Question 1

A 3 kg block is tied to the end of a 2 m string and slides around in a circle on a frictionless table, completing a rotation every 4 seconds. What is the tension in the string?

Accepted Answer

$$T = 7.4\ \mathrm{N}$$

Question 2

Which of the following best describes the direction of the centripetal force acting on an object in uniform circular motion?

Accepted Answer

Toward the center of the circle

Question 3

A 4 kg block is tied to the end of a 3 m string and slides around in a circle on a frictionless table. If the string breaks at 50 N, what is the maximum speed the block can have without breaking the string?

Accepted Answer

$$v_{max} = 6.1\ \mathrm{m/s}$$

Question 4

A 0.50 kg ball is tied to a 4 m cord and spun in a horizontal circle, with the cord making a 30° angle with the vertical. What is the correct approach to find the ball’s speed?

Accepted Answer

Set the vertical component of tension equal to $$mg$$ and use the horizontal component for centripetal force.

Question 5

For a car of mass $$m$$ driving around a flat curve of radius $$R$$ with coefficient of static friction $$\mu_s$$, what is the maximum speed before slipping?

Accepted Answer

$$v_{max} = \sqrt{gR\mu_s}$$

Question 6

A truck can go around a flat curve of radius 150 m at 32 m/s before slipping. What is the maximum speed it can go around a curve of radius 75 m?

Accepted Answer

$$v_{max} = 22.7\ \mathrm{m/s}$$

Question 7

On a frictionless banked curve, what provides the centripetal force required for circular motion?

Accepted Answer

The horizontal component of the normal force

Question 8

An 800 kg racecar drives around a banked, frictionless curve inclined at 37° with a radius of 200 m. What is the formula for the exact speed so it moves without sliding up or down?

Accepted Answer

$$v = \sqrt{gR	an	heta}$$

Question 9

A bobsled turn banked at 78° is taken at 24 m/s. If the turn is ideally banked and frictionless, what is the centripetal acceleration?

Accepted Answer

$$a_c = 46.1\ \mathrm{m/s^2$}$$

Question 10

In vertical circular motion, such as a rollercoaster loop, why is the speed not constant?

Accepted Answer

Because gravity does work on the object, changing its kinetic energy

Question 11

A 1,800 kg car passes over a bump in a roadway that follows the arc of a circle of radius 20 m at 9 m/s. What force does the road exert on the car at the top of the bump?

Accepted Answer

$$F_N = 10,350\ \mathrm{N}$$

Question 12

For a satellite in a circular orbit, what provides the centripetal force?

Accepted Answer

Gravitational force

Question 13

What is the correct formula for the orbital speed of a satellite in a circular orbit of radius $$r$$ around a planet of mass $$M$$?

Accepted Answer

$$v_{sat} = \sqrt{\frac{GM}{r}}$$

Question 14

If the orbital radius of a satellite is increased, what happens to its orbital speed and period?

Accepted Answer

Speed decreases, period increases

Question 15

Given the gravitational force $$F_G = \frac{Gm_1m_2}{r^2$}$$, what happens to the force if the distance between two masses is doubled?

Accepted Answer

The force becomes one-fourth as large

Question 16

A satellite orbits the Moon with a period of 2 hours. What is the correct formula to find its orbital altitude?

Accepted Answer

$$T^2$$ = \frac{4\$$pi^2$$ $$r^3$$}{GM}$$

Question 17

A planet orbits a star three times the mass of our Sun and feels a gravitational force of $$2 	imes 10$$^{26}$$ N. If the planet’s mass is 8$$ 	imes $$10^{26} kg$$, what is the correct formula for its orbital speed?

Accepted Answer

$$v = \sqrt{\frac{GM}{r}}$$

Question 18

Which of the following best describes the escape speed from a planet of mass $$M$$ and radius $$R$$?

Accepted Answer

$$v_{escape} = \sqrt{\frac{2GM}{R}}$$

Question 19

A baseball is thrown horizontally from the surface of a small asteroid. What is the minimum speed so that it just barely goes around the asteroid without hitting anything?

Accepted Answer

$$v_{min} = \sqrt{\frac{GM}{R}}$$

Dynamics II: Motion in a Plane – Centripetal Forces and Satellite Motion

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