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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 \( (1.2\,W) \)?

Beginner
Mathematical
GQ

A spring in a pogo-stick is compressed \( 12 \) \( \text{cm} \) when a \( 40. \) \( \text{kg} \) girl stands on it. What is the spring constant for the pogo-stick spring?

Intermediate
Mathematical
MCQ

A rod of length \( L \) is rotated about its center with \( I = \frac{ML^{2}}{12} \). What is the moment of inertia at either end of the rod?

Intermediate
Conceptual
MCQ

A constant force of strength \( 20 \) \( \text{N} \) acts on an object of mass \( 3 \) \( \text{kg} \) as it moves a distance of \( 4 \) \( \text{m} \). If this force is applied perpendicular to the \( 4 \) \( \text{m} \) displacement, the work done by the force is equal to:

Intermediate
Mathematical
GQ

A person whose weight is \(4.92 \times 10^2 \, \text{N}\) is being pulled up vertically by a rope from the bottom of a cave that is \(35.2 \, \text{m}\) deep. The maximum tension that the rope can withstand without breaking is \(592 \, \text{N}\). What is the shortest time, starting from rest, in which the person can be brought out of the cave?

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
Conceptual
MCQ

A clothesline is stretched between two trees. A tire hangs in the middle of the line, and the two halves of the line make equal angles with the horizontal. The tension in the line is

Advanced
Mathematical
GQ

The graph above shows velocity \( v \) versus time \( t \) for an object in linear motion. Which of the following is a possible graph of position (\( x \)) versus time (\( t \)) for this object?

Beginner
Conceptual
MCQ

The box in the diagram is sliding to the right across a horizontal table, under the influence of the forces shown. Which force(s) is doing negative work on the box?

Intermediate
Mathematical
MCQ

Consider a solid uniform sphere of radius \(R\) and mass \(M\) rolling without slipping. Which form of its kinetic energy is larger, translational or rotational?

Intermediate
Mathematical
FRQ

Will Clark throws a baseball with a horizontal component of velocity of \(25 \, \text{m/s}\). It takes \(3 \, \text{s}\) to come back to its original height. Calculate the baseball’s:

Advanced
Mathematical
GQ

An airplane can safely bank when subjected to a centripetal acceleration of 8 g’s. If the airplane flies at a constant speed of 400 m/s, how long does it take to make a 180° turn?

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 \(I_{center}=\frac{1}{2}M R^{2}\).

Beginner
Proportional Analysis
MCQ

What is the effect on the period of a pendulum if you double its length?

Advanced
Mathematical
GQ

A \(2 \, \text{kg}\) object slides east at \(4 \, \text{m/s}\) and collides with a stationary \(3 \, \text{kg}\) object. After the collision, the \(2 \, \text{kg}\) object is traveling at an unknown velocity at \(15^\circ\) north of east and the \(3 \, \text{kg}\) object is traveling at \(38^\circ\) south of east. What is each object’s final velocity?

Intermediate
Mathematical
MCQ

A system of two wheels fixed to each other is free to rotate about a frictionless axis through the common center of the wheels and perpendicular to the page. Four forces are exerted tangentially to the rims of the wheels, as shown in the figure. The magnitude of the net torque on the system about the axis is

Intermediate
Conceptual
MCQ

The box is sitting on the floor of an elevator. The elevator is accelerating upward. The magnitude of the normal force on the box is

Intermediate
Mathematical
GQ

A communications satellite orbits the Earth at an altitude of \(35{,}000 \, \text{km}\) above the Earth’s surface. Take the mass of Earth to be \(6 \times 10^{24} \, \text{kg}\) and the radius of Earth to be \(6.4 \times 10^6 \, \text{m}\). What is the satellite’s velocity?

Intermediate
Mathematical
MCQ

A pendulum with a period of \( 1 \) \( \text{s} \) on Earth, where the acceleration due to gravity is \( g \), is taken to another planet, where its period is \( 2 \) \( \text{s} \). The acceleration due to gravity on the other planet is most nearly

Intermediate
Mathematical
FRQ

 

Replicated & enhanced diagram

Intermediate
Conceptual
MCQ

One end of a string is wrapped around a pulley that is free to rotate with negligible friction about an axle at its center. The other end of the string is attached to a block. The block is released from rest and moves downward with constant acceleration. Which of the following correctly indicates whether the amount of work done on the pulley by the string during each successive complete rotation remains constant or increases, and provides a valid justification?

Advanced
Mathematical
GQ

A ball is dropped off a high cliff, and \( 2 \) \( \text{s} \) later another ball is thrown vertically downward with an initial speed of \( 30 \) \( \text{m/s} \). How long will it take the second ball to overtake the first?

Advanced
Mathematical
FRQ

Refer to the diagram above and solve all equations in terms of \(R\), \(M\), \(k\), and constants.

Intermediate
Mathematical
GQ

A ball is launched and lands \( 20 \) \( \text{m} \) away below the launch point \( 2.5 \) \( \text{s} \) later. The maximum height reached is \( 8.0 \) \( \text{m} \). What was the original launch velocity?

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