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Intermediate
Mathematical
MCQ

A rod  is initially at rest on a rough horizontal surface. Three forces are exerted on the rod with the magnitudes and directions shown in the figure. The force exerted in the center of the rod is an equidistant 0.5 m from both ends of the rod. If friction between the rod and the table prevents the rod from rotating, what is the magnitude of the torque exerted on the rod about its center from frictional forces?

Advanced
Mathematical
MCQ

A simple pendulum consists of a sphere tied to the end of a string of negligible mass. The sphere is pulled back until the string is horizontal and then released from rest. Assume the gravitational potential energy is zero when the sphere is at its lowest point.

What angle will the string make with the horizontal when the kinetic energy and the potential energy of the sphere-Earth system are equal?

Intermediate
Mathematical
FRQ

A block hangs from the ceiling by a massless rope. A \( 3.0 \, \text{kg} \) block is attached to the first block and hangs below it on another piece of massless rope. The tension in the top rope is \( 63.0 \, \text{N} \).

Beginner
Mathematical
FRQ

A \(0.025 \, \text{kg}\) golf ball moving at \(18.0 \, \text{m/s}\) crashes through the window of a house in \(5.0 \times 10^{-4} \, \text{s}\). After the crash, the ball continues in the same direction with a speed of \(10.0 \, \text{m/s}\).

Intermediate
Mathematical
MCQ

A cube of unknown material and uniform density floats in a container of water with \(60\%\) of its volume submerged. If this same cube were placed in a container of oil with density \(800\) \(\text{kg/m}^3\), what portion of the cube’s volume would be submerged while floating?

Beginner
Mathematical
GQ

Diamond has a density of \( 3500 \) \( \text{kg/m}^3 \). During a physics lab, a diamond drops out of Virginia’s necklace and falls into her graduated cylinder filled with \( 5.00 \times 10^{-5} \) \( \text{m}^3 \) of water. This causes the water level to rise to the \( 5.05 \times 10^{-5} \) \( \text{m}^3 \) mark. What is the mass of Virginia’s diamond?

Beginner
Conceptual
MCQ

For an object oscillating in SHM, what is the relationship between its displacement, velocity, and acceleration graphs as a function of time?

Intermediate
Conceptual
GQ

Water balloons are tossed from the roof of a building, all with the same speed but with different launch angles. Which one has the highest speed when it hits the ground? Ignore air resistance. Without using equations, explain your answer.

Advanced
Mathematical
FRQ

A snowboarder starts from rest and slides down a \(32^\circ\) incline that’s \(75 \, \text{m}\) long.

Advanced
Mathematical
GQ

A \(3800 \, \text{kg}\) open railroad car coasts along with a constant speed of \(8.60 \, \text{m/s}\) along a level track. Snow begins to fall vertically and fills the car at a rate of \(3.50 \, \text{kg/min}\). Ignoring friction with the tracks, what is the speed of the car after \(90 \, \text{min}\)?

Advanced
Mathematical
GQ

Riders in a carnival ride stand with their backs against the wall of a circular room of diameter \(8.0 \, \text{m}\). The room is spinning horizontally about an axis through its center at a rate of \(45 \, \text{rev/min}\) when the floor drops so that it no longer provides any support for the riders. What is the minimum coefficient of static friction between the wall and the rider required so that the rider does not slide down the wall?

Beginner
Mathematical
FRQ

A high-speed drill rotating counterclockwise at \( 2400 \) \( \text{rpm} \) comes to a halt in \( 2.5 \) \( \text{s} \).

Intermediate
Conceptual
MCQ

A block attached to a spring undergoes simple harmonic motion. The acceleration of the block has its maximum magnitude at the point where:

Beginner
Mathematical
GQ

A centrifuge accelerates uniformly from rest to 15,000 rpm in 240 s. Through how many revolutions did it turn in this time?

Beginner
Mathematical
MCQ

A block is attached to a horizontal spring. The block is held so the spring is stretched and the block is released from rest, undergoing simple harmonic motion with a frequency of \( 2 \) \( \text{Hz} \). How long after release will the block first reach a point where it is momentarily at rest?

Intermediate
Mathematical
GQ

Find the tension in each cable supporting the gymnast who weighs \( 600 \) \( \text{N} \). The gymnast is at rest, holding a junction point where two cables are attached: one cable is horizontal, and the second cable is attached to the ceiling making an angle of \( 37^{\circ} \) above the horizontal, as shown in the diagram.

Beginner
Mathematical
MCQ

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

Intermediate
Mathematical
FRQ

A \( 240 \) \( \text{kg} \) block is dropped from \( 3.0 \) meters onto a spring, compresses the spring and comes to rest.

Advanced
Conceptual
MCQ

A block is projected up a ramp with an initial speed \( v_0 \). It travels along the surface of the ramp with constant acceleration \( a \). Take the positive direction of motion to be up the ramp. If the acceleration vector points opposite the initial velocity vector, which of the following MUST be true?

Beginner
Conceptual
MCQ

Which car controls directly allow the driver to cause acceleration?

Advanced
Conceptual
MCQ

When the speed of a rear-drive car is increasing on a horizontal road, what is the direction of the frictional force on the tires?

Advanced
Mathematical
GQ

The difference in pressure between the atmosphere and the human lungs is \( 1.05 \times 10^5 \) \( \text{Pa} \). What is the longest straw you could use to draw up milk whose density is \( 1030 \) \( \text{kg/m}^3 \)?

Intermediate
Mathematical
GQ

A loop-de-loop roller coaster has a radius of \( 30 \) \( \text{m} \). Determine the apparent weight a \( 500 \) \( \text{N} \) person will feel at the bottom of the loop while traveling at a speed of \( 25 \) \( \text{m/s} \) and at the top of the loop while traveling at a speed of \( 20 \) \( \text{m/s} \).

Beginner
Mathematical
GQ

What is the weight of a person who has a mass of \(75 \, \text{kg}\)?

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