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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
Conceptual
MCQ

You are lying in bed and want to shut your bedroom door. You have a bouncy “superball” and a blob of clay, both with the same mass \( m \). Which one would be more effective to throw at your door to close it?

Beginner
Mathematical
MCQ

A liquid flows at a constant flow rate through a pipe with circular cross-sections of varying diameters. At one point in the pipe, the diameter is \(2\) \(\text{cm}\) and the flow speed is \(18\) \(\text{m/s}\). What is the flow speed at another point in this pipe, where the diameter is \(3\) \(\text{cm}\).

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.

Intermediate
Mathematical
MCQ

When the mass of a simple pendulum is tripled, the time required for one complete vibration

Intermediate
Mathematical
MCQ

A solid disk has a mass \( M \) and radius \( R \). What is the moment of inertia about an axis that is perpendicular to the plane of the disk and passes through its edge? Hint: the moment of inertia about the disk center is given as \(I_{center}=\frac{1}{2}M R^{2}\).

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
A side view diagram showing a uniform rod of length L pivoted at its upper left end. The rod is positioned at an angle of 45 degrees below the horizontal. A dashed horizontal reference line is drawn through the pivot point. An arc-shaped arrow indicates the clockwise motion of the rod towards the vertical. The pivot point is represented by a small filled circle.

A uniform rod of length \( L \) is pivoted at one end \(45^{\circ}\) below the horizontal and released from rest. The rod swings freely downward. Which of the following best describes the angular acceleration of the rod as it swings from the initial position to the vertical position?

Intermediate
Conceptual
MCQ

 

In an experiment, an external torque is applied to the edge of a disk of radius \( 0.5 \) \( \text{m} \) such that the edge of the disk speeds up as it continues to rotate. The tangential speed as a function of time is shown for the edge of the disk. The rotational inertia of the disk is \( 0.125 \) \( \text{kg} \cdot \text{m}^2 \). Can a student use the graph and the known information to calculate the net torque exerted on the edge of the disk?

Beginner
Conceptual
MCQ

A student kicks a soccer ball. The ball exerts a force back on the student’s foot. Why doesn’t the student’s foot accelerate backward as much as the ball accelerates forward?

Intermediate
Mathematical
MCQ

A rubber ball with a mass of \(0.25 \, \text{kg}\) and a speed of \(19.0 \, \text{m/s}\) collides perpendicularly with a wall and bounces off with a speed of \(21 \, \text{m/s}\) in the opposite direction. What is the magnitude of the impulse acting on the rubber ball?

Advanced
Mathematical
GQ

Two wires are tied to the \(500 \, \text{g}\) sphere as shown above. The sphere revolves in a horizontal circle at a constant speed of \(7.2 \, \text{m/s}\). What is the tension in the upper wire? What is the tension in the lower wire?

Beginner
Conceptual
MCQ

An ice skater performs a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rotation?

Intermediate
Mathematical
GQ

A Venturi tube has a pressure difference of \( 15\,000 \) \( \text{Pa} \). The entrance radius is \( 3 \) \( \text{cm} \), while the exit radius is \( 1 \) \( \text{cm} \). What are the entrance velocity, exit velocity, and flow rate if the fluid is gasoline \( (\rho = 700 \) \( \text{kg/m}^3 ) \)?

Intermediate
Conceptual
MCQ

Why do raindrops fall with constant speed during the later stages of their descent?

Intermediate
Conceptual
MCQ
Experiment Initial Velocity of Cart X \( (\text{m/s}) \) Initial Velocity of Cart Y \( (\text{m/s}) \) Final Velocity of Cart X \( (\text{m/s}) \) Final Velocity of Cart Y \( (\text{m/s}) \)
\( 1 \) \( 1 \) \( 0 \) \( 0 \) \( 1 \)
\( 2 \) \( 1 \) \( -1 \) \( -1 \) \( 1 \)
\( 3 \) \( 2 \) \( 1 \) \( 1 \) \( 2 \)

A student performs several experiments in which two carts collide as they travel along a horizontal surface. Cart X and Cart Y both have a mass of \( 1 \) \( \text{kg} \). Data collected from the three experiments are shown in the table above. During which experiment does the center of mass of the system of two carts have the greatest change in its momentum?

Intermediate
Mathematical
GQ

A car is going over the top of a hill whose curvature approximates a circle of radius \( 350 \) \( \text{m} \). At what velocity will the occupants of the car appear to weigh \( 10\% \) less than their normal weight?

Intermediate
Mathematical
MCQ

A golf club exerts an average horizontal force of \(1000 \, \text{N}\) on a \(0.045 \, \text{kg}\) golf ball that is initially at rest on the tee. The club is in contact with the ball for \(1.8 \, \text{milliseconds}\). What is the speed of the golf ball just as it leaves the tee?

Intermediate
Mathematical
MCQ

A wheel of moment of inertia of \( 5.00 \) \( \text{kg} \cdot \text{m}^2 \) starts from rest and accelerates under a constant torque of \( 3.00 \) \( \text{N} \cdot \text{m} \) for \( 8.0 \) \( \text{s} \). What is the wheel’s rotational kinetic energy at the end of \( 8.0 \) \( \text{s} \)?

Intermediate
Mathematical
GQ

A bird, traveling at \(50 \, \text{m/s}\) wants to hit a man \(100 \, \text{m}\) below with a dropping. How far in distance before flying directly over the man should the bird release it?

Advanced
Mathematical
FRQ

A ball of mass \( M \) is attached to a string of length \( L \). It moves in a vertical circle and at the bottom the ball just clears the ground. The tension at the bottom of the path is \( 3 \) times the weight of the ball. Give all answers in terms of \( M \), \( L \), and \( g \).

Beginner
Conceptual
MCQ

In an experiment where a constant horizontal force pulls on a box across a rough floor starting from rest, what would happen to the acceleration of the box if its mass were doubled but the pulling force remained unchanged?

Advanced
Mathematical
MCQ

In a lab experiment, a ball is rolled down a ramp so that it leaves the edge of the table with a horizontal velocity \(v\). Assume there are no frictional forces. If the table has a height \(h\) above the ground, how far away from the edge of the table, a distance \(x\), does the ball land?

Beginner
Mathematical
GQ

A race car traveling at a constant speed of \( 50 \) \( \text{m/s} \) drives around a circular track that is \( 500 \) \( \text{m} \) in diameter. What is the magnitude of the acceleration of the car?

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