Show:
Uniform Circular Motion
Dynamics of Circular Motion
Orbits and Weightlessness
Kepler's Laws and Gravitation
Mixed Review Questions
100

When an object moves in uniform circular motion, the direction of its acceleration is __.

Directed towards the center of the circular path.

100

A car goes around a circular curve on a horizontal road at constant speed. What is the direction of the friction force on the car due to the road?

Directed to the center of the circular path that the car is on.

100

The reason an astronaut in an earth satellite feels weightless is that ___.

The astronaut is in free-fall as they are orbiting around the Earth - they are continually falling around the earth.

100
Two small blocks, A and B, attract each other gravitationally with a force of magnitude F. If we now double both masses and double the separation of the blocks, what will now be the magnitude of the attractive force on each one?
F
100
If you stood on a planet having a mass four times that of Earth's mass, and a radius two times that of Earth's radius, you would weigh ___.
The same as you do on Earth.
200

What is the name given to the "force" that seems to push an object to the outside of its circular path?  This "force" is really a result of what?

Centrifugal force (which is not real) -- the effect is the result of inertia and centripetal force.

200

When a car goes around a circular curve on a horizontal road at constant speed, what force causes it to follow the circular path?

The friction force from the road on the car - directed inward.

200

Describe the motion of planets around the Sun. Be as specific as you can!

Elliptical path. Travel faster when they are closer to the Sun, and travel slower when they are further away from the Sun.  Gravitational force is the centripetal force. Sun is at one of the foci.

200
Two small objects, with masses m and M, are originally a distance r apart, and the magnitude of the gravitational force on each one is F. The masses are changed to 2m and 2M, and the distance is changed to 4r. What is the magnitude of the new gravitational force?
(1/4)F
200
A 600-kg car is going around a banked curve with a radius of 110 m at a steady speed of 24.5 m/s. What is the appropriate banking angle so that the car stays on its path without the assistance of friction?
29.1 degrees
300

Each year, the moon gets a little bit farther away from the Earth, increasing the radius of its orbit. How does this change affect the length of the month?

A month will get longer.

300

A 1000-kg car is moving at 30 m/s around a horizontal unbanked curve whose diameter is 0.20 km. What is the magnitude of the friction force required to keep the car from sliding?

9000 N

Fc = mv2/r = (1000kg)(900m/s2)/(100m)

= 9000N

300
Who was the 15th century Polish astronomer who proposed a heliocentric model of the solar system and had the mathematical derivations to support his claim?
Nicolaus Copernicus
300
Two planets have the same surface acceleration due to gravity, but planet B has twice the radius of planet A. If planet A has mass m, what is the mass of planet B?
4m
300
From what height above the surface of the earth should an object be dropped to initially experience an acceleration of 0.54g?
2,300,000 m
400

You are making a circular turn in your car on a horizontal road when you hit a big patch of ice, causing the force of friction between the tires and the road to become zero. While the car is on the ice, what kind of motion does it have?

It moves along a straight-line path in its original direction - inertia.

400

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?

54 m/s

f = μN = (0.40)(mg) = (0.4)(9.8)m = 3.92m

mv2/r = 3.92m 

v2 = 3.92(r) = 2900

v = 54 m/s

400
A future use of space stations may be to provide hospitals for severely burned persons. It is very painful for a badly burned person on Earth to lie in bed. In a space station, the effect of gravity can be reduced or even eliminated. How long should each rotation take for a doughnut-shaped hospital of 200-m radius so that persons on the outer perimeter would experience 1/10 the normal gravity of Earth?
1.5 minutes
400
What is the gravitational force acting on a 59-kg person due to another 59-kg person standing 2.0 m away? We can model each person as a small sphere.
5.8 × 10^-8 N
400
Find the orbital speed of an ice cube in the rings of Saturn. The mass of Saturn is 5.68 x 1026 kg, and use an orbital radius of 1.00 x 105 km.
19.5 km/s
500

Riding in the bed of a pick-up truck can be very dangerous. If the truck turns suddenly, the riders can be thrown from the truck bed. Why are the riders ejected from the bed?

The riders' inertia tends to keep them moving in the same straight-line motion while the truck turns beneath them. The walls of the bed of the pick-up truck are low so won't provide much centripetal force to hold the riders in the truck as it turns.

500

A 2.0-kg ball is moving with a constant speed of 5.0 m/s in a horizontal circle whose diameter is 1.0 m. What is the magnitude of the net force on the ball?

100 N

r = 0.50m  Fc = mv2/r = (2.0kg)(25.0 m2/s2)/0.50

= 100N

500
True or false: If you swing a bucket of water fast enough in a vertical circle, at the highest point the water does not spill out. This happens because an outward force balances the pull of gravity on the water. EXPLAIN YOUR ANSWER!!!
False. The water doesn't spill out because of the normal force of the bucket on the water directed towards the center of the circular path.
500
Planet Z-34 has a mass equal to one-third that of Earth and a radius equal to one-third that of Earth. With g representing, as usual, the acceleration due to gravity at the surface of Earth, the acceleration due to gravity at the surface of Z-34 is ___.
3g
500
What is the relationship between the orbital period of a planet and its orbital radius?
T squared ~ R cubed The further away you are from the Sun, the longer it takes the planet to orbit.