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Advanced
Mathematical
MCQ

The elliptical orbit of a comet is shown above. Positions 1 and 2 are, respectively, the farthest and nearest positions to the Sun, and at position 1 the distance from the comet to the Sun is 10 times that at position 2. What is the ratio \( F_1 / F_2 \), the force on the comet at position 1 to the force on the comet at position 2?

Advanced
Mathematical
MCQ

A boy of mass \( m \) and a girl of mass \( 2m \) are initially at rest at the center of a frozen pond. They push each other so that she slides to the left at speed \( v \) across the frictionless ice surface and he slides to the right. What is the total work done by the children?

Advanced
Conceptual
GQ

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

Advanced
Mathematical
FRQ

A pump, submerged at the bottom of a well that is \( 35 \) \( \text{m} \) deep, is used to pump water uphill to a house that is \( 50 \) \( \text{m} \) above the top of the well, as shown to the right. The density of water is \( 1000 \) \( \text{kg/m}^3 \). All pressures are gauge pressures. Neglect the effects of friction, turbulence, and viscosity.

Intermediate
Conceptual
MCQ

A truck going 15 km/h has a head-on collision with a small car going 30 km/h. Which statement best describes the situation?

Intermediate
Conceptual
MCQ

A horizontal tube with two vertical T-branches (A and B) is partially submerged in a liquid, with the open ends of the branches exposed to the air. However, the section of the tube above point B is hidden from view and may either be wider or narrower than the section above A.

Air is blown through the horizontal tube, causing the liquid levels in the vertical branches to rise as shown. Based on the observed water levels, which of the following best describes the characteristics of the hidden section of the tube above B?

Beginner
Conceptual
MCQ

Water flowing in a horizontal pipe speeds up as it goes from a section with a large diameter to a section with a small diameter. Which of the following can explain why the speed of the water increases?

Advanced
Mathematical
FRQ

A vehicle is moving at a speed of 12.3 m/s on a decline when the brakes of all four wheels are fully applied, causing them to lock. The slope of the decline forms an angle of 18.0 degrees with the horizontal plane. Given that the coefficient of kinetic friction between the tires and the road surface is 0.650.

Beginner
Mathematical
GQ

Car A, mass 1000 kg, is traveling at 40 m/s when it collides with a stationary car B. They stick together and travel at 7 m/s. What is the mass of car B?

Intermediate
Mathematical
FRQ

Friction provides the force needed for a car to travel around a flat, circular race track. Answer the following:

Intermediate
Mathematical
GQ

A person is trying to judge whether a picture (mass = 1.42 kg) is properly positioned by temporarily pressing it against a wall. The pressing force is perpendicular to the wall. The coefficient of static friction between the picture and the wall is 0.62. What is the minimum amount of pressing force that must be used?

Beginner
Conceptual
MCQ

Consider a ball thrown up from the surface of the earth into the air at an angle of \( 30^\circ \) above the horizontal. Air resistance is negligible. The ball’s acceleration just after release is most nearly

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