# Worksheet: Centripetal Force

In this worksheet, we will practice demonstrating how an object following a circular path experiences acceleration toward the center of the circle.

**Q7: **

In a particle accelerator, a proton moves along a circular path of 5.55 km radius at a speed of m/s. The mass of a proton is kg.

What is the magnitude of the centripetal acceleration of the proton?

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

What is the magnitude of the centripetal force on the proton?

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

**Q8: **

The Sun orbits the Milky Way galaxy once each years, with a roughly circular orbit averaging a radius of light-years.

Calculate the centripetal acceleration of the Sun in its galactic orbit.

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

Calculate the average speed of the Sun in its galactic orbit.

- A m/s
- B m/s
- C m/s
- D m/s
- E m/s

**Q9: **

A particle is moving along a circular path in the xy-plane. The radius of the circular path is 5.0 m, and at time the particle has a velocity that points in the positive y-direction and a centripetal acceleration of in the negative x-direction. What is the particle's velocity at ?

- A m/s
- B m/s
- C m/s
- D m/s
- E m/s

**Q11: **

A large centrifuge has an arm with a length of 12.7 m. At the end of the centrifuge arm hangs a cage on a pivot.

What angular velocity of the centrifuge will produce a centripetal acceleration of on the cage?

At what angle below the horizontal will the cage hang at when the cage experiences a centripetal acceleration of ?

**Q12: **

At takeoff, a commercial jet has a speed of 60.0 m/s. Its tires have a diameter of 0.850 m.

At how many revolutions per minute are the tires rotating?

- A
- B
- C
- D
- E

What is the centripetal acceleration at the edge of the tire?

- A
- B
- C
- D
- E

With what force must a determined bacterium cling to the rim?

- A
- B
- C
- D
- E

What is the ratio of this force to the bacterium’s weight?

**Q13: **

A car that has a mass of 900.0 kg drives along a circular unbanked curve at a constant speed of 25.000 m/s. The radius of the curve is 500.0 m.

What magnitude force acts on the car to maintain its speed and direction as it follows the curve?

What is the minimum possible value for the coefficient of static friction between the car’s tires and the road surface?

**Q15: **

A bobsled can travel along a curved path despite there being negligible friction between the bobsled and the ice that it slides over. In order for the bobsled to turn, the surface that it slides along must be banked so that the bobsled slides toward the center of curvature of the path followed. What speed should a bobsled be launched at so that it follows a circular curved path of radius 100.0 m that is banked at an angle of ?

**Q16: **

Calculate the angular velocity of an electron in the second excited state in a hydrogen atom. Use a value of m for the orbit’s radius, and model the orbit as circular. Assume that the proton is stationary and the centripetal force on the electron is supplied by Coulomb attraction.

- A rad/m
- B rad/m
- C rad/m
- D rad/m
- E rad/m