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Intermediate
Mathematical
FRQ

A 0.2 kg object is attached to a horizontal spring undergoes SHM with the total energy of 0.4 J. The kinetic energy as a function of position presented by the graph.

Intermediate
Mathematical
GQ

A boat is rowed directly upriver at a speed of \(2.5 \, \text{m/s}\) relative to the water. Viewers on the shore find that it is moving at only \(0.5 \, \text{m/s}\) relative to the shore. What is the speed of the river? Is it moving with or against the boat?

Beginner
Conceptual
MCQ

A student is designing an experiment to find the spring constant \( k \) of a spring using only a set of known masses and a stopwatch. Which procedure would work?

Intermediate
Mathematical
GQ

A car can decelerate at \( -3.80 \, \text{m/s}^2 \) without skidding when coming to rest on a level road. What would its deceleration be if the road is inclined at \( 9.3^\circ \) and the car moves uphill? Assume the same static friction coefficient.

Intermediate
Conceptual
MCQ

An object’s velocity \(v\) as a function of time \(t\) is given in the graph. Which of the following statements is true about the motion of the object?

Advanced
Mathematical
GQ

A \(6 \, \text{kg}\) cube rests against a compressed spring with a force constant of \(1{,}800 \, \text{N/m}\), initially compressed by \(0.3 \, \text{m}\). Upon release, the cube slides on a horizontal surface with a kinetic friction coefficient of \(\mu_k = 0.12\) for \(3 \, \text{m}\), then ascends a \(12^\circ\) slope, stopping after \(4.5 \, \text{m}\). Determine the coefficient of kinetic friction on the slope.

Intermediate
Mathematical
FRQ

A motorcycle has tires with a diameter of \( 44.0 \) \( \text{cm} \). Cruising down the highway, they are rotating at \( 1150 \) \( \text{rpm} \) (revolutions per minute).

Advanced
Conceptual
MCQ

A ladder at rest is leaning against a wall at an angle. Which of the following forces must have the same magnitude as the frictional force exerted on the ladder by the floor?

Beginner
Mathematical
GQ

A \( 6.00 \, \text{m} \) long, \( 500 \, \text{kg} \) steel uniform beam extends horizontally from the point where it has been bolted to the framework of a new building under construction. A \( 70 \, \text{kg} \) construction worker stands at the far end of the beam. What is the magnitude of the torque about the bolt due to the worker and the weight of the beam?

Beginner
Conceptual
MCQ

When we refer to an object’s speed, we’re talking about:

Intermediate
Mathematical
GQ

A mine shaft is known to be 57.8 m deep. If you dropped a rock down the shaft, how long would it take for you to hear the sound of the rock hitting the bottom of the shaft knowing that sound travels at a constant velocity of 345 m/s?

Advanced
Mathematical
FRQ
A physical setup diagram showing a tall vertical tower with a pivot point at the top. A single chain of length 10 meters hangs from the pivot, connected to a chair. The chair and chain are drawn at an angle theta from the vertical. The child is depicted as a simplified block sitting in the chair. A dashed circular path is drawn indicating the radius of rotation of the chair. A horizontal dimension line indicates the radius r, and an arc marker labels the angle theta between the vertical tower and the taut chain.

A neighbor’s child wants to go to a carnival to experience the wild rides. The neighbor is worried about safety because one of the rides looks particularly dangerous. She knows that you have taken physics and so asks you for advice. The ride in question has a \(4 \, \text{kg}\) chair which hangs freely from a \(10 \, \text{m}\) long chain attached to a pivot on the top of a tall tower. When the child enters the ride, the chain is hanging straight down. The child is then attached to the chair with a seat belt and shoulder harness. When the ride starts up, the chain rotates about the tower. Soon the chain reaches its maximum speed and remains rotating at that speed, which corresponds to one rotation about the tower every \(3 \, \text{seconds}\). When you ask the operator, he says the ride is perfectly safe. He demonstrates this by sitting in the stationary chair. The chain creaks but holds, and he weighs \(90 \, \text{kg}\).

