) that frequency and (b) the tension in the wire. Take the speed of sound as 343 m/s.

At a depth of 10.9 km, the Challenger Deep in the Marianas Trench of the Pacific Ocean is the deepest site in any ocean. Assuming that seawater has a uniform density of 1024 kg/m³, approximate the hydrostatic pressure (in atmospheres) that the bathyscaph Trieste had to withstand.

A plastic tube has a cross-sectional area of 5.00 cm². The tube is filled with water until the short arm, of length d = 0.800 m, is full. Then the short arm is sealed and more water is gradually poured into the long arm. If the seal will pop off when the net upward force on it exceeds 9.80 N, what total height of water in the long arm will put the seal on the verge of popping?

A hollow sphere of inner radius 8.0 cm and outer radius 9.0 cm floats half-submerged in a liquid of density 820 kg/m³. (a) What is the mass of the sphere? (b) Calculate the density of the material of which the sphere is made.

A water pipe having a 2.5 cm inside diameter carries water into the basement of a house at a speed of 0.90 m/s and a pressure of 190 kPa. If the pipe tapers to 1.2 cm and rises to the second floor 7.6 m above the input point, what are the (a) speed and (b) water pressure at the second floor?

How much heat must be absorbed by ice of mass 720 g at −10°C to take it to liquid state at 15°C? If we supply the ice with a total energy of only 210 kJ as heat, what then are the final state and temperature of the water? Use c_ice = 2220 J/(kg·K), L_f = 333 kJ/kg, and c_water = 4190 J/(kg·K).

Let 1.00 kg of liquid water at 100°C be converted to steam at 100°C by boiling at standard atmospheric pressure, 1.01×10⁵ Pa. The volume changes from 1.00×10⁻³ m³ as a liquid to 1.671 m³ as steam. (a) How much work is done by the system? (b) How much energy is transferred as heat? Use L_v = 2256 kJ/kg. (c) What is the change in the system's internal energy?

Determine the average translational kinetic energy per molecule of an ideal gas at (a) 20.0°C and (b) 80.0°C. What is the translational kinetic energy per mole at (c) 20.0°C and (d) 80.0°C?

Suppose 12.0 g of O₂ gas is heated at constant atmospheric pressure from 25.0°C to 125°C. Assume the molecules rotate but do not vibrate. (a) How many moles are present? (b) How much energy is transferred to the gas as heat? (c) What fraction of that heat raises the internal energy? Use molar mass 32.0 g/mol.

A Carnot engine has an efficiency of 22.0%. It operates between constant-temperature reservoirs that differ in temperature by 75.0 K. Find the temperatures of (a) the colder and (b) the hotter reservoir.

A 50.0 g block of copper at 200 K is placed in an insulated box with a 100 g block of lead at 400 K. Find (a) the equilibrium temperature, (b) the change in total internal energy of the two-block system, and (c) the total entropy change. Use c_Cu = 386 J/(kg·K) and c_Pb = 128 J/(kg·K).

In a thermally isolated experiment, 400 g of aluminum at 100°C is mixed with 50.0 g of water at 20.0°C. Find (a) the equilibrium temperature and the entropy changes of (b) the aluminum, (c) the water, and (d) the combined system. Use c_Al = 900 J/(kg·K) and c_water = 4190 J/(kg·K).

Six independent molecules can each be in the left or right half of a box. (a) How many microstates have exactly three molecules on the left? (b) Compare this with the macrostate in which all six are on the left. (c) Find ΔS = k_B ln(Ω_3/Ω_6).