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Intermediate
Mathematical
MCQ

Consider a rigid body that is rotating. Which of the following is an accurate statement?

Advanced
Mathematical
GQ

A spacecraft somewhere in between the Earth and the Moon experiences zero net force acting on it. This is because the Earth and the Moon pull the spacecraft in equal but opposite directions. Find the distance \(D\) away from Earth such that the spacecraft experiences zero net force. The distance between the Moon and Earth is \(\sim 3.844 \times 10^8 \, \text{m}\).

Note: You may need the mass of the Earth and the Moon. You can find this in the formula table.

Intermediate
Conceptual
MCQ

Angular momentum cannot be conserved if

Advanced
Mathematical
GQ

A baseball rolls off a 0.70 m high desk and strikes the floor 0.25 m away from the base of the desk. How fast was the ball rolling?

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
FRQ

A car of mass \( M \) moves around a circularly banked curve on a freeway off-ramp. The off-ramp has a radius of curvature \( R \) and is raised to an angle \( \theta \) from the horizontal. The road is slick, and friction is negligible.

Intermediate
Conceptual
MCQ

A blue sphere and a red sphere with the same diameter are released from rest at the top of a ramp. The red sphere takes a longer time to reach the bottom of the ramp. The spheres are then rolled off a horizontal table at the same time with the same speed and fall freely to the floor. Which sphere reaches the floor first?

Intermediate
Mathematical
GQ

A car is going over the top of a hill whose curvature approximates a circle of radius \( 350 \) \( \text{m} \). At what velocity will the occupants of the car appear to weigh \( 10\% \) less than their normal weight?

Beginner
Mathematical
GQ

Police officers have measured the length of a car’s tire skid marks to be \( 23 \, \text{m} \). This particular car is known to decelerate at a constant \( 7.5 \, \text{m/s}^2 \). What was the car’s initial velocity?

Intermediate
Conceptual
MCQ

A rubber ball bounces off of a wall with an initial speed \(v\) and reverses its direction so its speed is \(v\) right after the bounce. As a result of this bounce, which of the following quantities of the ball are conserved?

Intermediate
Conceptual
MCQ

Which of the following graphs shows runners moving at the same speed? Assume the \(y\)-axis is measured in meters and the \(x\)-axis is measured in seconds.

Intermediate
Mathematical
MCQ

A solid plastic cube with uniform density (side length = \(0.5\) \(\text{m}\)) of mass \(100\) \(\text{kg}\) is placed in a vat of fluid whose density is \(1200\) \(\text{kg/m}^3\). What fraction of the cube’s volume floats above the surface of the fluid?

Intermediate
Mathematical
GQ

A block starts from rest at the top of a \(50^\circ\) incline. The coefficient of kinetic friction between the block and the incline is \(0.4\). If the block reaches a velocity of \(7 \, \text{m/s}\) at the bottom of the incline, what is the length of the incline?

Intermediate
Conceptual
MCQ

Two forces produce equal torques on a door about the door hinge. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force has a greater magnitude?

Advanced
Proportional Analysis
MCQ

A rock is whirled on the end of a string in a horizontal circle of radius \(R\) with a constant period \(T\). If the radius of the circle is reduced to \(R/3\), while the period remains \(T\), what happens to the centripetal acceleration (\(a_c\)) of the rock?

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?

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

Beginner
Conceptual
GQ

A solid sphere is rotating about an axis through its center at a constant rotation rate. Another hollow sphere of the same mass and radius is rotating about its axis through the center at the same rotation rate. Which sphere has a greater rotational kinetic energy?

Advanced
Conceptual
MCQ

A block is attached to a horizontal spring and is initially at rest at the equilibrium position \( x = 0 \), as shown in Figure \( 1 \). The block is then moved to position \( x = -A \), as shown in Figure \( 2 \), and released from rest, undergoing simple harmonic motion. At the instant the block reaches position \( x = +A \), another identical block is dropped onto and sticks to the block, as shown in Figure \( 3 \). The two–block–spring system then continues to undergo simple harmonic motion. Which of the following correctly compares the total mechanical energy \( E_{\text{tot},2} \) of the two–block–spring system after the collision to the total mechanical energy \( E_{\text{tot},1} \) of the one–block–spring system before the collision?

Advanced
Mathematical
FRQ

Two masses, \( m_1 \) and \( m_2 \), are suspended on either side of a pulley with a radius \( R \), as shown. The heavier mass, \( m_2 \), is initially held at rest above the ground by a distance \( h \) before being released. An student measures that it takes an amount of time \( t \) for the heavier mass to hit the ground after being released.

Advanced
Conceptual
MCQ

A fisherman is standing in the back of his small fishing boat (the mass of the fisherman is the same as the mass of the boat) and he is a few meters from shore. He is done fishing so he starts walking towards the shore so he can get off the boat. What happens to the boat and the fisherman? Select all that apply and assume there is no friction between the boat and the water.

Advanced
Conceptual
MCQ

A disk of radius \( R = 0.5 \) \( \text{cm} \) rests on a flat, horizontal surface such that frictional forces are considered to be negligible. Three forces of unknown magnitude are exerted on the edge of the disk, as shown in the figure. Which of the following lists the essential measuring devices that, when used together, are needed to determine the change in angular momentum of the disk after a known time of \( 5.0 \) \( \text{s} \)?

Beginner
Conceptual
MCQ

You drop a rock off a bridge. When the rock has fallen \( 4 \) \( \text{m} \), you drop a second rock. As the two rocks continue to fall, what happens to their velocities?

Beginner
Mathematical
MCQ

A car travels \( 60 \) \( \text{km} \) at \( 30 \) \( \text{km/h} \), then \( 60 \) \( \text{km} \) at \( 60 \) \( \text{km/h} \). What is its average speed over the entire trip?

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