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.

- A 0.179 N
- B 0.171 N
- C 0.193 N
- D 0.186 N
- E 0.198 N

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

- A 0.774 N
- B 0.768 N
- C 0.747 N
- D 0.730 N
- E 0.786 N

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

- A 0.862 N
- B 0.567 N
- C 0.960 N
- D 0.670 N
- E 0.796 N

**Q3: **

Railway tracks follow a circular curve of radius 500.0 m and are banked at an angle of . For trains of what speed are these tracks designed?

- A 17.0 m/s
- B 14.4 m/s
- C 22.3 m/s
- D 20.7 m/s
- E 24.9 m/s

**Q4: **

What is the ideal speed for a car to take a 55-m-circular radius curve that is banked at a angle?

**Q5: **

A banked highway is designed for traffic moving at 70.0 km/h. The radius of the curve is 277 m. What is the angle of banking of the highway?

- A
- B
- C
- D
- E

**Q6: **

An airplane flying at 188 m/s makes a circular turn that takes 225 s to complete.

What banking angle is required to make this turn?

What is the percentage increase in the perceived weight of the passengers on the airplane?

- A
- B
- C
- D
- E

**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 ?

**Q8: **

An ideally banked circular bobsled turn is banked at above the horizontal. A bobsled takes the turn at 30.0 m/s. Assume a coefficient of kinetic friction between bobsled and ice of 0.0300.

What is the radius of the turn?

Calculate the magnitude of the bobsled’s centripetal acceleration.

**Q9: **

A stunt cyclist rides around the curved interior surface of a cylindrical container, parallel to the cylinder’s 12-m-radius circular base. The coefficient of static friction between the tyres and the wall is 0.68. Find the minimum speed with which the cyclist must move.

- A 15 m/s
- B 9.6 m/s
- C 18 m/s
- D 13 m/s
- E 20 m/s

**Q10: **

A car rounds an unbanked curve of radius 65 m. If the coefficient of static friction between the road and car is 0.70, what is the maximum speed at which the car traverse the curve without slipping?

**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?

**Q13: **

An airplane flying at 120.0 m/s turns by
banking at a angle.
The airplane’s mass is kg.
Use a value of 9.8 m/s^{2}
for the acceleration due to gravity.

What is the magnitude of the lift force?

What is the radius of the turn?

**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 motion 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}

**Q15: **

Railroad tracks follow a circular curve of radius 500.0 m and are banked at an angle of . For trains of what speed are these tracks designed?

**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