Physics
Circular Motion Worksheet (Horizontal Circles including Newton’s Laws)
1. A 1000 kg car enters a circular turn (of radius of 25 m) with a constant speed of 25 m/s.
a)Is the car accelerating? If so, in what direction?
b)At every moment of time, what motion does the car want to undergoe?
c)What keeps the car going in a circular path?
d)What is the magnitude of this force?
e)Draw an FBD of the car, including all forces acting on it and the direction of the accel.
f)
2. A ball of mass 2.5 x 102 kg is swung at the end of a string in a horizontal circular path at a speed of 5.0 m/s. If the length of the string is 2.0 m,
a)what keeps the ball in its circular orbit?
b) what centripetal force does the string exert on the ball? c) what is the period of the motion.
3. Calculate the centripetal force exerted on a 5.0 kg mass that is moving at a speed of 3.0 m/s in a horizontal circular motion if the radius of the circle is:
a. 1.0 mb. 3.0 m
4. A washing machine drum rotates at 1200 revolutions per minute. A particle of water, 105 kg mass, adheres to a piece of cloth until the machine spins at 1200 r.p.m. The cloth is revolving in a circle of 0.40 m radius. What is the force of adhesion between the cloth and the water droplet?
5. An atom of hydrogen consists of an electron of mass 9.1 x 10 31 kg in circular orbit at uniform speed v. The orbital radius is 5.3 x 10 11 and the period is 1.4 x 10 16 sec. Calculate …
a. The speed of the electron and
b. The centripetal force holding it in its orbit.
6. A textile fiber (which is really just a piece of string) whirled in a constant speed testing machine can exert sufficient force to keep a 10.0 kg mass circling in a radius of 0.20 m. The fiber snaps if the speed increases. What is the minimum radius that a 2.5 kg mass may be whirled by the same fiber in this same machine at thissame speed?
7. A balance weight of mass 28 g is located on a wheel rim 33 cm from the center. What is the centripetal force the balance weight experiences when it is rotated at 27 m/sec?
8. A length of rope can just support a weight of 150 N without breaking.
a. At what speed can this rope be used to whirl a 3 kg mass in a horizontal circle of radius 2 m?
b. What is the period of this motion?
9. The moon’s mass is 7.35 x 1022 kg. The time for one revolution about the earth is about 27.3 days. Calculate the centripetal acceleration and speed of the moon as it “falls” toward the earth.
(Rmoon’s Orbit = 3.80 x 105km)
10. An automobile weighs 6.0 x 104 N. If it is driven around a horizontal curve that has a radius of 250 m at the rate of 22 m/s., what is the centripetal force of the road on the automobile?
11. A fly of mass 2 g is sunning itself on a phonograph turntable at a location that is 4 cm from the axis. When the turntable is turned on and rotates at 45 rev/min, calculate the inward (centripetal) force needed to keep the fly from slipping.
12. A car with a mass of 800 kg drives around a horizontal, circular curve whose radius is 25 m. The coefficient of friction between the car’s tires and the road is 0.8. What is the maximum speed with which the car can take the turn without slipping?
13. When the apparatus turns, both the water in the jar and floating bob want to travel in a straight line, and thus try to leave the circular path. They will both push toward the outside of the jar. However, since the bob is less dense than the water (which is why it floats) it will be pushed toward THE INSIDE because the water will force its way to the outside. Therefore, the floating bob will point INWARD.
14. There is no OUTWARD pointing centriFUGAL force. The car, and thus the people inside the car, want to move in a straight line, tangent to the circle, at every moment (due to Newton’s 1st Law). Since all tangents point OUT of the circle, the motion that the car and people want to continue is OUT of the circle. However, this is not an outward pointing force, but rather their inertia wanting to continue its motion.
15. HONORS ONLY: In deep space, the effects of gravity are not felt, and therefore space stations that operate in deep space need to provide “artificial gravity” for people in the space station to feel like they are on the earth. One way to do this is to have the space station rotate, thus producing the “feeling” of gravity. Some space stations are designed to look like donuts, other like cylinders. A cylindrical space station of diameter 500m is set spinning to provide the sensation of normal earth gravity. Assuming that people are standing inside the cylinder at the furthest point from the center of the space station, determine…
a)the speed of a point on the floor of the space station.
b)the period of one complete revolution.
c)the number of revolutions per minute.