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Beginner
Conceptual
GQ

Why is it impossible to build a perpetual motion machine?

Intermediate
Mathematical
GQ

A uniform, solid, \( 100 \) \( \text{kg} \) cylinder with a diameter of \( 1.0 \) \( \text{m} \) is mounted so it is free to rotate about a fixed, horizontal, frictionless axis that passes through the centers of its circular ends. A \( 10 \) \( \text{kg} \) block is hung from a very light, thin cord wrapped around the cylinder’s circumference. When the block is released, the cord unwinds and the block accelerates downward. What is the acceleration of the block?

Beginner
Mathematical
GQ

A child (\(m = 32 \, \text{kg}\)) in a boat (\(m = 71 \, \text{kg}\)) throws a \(7.1 \, \text{kg}\) package out horizontally with a speed of \(12.2 \, \text{m/s}\). Calculate the velocity of the boat immediately after, assuming it was initially at rest. Ignore water resistance.

Intermediate
Mathematical
GQ

How large must a heating duct be if air moving \( 3 \ \frac{\text{m}}{\text{s}} \) along it can replenish the air in a room of \( 300 \ \text{m}^3 \) volume every \( 15 \) minutes? Assume the air’s density remains constant.

Advanced
Mathematical
FRQ

Priscilla the Penguin stands at the edge of a rock ledge and tosses a small ice cube directly upward with an initial velocity of \( v_0 \). The ice cube’s initial height above the ground is \( 3.25 \, \text{m} \), and it reaches its maximum height above the ground \( 0.586 \, \text{s} \) after being thrown. The ice cube then plummets to the ground, missing the edge of the rock ledge on its way down.

Intermediate
Mathematical
MCQ

A ball falls straight down through the air under the influence of gravity. There is a retarding force \(F\) on the ball with magnitude given by \(F=bv\), where \(v\) is the speed of the ball and \(b\) is a positive constant. The ball reaches a terminal velocity after a time \(t\). The magnitude of the acceleration at time \(t/2\) is

Advanced
Conceptual
GQ

Why do you float higher in salt water than in fresh water?

Intermediate
Mathematical
GQ

The highest barrier that a projectile can clear is 16.2 m, when the projectile is launched at an angle of 22.0° above the horizontal. What is the projectile’s launch speed?

Intermediate
Conceptual
MCQ

A block sliding down an frictionless inclined plane is experiencing both gravitational and normal forces; which force’s magnitude changes when the angle of the incline is increased?

Advanced
Mathematical
GQ

A space probe far from the Earth is traveling at 14.8 km/s. It has mass 1312 kg. The probe fires its rockets to give a constant thrust of 156 kN for 220 seconds. It accelerates in the same direction as its initial velocity. In this time it burns 150 kg of fuel. Calculate final speed of the space probe in km/s.

Note: This is a bonus question. Skip if you haven’t yet taken calculus. 

Beginner
Conceptual
MCQ

A runner pushes against the track to sprint forward. Which two action–reaction FORCE pairs are involved? Select two letters.

Beginner
Mathematical
GQ

A boulder is raised above the ground so that its potential energy is \(550 \, \text{J}\). Then it is dropped. Assuming \(92 \, \text{J}\) of energy was lost to air resistance, what is the kinetic energy of the boulder just before it hits the ground?

Advanced
Mathematical
GQ

A concrete highway curve of radius \(60.0 \, \text{m}\) is banked at a \(12.0^\circ\) angle. What is the maximum speed with which a \(1300 \, \text{kg}\) rubber-tired car can take this curve without sliding? (Take the static coefficient of friction of rubber on concrete to be \(1.0\).)

Intermediate
Mathematical
GQ

A car moves at constant speed in a circle of radius 75 m on a horizontal road. The coefficient of static friction is 0.62. Find the maximum speed the car can go without sliding.

Advanced
Mathematical
FRQ

A uniform ladder with mass \( m_2 \) and length \( L \) rests against a smooth wall. A do-it-yourself enthusiast of mass \( m_1 \) stands on the ladder a distance \( d \) from the bottom (measured along the ladder). The ladder makes an angle \( \theta \) with the ground. There is no friction between the wall and the ladder, but there is a frictional force of magnitude \( f \) between the floor and the ladder. \( N_1 \) is the magnitude of the normal force exerted by the wall on the ladder, and \( N_2 \) is the magnitude of the normal force exerted by the ground on the ladder. Throughout the problem, consider counterclockwise torques to be positive.

Intermediate
Conceptual
MCQ

Which of the following graphs shows runners moving at the same speed? Assume the \(y\)-axis is measured in meters and the \(x\)-axis is measured in seconds.

Intermediate
Mathematical
GQ

Consider a neutron star with a mass equal to the sun, a radius of 10 km, and a rotation period of 1.0 s. What is the speed of a point on the equator of the star?

Beginner
Conceptual
MCQ

Which of the following statements is an expression of the equation of continuity?

Advanced
Conceptual
MCQ

Consider the following cases of inelastic collisions.
Case (1) – A car moving at \(75 \, \text{mph}\) collides with another car of equal mass moving at \(75 \, \text{mph}\) in the opposite direction and comes to a stop.
Case (2) A car moving at \(75 \, \text{mph}\) hits a stationary steel wall and rolls back.
The collision time is the same for both cases. In which of these cases would result in the greatest impact force?

Advanced
Mathematical
FRQ

A \( 1.5 \; \text{kg} \) mass attached to a spring with a force constant of \( 20.0 \; \text{N/m} \) oscillates on a horizontal, frictionless track. At \( t = 0 \), the mass is released from rest at \( x = 10.0 \; \text{cm} \). (That is, the spring is stretched by \( 10.00 \; \text{cm} \).)

Intermediate
Mathematical
FRQ

An object is suspended from a spring scale first in air, then in water, as shown in the figure above. The spring scale reading in air is \( 17.8 \) \( \text{N} \), and the spring scale reading when the object is completely submerged in water is \( 16.2 \) \( \text{N} \). The density of water is \( 1000 \) \( \text{kg/m}^3 \).

Intermediate
Mathematical
MCQ
Speed \( 10 \, \mathrm{m/s} \) \( 20 \, \mathrm{m/s} \) \( 30 \, \mathrm{m/s} \)
Braking Distance \( 6.1 \, \mathrm{m} \) \( 23.9 \, \mathrm{m} \) \( 53.5 \, \mathrm{m} \)

A car of mass \( 1500 \, \mathrm{kg} \) is traveling at one of the speeds listed when the brakes are first applied. Using the data above, what is the magnitude of the average braking force required to stop the car?

Intermediate
Mathematical
MCQ
Two rectangular blocks of different sizes positioned horizontally on a frictionless surface. Block 1 (on the left) and Block 2 (on the right) are connected by a coiled spring compressed between them. A velocity vector arrow pointing to the right labeled 'v' is shown above the center of mass of the two-block system. Below the blocks, a horizontal dashed line represents the path of motion.

Two blocks connected to a compressed spring move right at speed \( v \). After releasing the spring, the left block moves left at speed \( v_2 \), the right block moves right. What is the center speed of the blocks then?

Intermediate
Mathematical
GQ

A driver is driving at \( 40 \, \text{m/s} \) when the light turns red in front of her. It takes the driver \( 0.9 \, \text{s} \) to react and hit the brakes. After this, the car slows with an acceleration of \( 3.5 \, \text{m/s}^2 \). What is the total distance traveled by the car?

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