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Advanced
Mathematical
FRQ

Three blocks of masses \(m_3 = 1.0 \, \text{kg}\), \(m_2 = 2.0 \, \text{kg}\), and \(m_1 = 4.0 \, \text{kg}\) are connected by massless strings, one of which passes over a frictionless pulley of negligible mass, as shown above.

Beginner
Conceptual
MCQ

Which of the following statements is an expression of the equation of continuity?

Beginner
Conceptual
MCQ

Can an object’s average velocity equal zero when object’s speed is greater than zero? Explain using the formula for average velocity vs speed.

Intermediate
Mathematical
MCQ

A horizontal uniform rod of length L and mass M is pivoted at one end and is initially at rest. A small ball of mass M (same masses) is attached to the other end of the rod. The system is released from rest. What is the angular acceleration of the rod just immediately after the system is released?

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?

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.

Beginner
Conceptual
GQ

What would your bathroom scale read if you weighed yourself on an inclined plane? Assume the mechanism functions properly, even at an angle.

Beginner
Mathematical
GQ

A hypothetical planet has a radius \( 2.0 \) times that of Earth, but has the same mass. What is the acceleration due to gravity near its surface?

Beginner
Conceptual
MCQ

Two objects, \( A \) and \( B \), move toward one another. Object \( A \) has twice the mass and half the speed of object \( B \). Which of the following describes the forces the objects exert on each other when they collide and provides the best explanation?

Intermediate
Conceptual
MCQ

In which of the following is the rate of change of the particle’s momentum zero?

Advanced
Mathematical
GQ

A diver springs upward from a diving board. At the instant she contacts the water, her speed is \( 8.90 \, \text{m/s} \), and her body is extended at an angle of \( 75.0^\circ \) with respect to the horizontal surface of the water. At this instant, her vertical displacement is \( -3.00 \, \text{m} \), where downward is the negative direction. Determine her initial velocity, both magnitude and direction.

Beginner
Conceptual
MCQ

A skateboarder coasts to a stop on a flat sidewalk. The net force acting on the skateboarder must be ____.

Intermediate
Mathematical
FRQ

Young David experimented with slings before tackling Goliath. He found that he could develop an angular speed of \( 8.0 \) \( \text{rev/s} \) in a sling \( 0.60 \) \( \text{m} \) long. If he increased the length to \( 0.90 \) \( \text{m} \), he could revolve the sling only \( 6.0 \) times per second.

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
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?

Intermediate
Mathematical
FRQ

You throw a rock straight up with an initial velocity of \( 5.0 \, \text{m/s} \).

Intermediate
Conceptual
MCQ

Three identical blocks are being pulled or pushed across a rough horizontal surface by force of identical magnitude F, as shown in the drawing below. Rank the kinetic frictional forces that act on the blocks from smallest to greatest.

Intermediate
Mathematical
GQ

A solid titanium sphere of radius \( 0.35 \) \( \text{m} \) has a density \( 4500 \) \( \text{kg/m}^3 \). It is held suspended completely underwater by a cable. What is the tension in the cable?

Beginner
Conceptual
MCQ

Consider an object on a rotating disk at a distance \( r \) from its center, held in place on the disk by static friction. Which of the following statements is not true concerning this object?

Intermediate
Mathematical
FRQ

A \( 1 \) \( \text{kg} \) mass on a \( 37^{\circ} \) incline is connected to a \( 3.0 \) \( \text{kg} \) mass on a horizontal surface, as shown. The surfaces and the pulley are frictionless. If \( F = 12 \) \( \text{N} \):

Intermediate
Proportional Analysis
MCQ

Two thin coins are made from identically the same metal, but one coin has triple the diameter of the other. What is the ratio of the moment of inertia of the large coin compared to the small coin? Take the axis of rotation to be perpendicular to the coin and through its center; assume that the coins have the same thickness. Hint: The moment of inertia of a solid disk about its center is \(\frac{1}{2} M R^{2}\).

Advanced
Conceptual
MCQ

A disk of known radius and rotational inertia can rotate without friction in a horizontal plane around its fixed central axis. The disk has a cord of negligible mass wrapped around its edge. The disk is initially at rest, and the cord can be pulled to make the disk rotate. Which of the following procedures would best determine the relationship between applied torque and the resulting change in angular momentum of the disk?

Intermediate
Mathematical
MCQ

A block attached to a spring demonstrates simple harmonic motion about its equilibrium position with amplitude \( A \) and angular frequency \( \omega \). What is the maximum magnitude of the block’s velocity?

Advanced
Mathematical
FRQ

A block of mass \(M_1\) travels horizontally with a constant speed \(v_0\) on a plateau of height \(H\) until it comes to a cliff. A toboggan of mass \(M_2\) is positioned on level ground below the cliff. The center of the toboggan is a distance \(D\) from the base of the cliff.

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