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Exam 6: Gravity

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Question 51

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A car moving at a steady 10 m/s on a level highway encounters a bump that has a circular cross-section with a radius of 30 m. The car maintains its speed over the bump. What is the normal force exerted by the seat of the car on a 60.0-kg passenger when the car is at the top of the bump?

A) 200 N
B) 390 N
C) 790 N
D) 490 N
E) 590 N

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Question 52

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In a carnival ride, passengers stand with their backs against the wall of a cylinder. The cylinder is set into rotation and the floor is lowered away from the passengers, but they remain stuck against the wall of the cylinder. For a cylinder with a 2.0-m radius, what is the minimum speed that the passengers can have so they do not fall if the coefficient of static friction between the passengers and the wall is 0.25?

A) 8.9 m/s
B) 2.3 m/s
C) 3.0 m/s
D) 4.9 m/s
E) It depends on the mass of the passengers.

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Question 53

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The curved section of a horizontal highway is a circular unbanked arc of radius 740 m. If the coefficient of static friction between this roadway and typical tires is 0.40, what would be the maximum safe driving speed for this horizontal curved section of highway?

Suppose our sun had 4 times its present mass but the earth orbited it at the same distance as it presently does. What would be the length of the year on the earth under those conditions?

Two small objects, with masses m and M, are originally a distance r apart, and the gravitational force on each one has magnitude F. The second object has its mass changed to 2M, and the distance is changed to r/4. What is the magnitude of the new gravitational force?

Two identical tiny balls of highly compressed matter are 1.50 m apart. When released in an orbiting space station, they accelerate toward each other at 2.00 cm/s². What is the mass of each of them? (G = 6.67 × 10^-11 N ? m²/kg²)

A spherically symmetric planet has four times the earth's mass and twice its radius. If a jar of peanut butter weighs 12 N on the surface of the Earth, how much would it weigh on the surface of this planet?

Two planets have the same surface gravity, but planet B has twice the mass of planet A. If planet A has radius r, what is the radius of planet B?

$\begin{array} { | l | c | c | c | c | } \hline & \text { Mass } & \text { Radius } & \text { Orbital radius } & \text { Orbital period } \\\hline \text { Moon A } & 4.0 \times 10 ^ { 20 } \mathrm {~kg} & \text { unknown } & 2.0 \times 10 ^ { 8 } \mathrm {~m} & 4.0 \times 10 ^ { 6 } \mathrm {~s} \\\hline \text { Moon B } & 1.5 \times 10 ^ { 20 } \mathrm {~kg} & 2.0 \times 10 ^ { 5 } \mathrm {~m} & 3.0 \times 10 ^ { 8 } \mathrm {~m} & \text { unknown } \\\hline\end{array}$ Mithra is an unknown planet that has two moons, A and B, in circular orbits around it. The table summarizes the hypothetical data about these moons. What is the magnitude of the maximum gravitational force that Moon A exerts on Moon B? (G = 6.67 × 10^-11 N ? m²/kg²)

A 2.10-kg hammer is transported to the Moon. The radius of the Moon is 1.74 × 10⁶ m, its mass is 7.35 × 10²² kg, and G = 6.67 × 10^-11 N ∙ m²/kg². How much does the hammer weigh on Earth and on the Moon?

A curved portion of highway has a radius of curvature of 65 m. As a highway engineer, you want to bank this curve at the proper angle for a steady speed of 22 m/s. (a)What banking angle should you specify for this curve? (b)At the proper banking angle, what normal force and what friction force does the highway exert on a 750-kg car going around the curve at the proper speed?

An piece of space debris is released from rest at an altitude that is two earth radii from the center of the earth. Compared to its weight on Earth, the weight of this debris is

What would be the weight of a 59.1-kg astronaut on a planet with the same density as Earth and having twice Earth's radius?

The International Space Station is orbiting at an altitude of about 370 km above the earth's surface. The mass of the earth is 5.97 × 10²⁴ kg, the radius of the earth is 6.38 × 10⁶ m, and G = 6.67 × 10^-11 N ? m²/kg². Assume a circular orbit. (a)What is the period of the International Space Station's orbit? (b)What is the speed of the International Space Station in its orbit?

Two cars go around a banked curve at the proper speed for the banking angle. One car has tires with excellent traction, while the other car has bald slippery tires. Which of these cars is more likely to slide on the pavement as it goes around the curve?

An astronaut goes out for a "space-walk" at a distance above the earth equal to the radius of the earth. What is her acceleration due to gravity at that point?