# Centripetal Force Equation | Problems (And Solutions)

Centripetal force (Fc) is equal to mass (m) times the square of velocity (v2) divided by the radius (r). Using the equation of centripetal force: Fc = [m × v2] ÷ r, the value of centripetal force acting on an object can be calculated.

Let’s solve some problems based on this equation, so you’ll get a clear idea.

## Centripetal Force Practice Problems

Problem 1: A car of mass 1000 kg is moving in a circular path with the velocity of 1.8 km/h. If the radius of a circular path is 10 m, then what is the centripetal force acting on a car?

Solution:

Given data:
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
Centripetal force acting on a car, Fc = ?

Using the equation of centripetal force,
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: One boy of mass 30 kg is enjoying a merry-go-round ride. A boy sitting on a merry-go-round rotates in a circular path of radius 6 m with the velocity of 2 m/s. Calculate the centripetal force acting on a boy.

Solution:

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

Using the equation of centripetal force,
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 2500 kg truck moving with the 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

Using the equation of centripetal force,
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: What is the centripetal force acting on a sports bike of mass 140 kg moving in a circular path of radius 25 m with the 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

Using the equation of centripetal force,
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.

.
.
.

Related: