Download Homework Problems

Pre AP Physics
Circular Motion
1. A mass of 1.5 kg moves in a circular path with a constant speed of 3 m/s on a horizontal frictionless surface. The mass is
held to the circular path by a light cord 2.4 m long that has one end fixed and the other end attached to the mass. Calculate
the tension in the cord. [5.625 N]
2. An automobile of mass 1500 kg travels in a circular path of radius 20 m on a horizontal road surface at a speed of 12.5
m/s (around 72 mph). What is the coefficient of static friction between the tires and the road? [0.797]
3. Determine the centripetal force acting on a 40 kg child who makes 10 revolutions around in the Cliffhanger in 29.3 s. The
radius of the barrel of the ride is 2.9 m. [533.462 N]
4. A child whirls a stone of mass 0.5 kg in a vertical circle on the end of a string 40 cm long. At the lowest point of the circle
the velocity of the stone is 3 m/s. Calculate the tension in the string at this point. [16.15 N]
5. Anna Litical is riding on The Demon of Great America. Anna experiences a centripetal acceleration of 15.0 m/s2 at the top
of the loop of the roller coaster. Determine the normal force acting upon Anna’s 1000 kg roller coaster car at the top of the
loop. [5200 N]
6. What is the direction of the centripetal force of an object in uniform circular motion?
b. What is the direction of the centripetal acceleration?
7. What causes a tin can whirled on the end of a string to move in a circular path?
b. If the string breaks, what causes it to move in a straight-line path?
8. An 1800 kg car rounds a curve of radius 92 m with a speed of 3.0 m/s. If its wheels are on the verge of slipping on the
road, what is the force of friction? [176.087 N]
9. A model airplane is guided in a horizontal circular path by a cord of length 16 m. If it has a constant speed of 18 m/s and a
mass of 200 g, what is the tension in the cord? [4.05 N]
10. What is the centripetal acceleration of an object moving in a horizontal circular path of 20 m radius with a speed of 18
m/s? [16.2 m/s]
11. An automobile travels around a circular track of radius 0.120 km at a speed of 2.5 m/s. What is the centripetal
acceleration? [0.052 m/s2]
b. If the car has a mass of 1200 kg and the track is completely level, what is the coefficient of friction between the tires and
the track as the car travels on the circular track? [0.005]
12. If a car travels in a circle at a constant speed, what is the direction of the net force on the car?
b. What is the name of the net force for any uniform circular motion problem?
13. Anna Litical is practicing a centripetal force demonstration at home. She fills a bucket with water, ties it to a strong rope,
and spins it vertically in a circle. Anna spins the bucket when it is half-full of water and when it is quarter-full of water. In
which case is more force required to spin the bucket in a circle? Explain using an equation as a “guide to thinking”.
14. A Lincoln Continental and a VW Beatle are making a turn. The Lincoln is four times more massive than the Beatle. If they
make the turn at the same speed, then how do the centripetal forces acting on the two cars compare? Explain.
15. The Cajun Cliffhanger at Great America is a ride in which occupants line the perimeter of a cylinder and spin in a circle at
a high rate of turning. When the cylinder begins spinning very rapidly, the floor is removed from under the rider’s feet. What
effect does a tripling in speed have upon the centripetal force? Explain.
16. A 95 kg halfback makes a turn on the football field. The halfback sweeps out a path which is a portion of a circle with a
radius of 12 meters. The halfback makes a quarter of a turn around the circle in 2.1 seconds. Determine the speed,
acceleration and net force acting upon the halfback. [8.976 m/s, 6.714 m/s 2, 637.835 N]
17. A 1.5 kg bucket of water is tied by a rope and whirled in a circle with a radius of 1.0 m. At the top of the circular loop, the
speed of the bucket is 4.0 m/s. Determine the acceleration, the net force and the individual force values when the bucket is
at the top of the circular loop. [16 m/s2, T = 9.3 N, Fnet = 24 N, Fg = 14.7 N]
18. Noah Formula is riding a roller coaster and encounters a loop. Noah is traveling 6 m/s at the top of the loop and 18.0 m/s
at the bottom of the loop. The top of the loop has a radius of curvature of 3.2 m and the bottom of the loop has a radius of
curvature of 16.0 m. Use Newton’s second law to determine the normal force acting upon Noah’s 80 kg body at the top and
at the bottom of the loop. [FNtop = 116 N, FNbottom = 2404 N]
19. Anna Litical is riding a wooden roller coaster. Anna encounters the bottom of a small dip having a radius of curvature of
15.0 m. At the bottom of this dip Anna is traveling with a speed of 16.0 m/s and experiencing a much larger than usual
normal force. Determine the normal force acting upon Anna’s 50 kg body. [1343.33 N]
Chart of Standards:
Mass of Earth = 5.98 x 1024 kg
Mass of Sun = 1.99 x 1030 kg
Mass of Moon = 7.35 x 1022 kg
Radius of Earth = 6.38 x 103 km
Radius of Sun = 6.96 x 105 km
Radius of the Moon = 1.74 x 103 km
Distance between center of Sun and center of Earth and Moon = 1.50 x 10 8 km
Distance between center of Earth and center of Moon = 3.84 x 10 5 km
20. Determine the speed of the Hubble Telescope orbiting at a height of 5.96 x 10 5 m above the earth’s surface.
21. The moon orbits the earth once every 27.3 days. What is the centripetal acceleration of the moon?
22. A spacecraft orbits the moon in a circular orbit of radius 8.01 x 10 8 m. What is the velocity of the spacecraft as it orbits?
23. What is the gravitational attraction between the earth and the moon? Which force is the largest, the earth pulling on the
moon or the moon pulling on the earth?
24. What is the value of g (acceleration due to gravity) at a height of 1500 km above the earth’s surface? [6.42 m/s2]
25. Calculate the velocity that a satellite shot from Earth must have to orbit Earth 150 km above the surface of Earth.
[7815.503 m/s]
b. How long (in seconds) would it take the satellite to return to where it was shot? [5.25 x 10 3 sec]
26. The sun revolves around the center of the galaxy with a radius of 2.2 x 1020 m. The time for one rotation is 2.5 x 108
years.
a. Find the speed with which the sun moves around the center of the galaxy. [1.753 x 10 5 m/s]
b. Find the mass of the galaxy. [1.014 x 1041 kg]
c. Assuming that an average star in the galaxy has the mass of the sun, find the number of stars in the galaxy. [5.095 x 10 10
stars]
27. Two tennis balls weigh 1.64 kg and their centers are 0.020 m apart. Solve for the gravitational force between them.
[4.485 x 10-7 N]
28. Two balls have their centers of mass 2 m apart. One has a mass of 5 kg and the other has a mass of 8 kg.
a. What is the gravitational force between them? [6.67 x 10 -10 N]
b. The distance between the balls is now cut in half. What is the gravitational force between them? [2.668 x 10-9 N]
29. Calculate the acceleration due to gravity on the surface of the earth. [9.799 m/s 2]
30. Calculate the acceleration due to gravity on the surface of the moon. [1.619 m/s 2]
31. The planet Venus has a mass of 4.88 x 1024 kg and has a radius of 6.073 x 106 m.
a. Find the velocity of a satellite in orbit 377 km above its surface. [7103.837 m/s]
b. Calculate the period of the satellite. [5704.881 s]
32. What is the force of gravity acting on a 5000 kg space craft when it orbits three earth radii from the earth’s center? [5.44
x 103 N]
33. Two balls have their centers 5.0 m apart. One has a mass of 11.0 kg and the other has a mass of 7.0 kg. What is the
gravitational force between them? [2.054 x 10 -10 N]