Advanced
Proportional Analysis
MCQ

A \(250 \, \text{newton}\) centripetal force acts on a car moving at a constant speed in a horizontal circle. If the same force is applied, but the radius is made smaller, what happens to the speed \(v\) and the frequency \(f\) of the car?

Intermediate
Mathematical
GQ

In lacrosse, a typical throw is made by rotating the stick through an angle of roughly \(90^\circ\), then releasing the ball when the stick is vertical, as shown above. If the \(1 \, \text{meter}\) long stick is at rest when horizontal and the ball leaves the stick with a velocity of \(10 \, \text{m/s}\), what angular acceleration must the stick experience?

Advanced
Mathematical
FRQ

A diver descends from a salvage ship to the ocean floor at a depth of \(35 \text{ m}\) below the surface. The density of ocean water is \(1.025 \times 10^3 \text{ kg/m}^3\).

Advanced
Mathematical
FRQ

Priscilla the Penguin stands at the edge of a rock ledge and tosses a small ice cube directly upward with an initial velocity of \( v_0 \). The ice cube’s initial height above the ground is \( 3.25 \, \text{m} \), and it reaches its maximum height above the ground \( 0.586 \, \text{s} \) after being thrown. The ice cube then plummets to the ground, missing the edge of the rock ledge on its way down.

Intermediate
Mathematical
FRQ

Initially, a ball has an angular velocity of \( 5.0 \) \( \text{rad/s} \) counterclockwise. Some time later, after rotating through a total angle of \( 5.5 \) \( \text{radians} \), the ball has an angular velocity of \( 1.5 \) \( \text{rad/s} \) clockwise.

Intermediate
Mathematical
GQ

A Venturi tube has a pressure difference of \( 15\,000 \) \( \text{Pa} \). The entrance radius is \( 3 \) \( \text{cm} \), while the exit radius is \( 1 \) \( \text{cm} \). What are the entrance velocity, exit velocity, and flow rate if the fluid is gasoline \( (\rho = 700 \) \( \text{kg/m}^3 ) \)?

Intermediate
Mathematical
GQ

A crane’s trolley at point \( P \) moves for a few seconds to the right with constant acceleration, and the \( 870 \, \text{kg} \) load hangs on a light cable at a \( 5^\circ \) angle to the vertical as shown. What is the acceleration of the trolley and load?

Intermediate
Mathematical
FRQ

An airplane is traveling \( 900. \) \( \text{km/h} \) in a direction \( 38.5^\circ \) west of north.

Advanced
Conceptual
MCQ

A whiffle ball is tossed straight up, reaches a highest point, and falls back down. Air resistance is not negligible. Which of the following statements are true?

  1. The ball’s speed is zero at the highest point.
  2. The ball’s acceleration is zero at the highest point.
  3. The ball takes a shorter time to travel up to the highest point than to fall back down.
Intermediate
Conceptual
MCQ

A truck going \(15 \, \text{km/h}\) has a head-on collision with a small car going \(30 \, \text{km/h}\). Which statement best describes the situation?

Intermediate
Mathematical
MCQ

A windmill blade with a rotational inertia of \( 6.0 \) \( \text{kg} \cdot \text{m}^2 \) has an initial angular velocity of \( 8 \) \( \text{rad/s} \) in the clockwise direction. It is then given an angular acceleration of \( 4 \) \( \text{rad/s}^2 \) in the clockwise direction for \( 10 \) seconds. What is the change in rotational kinetic energy of the blade over this time interval?

Advanced
Mathematical
FRQ

On a frictionless horizontal air table, puck A (with mass \( 0.249 \) \( \text{kg} \)) is moving toward puck B (with mass \( 0.375 \) \( \text{kg} \)), which is initially at rest. After the collision, puck A has velocity \( 0.115 \) \( \text{m/s} \) to the left, and puck B has velocity \( 0.645 \) \( \text{m/s} \) to the right.

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