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Advanced
Proportional Analysis
GQ

A man weighing \( 700 \) \( \text{N} \) and a woman weighing \( 400 \) \( \text{N} \) have the same momentum. What is the ratio of the man’s kinetic energy \( K_m \) to that of the woman \( K_w \)?

Advanced
Mathematical
MCQ

A block attached to 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?

Beginner
Mathematical
GQ

A stone is thrown horizontally at \(8.0 \, \text{m/s}\) from a cliff \(80 \,\text{m}\) high. How far from the base of the cliff will the stone strike the ground?

Intermediate
Mathematical
GQ

A person’s center of mass is easily found by having the person lie on a reaction board. A horizontal, \( 2.3 \) \( \text{m} \)-long, \( 6.1 \) \( \text{kg} \) reaction board is supported only at the ends, with one end resting on a scale and the other on a pivot. A \( 64 \) \( \text{kg} \) woman lies on the reaction board with her feet over the pivot. The scale reads \( 27 \) \( \text{kg} \). What is the distance from the woman’s feet to her center of mass? Express your answer with the appropriate units.

Intermediate
Conceptual
MCQ

A solid ball and a cylinder roll down an inclined plane. Which reaches the bottom first?

Intermediate
Mathematical
FRQ

A textbook is launched up with a speed of 20 m/s, at an angle of 36°, from a 12 m high roof.

Advanced
Mathematical
MCQ

A meter stick with a uniformly distributed mass of \(0.5 \, \text{kg}\) is supported by a pivot placed at the \(0.25 \, \text{m}\) mark from the left. At the left end, a small object of mass \(1.0 \, \text{kg}\) is placed at the zero mark, and a second small object of mass \(0.5 \, \text{kg}\) is placed at the \(0.5 \, \text{m}\) mark. The meter stick is supported so that it remains horizontal, and then it is released from rest. Find the change in the angular momentum of the meter stick, one second after it is released.

Advanced
Mathematical
FRQ

A uniform ladder of length \(L\) and weight \(W = 50 \, \text{N}\) rests against a smooth vertical wall. If the coefficient of static friction between the ladder and the ground is \(\mu = 0.4\).

Beginner
Mathematical
FRQ

An object is thrown downward at \(23 ~\text{m/s}\) from the top of a \(200 ~\text{m}\) tall building.

Advanced
Conceptual
MCQ

A kickball is rolled by the pitcher at a speed of 10 m/s and it is kicked by another student. The kickball deforms a little during the kick, and then rebounds with a velocity of 15 m/s as its shape restores to a perfect sphere. Select all that must be true about the kickball and the kicking foot system.

Advanced
Mathematical
GQ

Water flows from point \( A \) to points \( D \) and \( E \) as shown. Some of the flow parameters are known, as shown in the table. Determine the unknown parameters. Note the diagram above does not show the relative diameters of each section of the pipe.

Section Diameter Flow Rate Velocity
\( \text{AB} \) \( 300 \) \( \text{mm} \)  \(\textbf{?}\)  \(\textbf{?}\)
\( \text{BC} \) \( 600 \) \( \text{mm} \)  \(\textbf{?}\) \( 1.2 \) \( \text{m/s} \)
\( \text{CD} \)  \(\textbf{?}\) \( Q_{CD} = 2Q_{CE} \) \( \text{m}^3/\text{s} \) \( 1.4 \) \( \text{m/s} \)
\( \text{CE} \) \( 150 \) \( \text{mm} \) \( Q_{CE} = 0.5Q_{CD} \) \( \text{m}^3/\text{s} \)  \(\textbf{?}\)

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