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Intermediate
Mathematical
GQ

A car is going through a dip in the road whose curvature approximates a circle of radius \( 200 \) \( \text{m} \). At what velocity will the occupants of the car appear to weigh \( 20\% \) more than their normal weight \( (1.2\,W) \)?

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?

Beginner
Conceptual
MCQ

The figure shows a graph of the position \(x\) of two cars, \(C\) and \(D\), as a function of time \(t\). According to this graph, which statements about these cars must be true? (There could be more than one correct choice.)

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 \(1.0\).)

Advanced
Mathematical
GQ

A uniform solid sphere of mass M and radius R is placed on a frictionless horizontal surface. A massless string is wrapped around the sphere and is pulled with a force F. The string makes an angle of θ with the horizontal. What is the minimum value of the coefficient of static friction between the sphere and the surface required for the sphere to start rolling without slipping?

Beginner
Mathematical
MCQ

A vertical rope of negligible mass supports a block that weighs \(30 N\). The breaking strength of the rope is \( 50 N\). The largest acceleration that can be given to the block by pulling up on it with the rope without breaking the rope is most nearly

Intermediate
Mathematical
MCQ

A block attached to a spring demonstrates simple harmonic motion about its equilibrium position with amplitude \( A \) and angular frequency \( \omega \). What is the maximum magnitude of the block’s velocity?

Intermediate
Mathematical
FRQ

A high-speed flywheel in a motor is spinning at \( 500 \) \( \text{rpm} \) when a power failure suddenly occurs. The flywheel has a mass of \( 40 \) \( \text{kg} \) and a diameter of \( 75 \) \( \text{cm} \). The power is off for \( 30 \) \( \text{s} \) and during this time the flywheel slows due to friction in its axle bearings. During this time the flywheel makes \( 200 \) complete revolutions.

Intermediate
Conceptual
MCQ

The figure shows a truck pulling three crates across a rough road. Which of the following best describes the directions of all the horizontal forces acting on crate 2?

Intermediate
Mathematical
GQ

At what distance from the Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull in opposite directions with equal force?

Beginner
Conceptual
MCQ

A runner completes one full lap around a \( 400 \) \( \text{m} \) track in \( 100 \) \( \text{s} \). What is their average velocity?

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?

Intermediate
Conceptual
MCQ

A person pulls a rope with a force \( F \) at an angle of \( 60^\circ \) to the horizontal. The rope is connected to a load over a frictionless pulley as shown in the diagram. The load is stationary. Which of the following is correct about the weight of the load and the net force exerted on the pulley by the rope?

Advanced
Mathematical
GQ

An \( 80 \, \text{kg} \) block is placed \( 2 \, \text{m} \) away from the endpoint of a horizontal steel beam of length \( 6.6 \, \text{m} \) and mass \( 1,450 \, \text{kg} \). The plank makes contact with a vertical wall on one end (assume it does not slip).  The other end of the beam is attached to a massless cable that makes an angle of \( 30^\circ \) with the horizontal and ties into the vertical wall as well. Calculate the (1) tension force in the cable and (2) the total force the wall exerts on the beam.

Advanced
Mathematical
FRQ

Shown above are three masses of \(6 \, \text{kg}\), \(3 \, \text{kg}\), and \(1 \, \text{kg}\) (in order from left to right). You pull on the 1kg mass with a force \(F\) of \(15 \, \text{N}\) along a frictionless surface.

Beginner
Conceptual
MCQ

Which car controls directly allow the driver to cause acceleration?

Intermediate
Conceptual
MCQ

A blue sphere and a red sphere with the same diameter are released from rest at the top of a ramp. The red sphere takes a longer time to reach the bottom of the ramp. The spheres are then rolled off a horizontal table at the same time with the same speed and fall freely to the floor. Which sphere reaches the floor first?

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?

Intermediate
Mathematical
MCQ

A group of students must study the oscillatory motion of a pendulum. One end of a light string is attached to the ceiling, and the other end of the string is attached to a mass hanger so that small disks of various masses may be stacked on the hanger.

Students are provided with data in which an experiment was conducted to determine the relationship between the length of the pendulum and the period of oscillation. The data include a pendulum of length 0.5 m, for which it took 81 s for the pendulum bob to oscillate 10 times. However, the experiment was conducted at a location that is not near Earth’s surface. The gravitational field strength where the experiment was conducted is most nearly

Beginner
Mathematical
MCQ

How long does it take for a rotating object to speed up from 15.0 rad/s to 33.3 rad/s if it has a uniform angular acceleration of 3.45 rad/s2?

Intermediate
Mathematical
FRQ

What is the rotational inertia \( I \) of a disk with a radius \( R = 4 \) \( \text{m} \) and a mass \( 2 \) \( \text{kg} \)? The same disk is rotated around an axis that is \( 0.5 \) \( \text{m} \) from the center of the disk. What is the new rotational inertia \( I \) of the disk? What would the rotational inertia be if the disk axis was \( 3.75 \) \( \text{m} \) from the center?

Advanced
Mathematical
GQ

A \( 1.5 \) \( \text{kg} \) block is pushed to the right with just enough force to get it to move. The block is pushed for five seconds with this constant force, then the force is released and the block slides to a stop. If the coefficient of kinetic friction is \( 0.300 \) and the coefficient of static friction is \( 0.400 \), calculate the amount of time that passes from when the force is applied to when the block stops.

Beginner
Proportional Analysis
MCQ

Which of the following situations will increase the moment of inertia of a solid cylinder \( I = \tfrac{1}{2} M R^{2} \) by the same amount?

Advanced
Mathematical
GQ

On a harsh winter day, a \( 1500 \) \( \text{kg} \) vehicle takes a circular banked exit ramp (radius \( R = 150 \) \( \text{m} \); banking angle of \( 10^\circ \)) at a speed of \( 30 \) \( \text{mph} \), since the speed limit is \( 35 \) \( \text{mph} \). However, the exit ramp is completely iced up (frictionless). To make matters worse, a wind is blowing parallel to the ramp in a downward direction. The wind exerts a force of \( 3000 \) \( \text{N} \). Under these conditions, can the driver continue to follow a safe horizontal circle on the exit ramp and stay below the speed limit?

To convert \( \text{mph} \) into \( \text{m/s} \), use \( 1 \) \( \text{mi} = 1607 \) \( \text{m} \) and \( 1 \) \( \text{hr} = 3600 \) \( \text{s} \).

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