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Beginner
Mathematical
FRQ

A tennis ball is thrown straight up with an initial speed of \( 22.5 \, \text{m/s} \). It is caught at the same distance above ground.

Intermediate
Conceptual
MCQ

An object’s velocity \(v\) as a function of time \(t\) is given in the graph. Which of the following statements is true about the motion of the object?

Advanced
Conceptual
MCQ

A planet of constant mass orbits the sun in an elliptical orbit. Neglecting any friction effects, what happens to the planet’s rotational kinetic energy about the sun’s center?

Beginner
Conceptual
GQ

In archery, should the arrow be aimed directly at the target? How should your angle of aim depend on the distance to the target? Explain without using equations.

Advanced
Mathematical
FRQ

A small block of mass \( M \) is released from rest at the top of the curved frictionless ramp shown above. The block slides down the ramp and is moving with a speed \( 3.5v_0 \) when it collides with a larger block of mass \( 1.5M \) at rest at the bottom of the incline. The larger block moves to the right at a speed \( 2v_0 \) immediately after the collision.

Express your answers to the following questions in terms of the given quantities and fundamental constants.

Advanced
Mathematical
FRQ

The graph above shows the angular velocity of a spinning wheel (radius = \( 25 \) \( \text{cm} \)) as a function of time.

Intermediate
Mathematical
FRQ

A car accelerates uniformly from rest to [katex] 29.4 [/katex] m/s in [katex] 6.93 [/katex] s along a level stretch of road. Ignoring friction, determine the average power in both watts and horsepower ([katex] 1 \text{ horsepower} = 745.7 \text{ Watts} [/katex]) required to accelerate the car if:

Advanced
Mathematical
GQ

An object of unknown mass is acted upon by multiple forces:

  • \(100 \, \text{N}\) to the right at \(20^\circ\)
  • \(400 \, \text{N}\) to the left at \(40^\circ\) below the horizontal
  • \(500 \, \text{N}\) to the right at \(10^\circ\) below the horizontal

The coefficients of friction are \(\mu_s = 0.6\) and \(\mu_k = 0.2\). Starting from rest, the object travels \(10 \, \text{m}\) in \(4.5 \, \text{s}\). What is the mass of the unknown object?

Advanced
Mathematical
FRQ

Two blocks made of different materials, connected by a thin cord, slide down a plane ramp inclined at an angle \( \theta = 32^\circ \) above the horizontal. If the coefficients of friction are \( \mu_A = 0.2 \) and \( \mu_B = 0.3 \) and if \( m_A = m_B = 5.0 \) \( \text{kg} \), determine:

Intermediate
Mathematical
MCQ

A small boat coasts at constant speed under a bridge. A heavy sack of sand is dropped from the bridge onto the boat. The speed of the boat will

Beginner
Mathematical
GQ

Johnny the auto mechanic is raising a \( 1200 \) \( \text{kg} \) car on her hydraulic lift so that she can work underneath. If the area of the input piston is \( 12 \) \( \text{cm}^2 \), while the output piston has an area of \( 700 \) \( \text{cm}^2 \), what force must be exerted on the input piston to lift the car?

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?

Advanced
Mathematical
FRQ

Flywheels (rapidly rotating disks) are widely used in industry for storing energy. They are spun up slowly when extra energy is available, then decelerate quickly when needed to supply a boost of energy. A flywheel, \( 20 \text{ cm} \) in diameter, can spin at \( 20{,}000 \text{ rpm} \).

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?

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?

Beginner
Conceptual
MCQ

A point P is at a distance \( R \) from the axis of rotation of a rigid body whose angular velocity and angular acceleration are \( \omega \) and \( \alpha \) respectively. The linear speed, centripetal acceleration, and tangential acceleration of the point can be expressed as:

Linear speed Centripetal acceleration Tangential acceleration
\( (a) \) \( R\omega \) \( R\omega^{2} \) \( R\alpha \)
\( (b) \) \( R\omega \) \( R\alpha \) \( R\omega^{2} \)
\( (c) \) \( R\omega^{2} \) \( R\alpha \) \( R\omega \)
\( (d) \) \( R\omega \) \( R\omega^{2} \) \( R\omega \)
\( (e) \) \( R\omega^{2} \) \( R\alpha \) \( R\omega^{2} \)
Advanced
Mathematical
FRQ

A ball of mass \( 0.5 \, \text{kg} \), initially at rest, is kicked directly toward a fence from a point \( 32 \, \text{m} \) away, as shown above. The velocity of the ball as it leaves the kicker’s foot is \( 20 \, \text{m/s} \) at an angle of \( 37^\circ \) above the horizontal. The top of the fence is \( 2.5 \, \text{m} \) high. The ball hits nothing while in flight and air resistance is negligible.

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
Mathematical
GQ

A projectile is launched at a speed of \( 22 \) \( \text{m/s} \) at an angle of \( 60^{\circ} \) above the horizontal. It lands on a ramp that is \( 5 \) \( \text{m} \) lower than the launch height. How long does it take for the projectile to hit the ramp?

Intermediate
Conceptual
MCQ

You kick a ball straight up. Compare the sign of the work done by gravity on the ball while it goes up with the sign of the work done by gravity while it goes down.

Beginner
Mathematical
FRQ

Find the following three values using just rotational kinematics.

Intermediate
Conceptual
MCQ

The rotating systems, shown in the figure above, differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left), or a distance r/2 from the axis of rotation (right). What happens if you release the hanging blocks simultaneously from rest?

Intermediate
Mathematical
FRQ

A block of mass \( m \), acted on by a force \( F \) directed horizontally, slides up an inclined plane that makes an angle \( \theta \) with the horizontal. The coefficient of sliding friction between the block and the plane is \( \mu \).

Beginner
Mathematical
MCQ

A \( 50 \, \text{kg} \) person is sitting on a seesaw \( 1.2 \, \text{m} \) from the balance point. On the other side, a \( 70 \, \text{kg} \) person is balanced. How far from the balance point is the second person sitting?

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