Centripetal force equation

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Centripetal force equation
Centripetal force equation | Image: Learnool

The centripetal force equation, given by Fc = (m × v2) ÷ r, is used to calculate the force required to keep an object moving in a circular path. In this equation, Fc represents the centripetal force, m is the mass of the object, v denotes the velocity of the object, and r signifies the radius of the circular path.

Practice problems

Problem #1

Determine the centripetal force acting on a car of mass 1000 kg as it moves in a circular path with a velocity of 1.8 km/h. The radius of the circular path is 10 m.

Solution

Given data:

  • Centripetal force acting on a car, Fc = ?
  • Mass of a car, m = 1000 kg
  • Velocity of a car, v = 1.8 km/h = 0.5 m/s
  • Radius of a circular path, r = 10 m

Applying the formula:

  • Fc = (m × v2) ÷ r
  • Fc = [1000 × (0.5)2] ÷ 10
  • Fc = 250 ÷ 10
  • Fc = 25 N

Therefore, the centripetal force acting on a car is 25 N.

Problem #2

Find the centripetal force acting on a boy of mass 30 kg who is enjoying a merry-go-round ride. The boy sits on a merry-go-round rotating in a circular path with a radius of 6 m and a velocity of 2 m/s.

Solution

Given data:

  • Centripetal force acting on a boy, Fc = ?
  • Mass of a boy, m = 30 kg
  • Radius of a circular path, r = 6 m
  • Velocity of a boy, v = 2 m/s

Applying the formula:

  • Fc = (m × v2) ÷ r
  • Fc = [30 × (2)2] ÷ 6
  • Fc = 120 ÷ 6
  • Fc = 20 N

Therefore, the centripetal force acting on a boy is 20 N.

Problem #3

Calculate the centripetal force acting on a truck weighing 2500 kg, which moves with a velocity of 1.2 km/h in a circular path of radius 15 m.

Solution

Given data:

  • Centripetal force acting on a truck, Fc = ?
  • Mass of a truck, m = 2500 kg
  • Velocity of a truck, v = 1.2 km/h = 0.33 m/s
  • Radius of a circular path, r = 15 m

Applying the formula:

  • Fc = (m × v2) ÷ r
  • Fc = [2500 × (0.33)2] ÷ 15
  • Fc = 272.25 ÷ 15
  • Fc = 18.15 N

Therefore, the centripetal force acting on a truck is 18.15 N.

Problem #4

Determine the centripetal force acting on a sports bike weighing 140 kg as it moves in a circular path with a radius of 25 m and a velocity of 2.5 km/h.

Solution

Given data:

  • Centripetal force acting on a sports bike, Fc = ?
  • Mass of a sports bike, m = 140 kg
  • Radius of a circular path, r = 25 m
  • Velocity of a sports bike, v = 2.5 km/h = 0.69 m/s

Applying the formula:

  • Fc = (m × v2) ÷ r
  • Fc = [140 × (0.69)2] ÷ 25
  • Fc = 66.654 ÷ 25
  • Fc = 2.6 N

Therefore, the centripetal force acting on a sports bike is 2.6 N.

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External links

Deep

Learnool.com was founded by Deep Rana, who is a mechanical engineer by profession and a blogger by passion. He has a good conceptual knowledge on different educational topics and he provides the same on this website. He loves to learn something new everyday and believes that the best utilization of free time is developing a new skill.

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