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Beginner
Proportional Analysis
MCQ

What is the effect on the period of a pendulum if you double its length?

Intermediate
Mathematical
MCQ

A \(15 \, \text{g}\) marble moves to the right at \(3.5 \, \text{m/s}\) and makes an elastic head-on collision with a \(22 \, \text{g}\) marble. The final velocity of the \(22 \, \text{g}\) marble is \(2.0 \, \text{m/s}\) to the right, and the final velocity of the \(15 \, \text{g}\) marble is \(5.4 \, \text{m/s}\) to the left. What was the initial velocity of the \(22 \, \text{g}\) marble?

Intermediate
Mathematical
GQ

A box is sliding down an incline at a constant speed of \( 2 \, \text{m/s} \). The angle of the incline is \( \theta \). The magnitude of the total of the opposing forces is \( 16 \, \text{N} \). Derive an equation for the force of gravity acting on the box.

Intermediate
Mathematical
FRQ

A 6.0-cm-diameter gear rotates with angular velocity \( \omega = \left(20-\frac {1}{2} t^2 \right) \, \text {rad/s} \), where \(t\) is in seconds. At \(t = 4.0 \, \text{s}\), what are

Intermediate
Mathematical
GQ

A big bird has a mass of about 0.021 kg. Suppose it does 0.36 J of work against gravity, so that it ascends straight up with a net acceleration of 0.625 m/s2. How far up does it move?

Intermediate
Mathematical
FRQ

A rescue helicopter lifts a 79 kg person straight up by means of a cable. The person has an upward acceleration of 0.70 m/s2 and is lifted through a distance of 11 m.

Beginner
Conceptual
FRQ

When a golf ball is dropped to the pavement, it bounces back up.

Beginner
Conceptual
GQ

An elevator starts at rest on the ground floor. It accelerates upward smoothly for \( 2 \) \( \text{s} \) until reaching a steady upward speed. It continues at that constant speed for \( 5 \) \( \text{s} \) before gently slowing to rest at the next floor in \( 3 \) \( \text{s} \). Draw the velocity vs. time graph.

Intermediate
Conceptual
MCQ

The figure shows a container filled with water to a depth \( d \). The container has a hole a distance \( y \) above its bottom, allowing water to exit with an initially horizontal velocity. Which of the following correctly predicts and explains how the speed of the water as it exits the hole would change if the distance \( y \) above the bottom of the container increased?

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
\( \text{AB} \) \( 300 \) \( \text{mm} \)  \(\textbf{?}\)  \(\textbf{?}\)
\( \text{BC} \) \( 600 \) \( \text{mm} \)  \(\textbf{?}\) \( 1.2 \) \( \text{m/s} \)
\( \text{CD} \)  \(\textbf{?}\) \( Q_{CD} = 2Q_{CE} \) \( \text{m}^3/\text{s} \) \( 1.4 \) \( \text{m/s} \)
\( \text{CE} \) \( 150 \) \( \text{mm} \) \( Q_{CE} = 0.5Q_{CD} \) \( \text{m}^3/\text{s} \)  \(\textbf{?}\)
Intermediate
Mathematical
MCQ

The diagram above shows a top view of a child of mass \(M\) on a circular platform of mass \(2M\) that is rotating counterclockwise. Assume the platform rotates without friction. Which of the following describes an action by the child that will increase the angular speed of the platform-child system and gives the correct reason why?

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