**Centripetal force **(F_{c}) is equal to **mass **(m) times the square of** velocity **(v^{2}) divided by the **radius **(r). Using the equation of centripetal force: **F**_{c}** = [m ×** **v**^{2}**] ÷ 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, F_{c} = ?

Using the equation of centripetal force,

F_{c} = [m × v^{2}] ÷ r

F_{c} = [1000 × (0.5)^{2}] ÷ 10

F_{c} = 250 ÷ 10

F_{c} = 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, F_{c} = ?

Using the equation of centripetal force,

F_{c} = [m × v^{2}] ÷ r

F_{c} = [30 × (2)^{2}] ÷ 6

F_{c} = 120 ÷ 6

F_{c} = 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, F_{c} = ?

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,

F_{c} = [m × v^{2}] ÷ r

F_{c} = [2500 × (0.33)^{2}] ÷ 15

F_{c} = 272.25 ÷ 15

F_{c} = 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, F_{c} = ?

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,

F_{c} = [m × v^{2}] ÷ r

F_{c} = [140 × (0.69)^{2}] ÷ 25

F_{c} = 66.654 ÷ 25

F_{c} = 2.6 N

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

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**Related:**

- Force Equation
- Normal Force Equation
- Net Force Formula
- Applied Force Formula
- Magnetic Force Equation
- Centrifugal Force Equation
- Spring Force Equation
- Tension Force Formula
- Electric Force Equation

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