# Worksheet: Sources of Centripetal Force

In this worksheet, we will practice identifying the physical causes of centripetal forces on objects and identifying whether such forces have position-dependent components.

**Q2: **

A 30.0-g ball at the end of a string is swung in a vertical circle with a radius of 25.0 cm. The rotational velocity is 200.0 cm/s.

Find the tension in the string at the top of the circle.

Find the tension in the string at the bottom of the circle.

Find the tension in the string at a distance of 12.5 cm from the center of the circle, when the string is horizontal.

**Q7: **

A child of mass 40.0 kg is in a roller coaster car that travels in a loop of radius 7.00 m. At point the speed of the car is 10.0 m/s, and at point , the speed is 10.5 m/s. Assume the child is not holding on and does not wear a seat belt.

What is the magnitude of the force of the car seat on the child at point ?

What is the magnitude of the force of the car seat on the child at point ?

What minimum speed is required to keep the child in his seat at point ?

**Q11: **

A body with a mass of 0.17 kg is attached to a massless vertical spring with an equilibrium length of 2.1 cm. The body extends the spring by 2.6 cm. The body and the spring are then placed on a frictionless horizontal surface and the spring returns to its equilibrium length. The end of the spring not touching the body is fixed and the spring plus the body are rotated steadily about this point at 2.4 rev/s. How much does the spring extend during this rotation? Assume that the mass of the spring is negligible.

**Q12: **

A ball of mass 1.3 kg at the end of a 1.5-m string swings in a vertical circle. At its lowest point the ball is moving with a speed of 9.5 m/s.

What is the speed of the ball at the top of its circular path?

What is the magnitude of the tension in the string when the ball is at the top of its circular?

What is the magnitude of the tension in the string when the ball is at the bottom of its circular path?

**Q14: **

Find the centripetal acceleration of the moon in its orbit around the earth. Use a value of km for the average distance between the centers of the earth and the moon. Use a value of 27.3 days for the orbital period of the moon around the earth, considering one day as s.

- A
m/s
^{2} - B
m/s
^{2} - C
m/s
^{2} - D
m/s
^{2} - E
m/s
^{2}

**Q16: **

Riders on an amusement park ride, shaped like a Viking ship hung from a large pivot, are rotated back and forth like a rigid pendulum. When the ship reaches its highest point, 14.0 m above the ground, it is momentarily motionless. The ship then swings down under the influence of gravity. The system’s center of mass travels in an arc and the riders are near the center of mass. Assume that friction is negligible.

Find the speed of the riders at the bottom of the arc.

What is the centripetal acceleration at the bottom of the arc?

Find the force exerted by the ride on a 60.0 kg rider.

- A N
- B N
- C N
- D N
- E N

**Q17: **

The frictionless track for a toy car includes a loop-the-loop of radius , as shown in
the diagram. At a point **1**, with a vertically upward displacement from the bottom
of the loop, the car can start from rest and travel on the section of the track
approaching the loop and then go on to travel all the way around the loop and remain in
contact with the track at the point **2**. What value must exceed?

- A
- B
- C
- D
- E