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Beginner
Proportional Analysis
GQ

A car rounds a curve at a steady \( 50 \) \( \text{km/h} \). If it rounds the same curve at a steady \( 70 \) \( \text{km/h} \), will its acceleration be any different?

Beginner
Mathematical
MCQ

A \(1200 \, \text{kg}\) car moving at \(15.6 \, \text{m/s}\) suddenly collides with a stationary car of mass \(1500 \, \text{kg}\). If the two vehicles lock together, what is their combined velocity immediately after the collision?

Beginner
Proportional Analysis
MCQ

A \( 4 \)-\( \text{kg} \) ball and a \( 1 \)-\( \text{kg} \) ball are positioned a distance \( L \) apart on a bar of negligible mass. How far from the \( 4 \)-\( \text{kg} \) mass should the fulcrum be placed to balance the bar?

Intermediate
Conceptual
MCQ

A system consists of a disk rotating on a frictionless axle and a piece of clay moving toward it, as shown in the figure above. The outside edge of the disk is moving at a linear speed \( v \), and the clay is moving at speed \( \frac{v}{2} \). The clay sticks to the outside edge of the disk. How does the angular momentum of the system after the clay sticks compare to the angular momentum of the system before the clay sticks, and what is an explanation for the comparison?

Intermediate
Conceptual
MCQ

A net torque is applied to the edge of a spinning object as it rotates about its internal axis. The table shows the net torque exerted on the object at different instants in time. How can a student use the data table to determine the change in angular momentum of the object from \( 0 \) to \( 6 \) \( \text{s} \)? Justify your selection.

Time \( (\text{s}) \) Net Torque \( (\text{N} \cdot \text{m}) \)
0 0
2 1.5
4 3.0
6 4.5
Beginner
Mathematical
FRQ

If a small motor does 520 J of work to move a toy car 260 meters in a time of 37 seconds.

Advanced
Mathematical
MCQ

Ball 1 is dropped from rest at time \( t = 0 \) from a tower of height \( h \). At the same instant, ball 2 is launched upward from the ground with the initial speed \( v_0 \). If air resistance is negligible, at what time \( t \) will the two balls pass each other?

Intermediate
Conceptual
FRQ

A box rests on the (frictionless) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed.

Intermediate
Mathematical
GQ

The side of an above-ground pool is punctured, and water gushes out through the hole. If the total depth of the pool is \( 2.5 \) \( \text{m} \), and the puncture is \( 1 \) \( \text{m} \) above the ground level, what is the efflux speed of the water?

Intermediate
Mathematical
GQ

Consider a neutron star with a mass equal to the sun, a radius of 10 km, and a rotation period of 1.0 s. What is the radius of a geosynchronous orbit about the neutron star? The mass of the sun can be found in the formula sheet above.

Advanced
Mathematical
FRQ

Two balls are launched at the same time from opposite sides of a \( 100 \) \( \text{m} \) wide and \(1000 ~\text{m}\) canyon. Ball A is launched at \( 20 \) \( \text{m/s} \) at \( 45^{\circ} \) from the left side. Ball B is launched at \( 20 \) \( \text{m/s} \) at \( 45^{\circ} \) from the right side.

Intermediate
Mathematical
FRQ

A \(30 \, \text{g}\) bullet is fired with a speed of \(500 \, \text{m/s}\) into a wall.

Beginner
Conceptual
GQ

Only \( 1 \) non-zero force acts on an object. Can the object have \( 0 \) acceleration? Can it have \( 0 \) velocity? Explain.

Intermediate
Conceptual
MCQ

Two blocks of the same size are floating in a container of water. The first block is submerged \( 80\% \) while the second block is submerged by \( 20\% \) beneath the water. Which of the following is a correct statement about the two blocks?

Beginner
Mathematical
MCQ

An object is released from rest near the surface of a planet. The velocity of the object as a function of time is expressed in the following equation. \( v_y = (-3) \, \text{m/s}^2 \, t \) All frictional forces are considered to be negligible. What distance does the object fall \( 10 \) \( \text{s} \) after it is released from rest?

Intermediate
Mathematical
GQ

By pressing a painting of mass \( 2.00 \) \( \text{kg} \) against a wall, a man is trying to determine whether it is appropriately positioned. The wall is perpendicular to the pushing force. The coefficient of static friction between the image and the wall is \( 0.660 \). What is the bare minimum pushing force that must be applied?

Intermediate
Conceptual
MCQ

A person pulls a rope with a force \( F \) at an angle of \( 60^\circ \) to the horizontal. The rope is connected to a load over a frictionless pulley as shown in the diagram. The load is stationary. Which of the following is correct about the weight of the load and the net force exerted on the pulley by the rope?

Intermediate
Proportional Analysis
MCQ

The figure shows a horizontal pipe with sections with different cross-sectional areas. Small tubes extend from the top of each section. The cross-sectional area of the pipe at location C is half that at A, and the areas at A and D are the same. Water flows in the pipe from left to right. Which of the following correctly ranks the height \( h \) of the water in the tubes above the labeled locations?

Beginner
Conceptual
GQ

Why do you tend to slide across the car seat when the car makes a sharp turn?

Intermediate
Mathematical
FRQ

A cylindrical tank of water (height \( H \)) is punctured at a height \( h \) above the bottom. How far from the base of the tank will the water stream land (in terms of \( h \) and \( H \))? What must the value of \( h \) be such that the distance at which the stream lands will be equal to \( H \)?

Beginner
Mathematical
FRQ

Find the following three values using just rotational kinematics.

Beginner
Mathematical
MCQ

A pendulum has a period of \(2.0 \, \text{s}\) on Earth. What is its length?

Advanced
Conceptual
MCQ

A person is standing on a railroad station platform when a high-speed train passes by. The person will tend to be

Advanced
Mathematical
MCQ
Wagon Wheel Structure Moment of Inertia Wheel Mass Wheel Radius
Wagon \(A\) Solid disk \[\frac{1}{2} M R^2\] \[ 0.5 \, \text{kg} \] \[ 0.1 \, \text{m} \]
Wagon \(B\) Solid disk \[\frac{1}{2} M R^2\] \[ 0.2 \, \text{kg} \] \[ 0.1 \, \text{m} \]
Wagon \(C\) Hollow hoop \[M R^2\] \[ 0.1 \, \text{kg} \] \[ 0.1 \, \text{m} \]

Three wagons have identical total mass (including their wheels) and each has four wheels. However, the wheels on each wagon have different designs with varying mass distributions and radii as shown in a reference chart. When accelerating each wagon from a standstill to \( 10 \) \( \text{m/s} \), which wagon requires the most energy input?

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