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Intermediate
Conceptual
GQ

Suppose you are a passenger traveling in car along a road that bends to the left. Why will you feel like you are being thrown against the door. What causes this force?

Beginner
Conceptual
MCQ

When a box is about to slide but hasn’t moved yet, which friction is acting?

Advanced
Mathematical
MCQ

A ball of mass m is fastened to a string. The ball swings at constant speed in a vertical circle of radius R with the other end of the string held fixed. Neglecting air resistance, what is the difference between the string’s tension at the bottom of the circle and at the top of the circle?

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?

Intermediate
Mathematical
FRQ
A right-triangle ramp is drawn on the left side of a horizontal baseline. The ramp’s hypotenuse slopes downward from left to right at an angle labeled “θ0” between the hypotenuse and the rightward horizontal baseline. The horizontal run of the ramp (its base) is marked as length D, starting at x = –D on the leftmost top point of the ramp and ending at x = 0 at the foot of the ramp. From x = 0 to x = 4D, the baseline is a straight horizontal line representing the rough surface. Tick marks on the baseline indicate positions x = 0, D, 2D, 3D, and 4D. The inclined segment is frictionless; the horizontal segment is shaded or marked as rough. No block is explicitly drawn on the diagram.

A block is initially at rest on top of an inclined ramp that makes an angle \( \theta_0 \) with the horizontal. The distance measured along the base of the ramp is \( D \). After the block is released from rest, it slides down the frictionless ramp and then continues onto a rough horizontal surface until it finally comes to rest at the position \( x = 4D \) measured from the base of the ramp. The coefficient of kinetic friction between the block and the rough horizontal surface is \( \mu_k \).

Advanced
Mathematical
GQ

A \(81 \, \text{kg}\) student dives off a \(45 \, \text{m}\) tall bridge with an \(18 \, \text{m}\) long bungee cord tied to his feet and to the bridge. You can consider the bungee cord to be a flexible spring. What spring constant must the bungee cord have for the student’s lowest point to be \(2.0 \, \text{m}\) above the water?

Intermediate
Mathematical
MCQ

A linear spring of force constant \( k \) is used in a physics lab experiment. A block of mass \( m \) is attached to the spring and the resulting frequency, \( f \), of the simple harmonic oscillations is measured. Blocks of various masses are used in different trials, and in each case, the corresponding frequency is measured and recorded. If \( f^{2} \) is plotted versus \( \frac{1}{m} \), the graph will be a straight line with slope

Advanced
Mathematical
GQ

A person shoots a basketball with a speed of \( 12 \, \text{m/s} \) at an angle of \( 35^\circ \) above the horizontal. If the person is \( 2.4 \, \text{m} \) tall and the hoop is \( 3.05 \, \text{m} \) above the ground, how far back must the person stand in order to make the shot?

Beginner
Proportional Analysis
MCQ

Two uniform disks have the same mass but different radii: disk \( 1 \) has a radius \( R \) and disk \( 2 \) has a radius \( 2R \). What is the ratio of the moment of inertia of the first disk to the second disk?

Beginner
Conceptual
MCQ

A runner pushes against the track to sprint forward. Which two action–reaction FORCE pairs are involved? Select two letters.

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?

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