Centripetal Force Equation | Problems (And Solutions)

by
Centripetal Force Equation

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:

Also Read:

Leave a Comment