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Beginner
Mathematical
MCQ

A forward horizontal force of \(12 \, \text{N}\) is used to pull a \(240 \, \text{N}\) crate at constant velocity across a horizontal floor. The coefficient of friction is

Advanced
Mathematical
FRQ

The diagram above shows a hydraulic chamber with a spring \( (k_s = 1250 \, \text{N/m}) \) attached to the input piston and a rock of mass \( 55.2 \, \text{kg} \) resting on the output plunger. The input piston and output plunger are at about the same height, and each has negligible mass. The chamber is filled with water.

Intermediate
Mathematical
MCQ

The graph in the figure shows the position of a particle as it travels along the x-axis. At what value of \(t\) is the speed of the particle equal to \(0 \, \text{m/s}\)?

note that the slope of position vs time is velocity. And the graph most closely reemsbles a flat or 0 slope at 3 seconds

Advanced
Conceptual
MCQ

Three identical rocks are launched with identical speeds from the top of a platform of height \( h_0 \).

  • Rock 1 is launched at a \( 45^\circ \) angle above the horizontal
  • Rock 2 is launched at a \( 45^\circ \) angle below the horizontal
  • Rock 3 is launched horizontally

Which of the following correctly relates the magnitude \( v_y \) of the vertical component of the velocity of each rock immediately before it hits the ground?

Intermediate
Mathematical
FRQ

Two racing boats set out from the same dock and speed away at the same constant speed of 101 km/h for half an hour (0.5 hr). Boat 1 is headed 27.6° south of west, and Boat 2 is headed 35.3° south of west, as shown in the graph above. During this half-hour calculate:

Advanced
Mathematical
MCQ

An apple is released from rest \(500 \, \text{m}\) above the ground. Due to the combined forces of air resistance and gravity, it has a speed of \(40 \, \text{m/s}\) when it reaches the ground. What percentage of the initial mechanical energy of the apple–Earth system was dissipated due to air resistance? Take the potential energy of the apple–Earth system to be zero when the apple reaches the ground.

Intermediate
Mathematical
MCQ

A child pushes horizontally on a box of mass m with constant speed v across a rough horizontal floor. The coefficient of friction between the box and the floor is µ. At what rate does the child do work on the box?

Intermediate
Mathematical
GQ

You are a bungee jumping fanatic and want to be the first bungee jumper on Jupiter. The length of your bungee cord is \( 45.0 \) \( \text{m} \). Free fall acceleration on Jupiter is \( 23.1 \) \( \text{m/s}^2 \). What is the ratio of your speed on Jupiter to your speed on Earth when you have dropped \( 45 \) \( \text{m} \)? Ignore the effects of air resistance and assume that you start at rest.

Intermediate
Mathematical
GQ

A 84.4 kg climber is scaling the vertical wall. His safety rope is made of a material that behaves like a spring  that has a spring constant of 1.34 x 103 N/m. He accidentally slips and falls 0.627 m before the rope runs out of slack. How much is the rope stretched when it breaks his fall and momentarily brings him to rest?

Beginner
Mathematical
MCQ

A car accelerates from \( 0 \) to \( 25 \) \( \text{m/s} \) in \( 5 \) \( \text{s} \). If the car’s tires have a diameter of \( 70 \) \( \text{cm} \), how many revolutions does a tire make while accelerating?

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.

Advanced
Mathematical
GQ

A spring launches a \(4 \, \text{kg}\) block across a frictionless horizontal surface. The block then ascends a \(30^\circ\) incline with a kinetic friction coefficient of \(\mu_k = 0.25\), stopping after \(55 \, \text{m}\) on the incline. If the spring constant is \(800 \, \text{N/m}\), find the initial compression of the spring. Disregard friction while in contact with the spring.

Intermediate
Conceptual
MCQ

The motion of a particle is described in the velocity vs. time graph shown above. Over the nine-second interval shown, we can say that the speed of the particle…

Intermediate
Mathematical
FRQ

A drinking fountain projects water at an initial angle of \( 50^ \circ \) above the horizontal, and the water reaches a maximum height of \( 0.150 \) \( \text{m} \) above the point of exit. Assume air resistance is negligible.

Intermediate
Mathematical
GQ

A helicopter is ascending vertically with a speed of \( 5.40 \) \( \text{m/s} \). At a height of \( 105 \) \( \text{m} \) above the Earth, a package is dropped from the helicopter. How much time does it take for the package to reach the ground?

Advanced
Mathematical
GQ

The axle (the black dot) in Figure 1 is half the distance from the center to the rim. Suppose \( d = 30 \) \( \text{cm} \). What is the torque that the axle must apply to prevent the disk from rotating? Express your answer in newton-meters. Use positive value for the counterclockwise torque and negative value for the clockwise torque.

Beginner
Mathematical
GQ

A ball is dropped from a window \(10 \, \) above the sidewalk. Determine the time it takes for the ball to fall to the sidewalk.

Intermediate
Mathematical
GQ

The cart with mass \( M = 3 \, \text{kg} \) is pulled by a massless string and moving on a horizontal track. A weight with mass \( m = 1 \, \text{kg} \) is hung from the other end of the string through a pulley system. Due to the gravitational force acting on the weight of mass \( m \), the cart is accelerated to the left. Find the tension in the string.

Beginner
Conceptual
MCQ

The magnitude of a component of a vector must be

Intermediate
Conceptual
MCQ

A girl throws a stone from a bridge. Consider the following ways she might throw the stone. The speed of the stone as it leaves her hand is the same in each case.

Case A: Thrown straight up.

Case B: Thrown straight down.

Case C: Thrown out at an angle of 45° above horizontal.

Case D: Thrown straight out horizontally.

In which case will the speed of the stone be greatest when it hits the water below if there is no significant air resistance, assuming equal initial speeds?

Intermediate
Proportional Analysis
GQ

The magnitude of the gravitational field on the surface of a new planet is \(20 \, \text{N/kg}\). The planet’s mass is half the mass of Earth. The radius of Earth is \(6400 \, \text{km}\). What is the radius of the new planet?

Advanced
Mathematical
GQ

Suppose we wish to make a neutrally buoyant hollow sphere out of titanium (\(\rho = 4500 \text{kg/m}^3\)). If the sphere has an outer radius of \( 1.5 \) \( \text{m} \), what must be its inner radius?

Intermediate
Conceptual
MCQ

Two blocks of the same size are floating in a container of water. The first block is submerged \( 80\% \) while the second block is submerged by \( 20\% \) beneath the water. Which of the following is a correct statement about the two blocks?

Intermediate
Mathematical
MCQ

A plane, 220 meters high, is dropping a supply crate to an island below. It is traveling with a horizontal velocity of 150 m/s. At what horizontal distance must the plane drop the supply crate for it to land on the island? Use \( g = 9.81 \, m/s^2\).

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