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Intermediate
Mathematical
GQ

A big bird has a mass of about \(0.021 \, \text{kg}\). Suppose it does \(0.36 \, \text{J}\) of work against gravity, so that it ascends straight up with a net acceleration of \(0.625 \, \text{m/s}^2\). How far up does it move?

Intermediate
Conceptual
MCQ

A ladder is leaning against a wall at an angle. Which of the following forces must have the same magnitude as the frictional force exerted on the ladder by the floor?

Beginner
Conceptual
MCQ

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

Beginner
Conceptual
MCQ

What is the relationship between the period \( T \) and frequency \( f \) of an object in simple harmonic motion?

Intermediate
Mathematical
GQ

In lacrosse, a typical throw is made by rotating the stick through an angle of roughly \(90^\circ\), then releasing the ball when the stick is vertical, as shown above. If the \(1 \, \text{meter}\) long stick is at rest when horizontal and the ball leaves the stick with a velocity of \(10 \, \text{m/s}\), what angular acceleration must the stick experience?

Advanced
Mathematical
GQ

An elevator of height \(h\) ascends with constant acceleration \(a\). When it crosses a platform, it has acquired a velocity \(u\). At this instant a bolt drops from the top of the elevator. Find the time for the bolt to hit the floor of the elevator. Give your answer in terms of \(h\), \(a\), and any constant.

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
A physical setup diagram showing a tall vertical tower with a pivot point at the top. A single chain of length 10 meters hangs from the pivot, connected to a chair. The chair and chain are drawn at an angle theta from the vertical. The child is depicted as a simplified block sitting in the chair. A dashed circular path is drawn indicating the radius of rotation of the chair. A horizontal dimension line indicates the radius r, and an arc marker labels the angle theta between the vertical tower and the taut chain.

A neighbor’s child wants to go to a carnival to experience the wild rides. The neighbor is worried about safety because one of the rides looks particularly dangerous. She knows that you have taken physics and so asks you for advice. The ride in question has a \(4 \, \text{kg}\) chair which hangs freely from a \(10 \, \text{m}\) long chain attached to a pivot on the top of a tall tower. When the child enters the ride, the chain is hanging straight down. The child is then attached to the chair with a seat belt and shoulder harness. When the ride starts up, the chain rotates about the tower. Soon the chain reaches its maximum speed and remains rotating at that speed, which corresponds to one rotation about the tower every \(3 \, \text{seconds}\). When you ask the operator, he says the ride is perfectly safe. He demonstrates this by sitting in the stationary chair. The chain creaks but holds, and he weighs \(90 \, \text{kg}\).

Beginner
Mathematical
MCQ

A meter stick of mass \( .2 \) kg is pivoted at one end and supported horizontally. A force of \( 3 \) N downwards is applied to the free end, perpendicular to the length of the meter stick. What is the net torque about the pivot point?

Advanced
Mathematical
GQ

A \(5\)-meter long ladder is leaning against a wall, with the bottom of the ladder \(3\) meters from the wall. The ladder is uniform and has a mass of \(20 \, \text{kg}\). A person of mass \(80 \, \text{kg}\) is standing on the ladder at a distance of \(4\) meters from the bottom of the ladder. What is the force exerted by the wall on the ladder?

Intermediate
Mathematical
MCQ

A wheel of radius \( R \) and negligible mass is mounted on a horizontal frictionless axle so that the wheel is in a vertical plane. Three small objects having masses \( m \), \( M \), and \( 2M \), respectively, are mounted on the rim of the wheel, as shown above. If the system is in static equilibrium, what is the value of \( m \) in terms of \( M \)?

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