## Question

An object of weight 150 N moves with a speed of 4.5 m/s in a circular path of radius 3 m. Calculate the centripetal acceleration and the magnitude of the centripetal force. [ Take g as 10 m/s^{2}]

### Answer

**The final answer to this question is centripetal acceleration equals to 6.75 meters per second square, and centripetal force equals 101.25 Newtons**.

#### Explanation

**Data: Revealed information from the question **

Weight of the object, W = 150 N

Speed of the object, V = 4.5 m/s

The radius of the circle, r = 3 m

**Unknown: Unrevealed information from the question from the question**

mass of the object, m = ?

Centripetal acceleration, a = ?

Centripetal force, F = ?

**Formula: The equations that will help us solve the problem**

**Step 1:** To find the mass of the object, we will apply

m = W / g [This is because weight (W) = mass (m) x force of gravity (g)]

We made m subject of the formula from W = m x g

**Step 2:** To find the centripetal acceleration, we will use

a = V^{2} / r

**Step 3:** Finally, to find the centripetal force, we will apply

F = mV^{2} / r

##### Solution

We will now insert our data into the formula to solve the problem

###### Mass of the object

Since m = W / g

We will now have

m = 150 / 10 = 15 kg

###### Centripetal Acceleration

We will now move to step 2 by applying a = V^{2} / r

Hence, a = V^{2} / r = (4.5)^{2} / 3 = 6.75 m/s^{2}

**Therefore, the centripetal acceleration is 6.75 meters per second square**

###### Centripetal Force

We will now use F = mV^{2} / r to find the centripetal force

Thus, F = mV^{2} / r = [15 x (4.5)^{2}] / 3 = 101.25 N

**Therefore, the centripetal force is 101.25 Newtons**

*You may also like to read:*

How to Calculate Centripetal Acceleration

How to Calculate Centripetal Force

Simple Harmonic Motion (SHM): Understanding the Basic Concepts