# An object of weight 150 N moves with a speed of 4.5 m/s

## 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/s2]

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 = V2 / r

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

F = mV2 / 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 = V2 / r

Hence, a = V2 / r = (4.5)2 / 3 = 6.75 m/s2

Therefore, the centripetal acceleration is 6.75 meters per second square

###### Centripetal Force

We will now use F = mV2 / r to find the centripetal force

Thus, F = mV2 / 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

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