# Centripetal force equation

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.

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## 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.