Q: It takes the planet Jupiter 12 years to orbit the sun once in a nearly circular orbit. Assuming that Jupiter's orbit is nearly circular, what is the distance from Jupiter to the sun, given that the distance from the earth to the sun is $$1.5 \times 10$$^{11}$$\ \mathrm{m}$$?

$$7.8 \times 10$$^{12}$$\ \mathrm{m}$$

Q: Two identical balls of highly compressed matter are $$1.50\ \mu\mathrm{m}$$ apart. When released in an orbiting space station, they accelerate toward each other at $$2.0\ \mathrm{cm/s^2$}. $$What is the mass of each ball? ($$G = 6.67 \times 10$$^{-11}$$\ \mathrm{N\cdot m^2$/kg^2$$}$)

$$6.75 \times 10^8$\ \mathrm{kg}$$

Q: 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. ($$G = 6.67 \times 10$$^{-11}$$\ \mathrm{N\cdot m^2$/kg^2$$}$)

$$5.8 \times 10$$^{-8}$$\ \mathrm{N}$$

Q: A satellite orbits Earth at a height where the acceleration due to gravity is $$6.0\ \mathrm{m/s^2$}. If $$the radius of Earth is $$6.4 \times 10^6$\ \mathrm{m}$$, what is the satellite's orbital radius?

$$8.2 \times 10^6$\ \mathrm{m}$$

Q: A geostationary satellite orbits Earth once every $$24$$ hours. What is the radius of its orbit? (Earth's mass $$= 5.97 \times 10$$^{24}$$\ \mathrm{kg}$$, $$G = 6.67 \times 10$$^{-11}$$\ \mathrm{N\cdot m^2$/kg^2$$}$)

$$4.2 \times 10^7$\ \mathrm{m}$$

Question 1

A 2.0-kg ball is attached to a light 120-cm-long string and moves in a horizontal circle with a constant speed of 1.5 m/s. If the angle the string makes with the vertical is measured to be $$28^\circ$$, what is the tension in the string?

Accepted Answer

$$4.6\ \mathrm{N}$$

Question 2

It takes the planet Jupiter 12 years to orbit the sun once in a nearly circular orbit. Assuming that Jupiter's orbit is nearly circular, what is the distance from Jupiter to the sun, given that the distance from the earth to the sun is $$1.5 	imes 10$$^{11}$$\ \mathrm{m}$$?

Accepted Answer

$$7.8 	imes 10$$^{12}$$\ \mathrm{m}$$

Question 3

Two identical balls of highly compressed matter are $$1.50\ \mu\mathrm{m}$$ apart. When released in an orbiting space station, they accelerate toward each other at $$2.0\ \mathrm{cm/s^2$}. $$What is the mass of each ball? ($$G = 6.67 	imes 10$$^{-11}$$\ \mathrm{N\cdot m^2$/kg^2$$}$)

Accepted Answer

$$6.75 	imes 10^8$\ \mathrm{kg}$$

Question 4

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. ($$G = 6.67 	imes 10$$^{-11}$$\ \mathrm{N\cdot m^2$/kg^2$$}$)

Accepted Answer

$$5.8 	imes 10$$^{-8}$$\ \mathrm{N}$$

Question 5

In order to simulate weightlessness for astronauts in training, they are flown in a vertical circle. If the passengers are to experience weightlessness, how fast should an airplane be moving at the top of a vertical circle with a radius of $$2.5 km$$?

Accepted Answer

$$160\ \mathrm{m/s}$$

Question 6

A pilot of mass $$78 kg $$flies a plane in a vertical circle at a speed of $$840 km/h. $$What is the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed $$6g$$?

Accepted Answer

$$930\ \mathrm{m}$$

Question 7

At the bottom of the vertical circle, what is the normal force acting on the $$78-kg $$pilot if the radius is $$930 m $$and the speed is $$840 km/h$$?

Accepted Answer

$$5400\ \mathrm{N}$$

Question 8

At the top of the vertical circle, what is the normal force acting on the $$78-kg $$pilot if the radius is $$930 m $$and the speed is $$840 km/h$$?

Accepted Answer

$$3800\ \mathrm{N}$$

Question 9

A satellite orbits Earth at a height where the acceleration due to gravity is $$6.0\ \mathrm{m/s^2$}. If $$the radius of Earth is $$6.4 	imes 10^6$\ \mathrm{m}$$, what is the satellite's orbital radius?

Accepted Answer

$$8.2 	imes 10^6$\ \mathrm{m}$$

Question 10

A $$5.0-kg $$mass is whirled in a horizontal circle of radius $$2.0 m at a $$constant speed of $$4.0 m/s. $$What is the tension in the string?

Accepted Answer

$$40\ \mathrm{N}$$

Question 11

A car of mass $$1200 kg $$rounds a curve of radius $$50 m at a $$speed of $$14 m/s. $$What is the minimum coefficient of friction required to prevent skidding?

Accepted Answer

$$0.40$$

Question 12

A geostationary satellite orbits Earth once every $$24$$ hours. What is the radius of its orbit? (Earth's mass $$= 5.97 	imes 10$$^{24}$$\ \mathrm{kg}$$, $$G = 6.67 	imes 10$$^{-11}$$\ \mathrm{N\cdot m^2$/kg^2$$}$)

Accepted Answer

$$4.2 	imes 10^7$\ \mathrm{m}$$

Question 13

A $$0.5-kg $$mass is attached to a string and swung in a vertical circle of radius $$1.2 m. $$What is the minimum speed at the top of the circle so that the string remains taut?

Accepted Answer

$$3.4\ \mathrm{m/s}$$

Question 14

A $$2.0-kg $$object moves in a circle of radius $$0.50 m at a $$constant speed of $$3.0 m/s. $$What is the net force acting on the object?

Accepted Answer

$$18\ \mathrm{N}$$

Question 15

A $$1000-kg $$car travels around a flat, circular track of radius $$80 m. If $$the maximum static friction force is $$7000 N$$, what is the maximum speed the car can have without skidding?

Accepted Answer

$$9.4\ \mathrm{m/s}$$

Question 16

A $$0.2-kg $$ball is swung in a horizontal circle of radius $$0.6 m at a $$speed of $$2.0 m/s. $$What is the period of revolution?

Accepted Answer

$$1.8\ \mathrm{s}$$

Question 17

A $$3.0-kg $$mass is attached to a $$2.0-m-$$long string and whirled in a vertical circle. What is the tension in the string at the bottom of the circle if the speed at the bottom is $$6.0 m/s$$?

Accepted Answer

$$54\ \mathrm{N}$$

Question 18

A $$1.0-kg $$object is moving in a circle of radius $$0.25 m at a $$constant speed. If the object completes $$2.0$$ revolutions per second, what is the magnitude of the centripetal force?

Accepted Answer

$$39.5\ \mathrm{N}$$

Question 19

A $$0.8-kg $$mass is attached to a string and swung in a horizontal circle of radius $$0.4 m at a $$speed of $$3.0 m/s. $$What is the angular velocity of the mass?

Accepted Answer

$$6.0\ \mathrm{rad/s}$$

Circular Motion and Gravitational Forces: Study Notes and Problem Solutions

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