Question

A 0.100 kg mass is attached to a string 75cm long and swings in a horizontal circle, revolving once every 0.80 s. Calculate the centripetal acceleration of the mass.

Answer 1

To calculate the centripetal acceleration of the mass, we'll follow these steps:

1. Find the Angular Velocity (
   `w`): Angular velocity is given by the formula
   `w=(2\pi )/(T)`, where
   `T` is the period of revolution.
2. Determine the Radius (
   `r`): The radius of the circle in which the mass swings is the length of the string, which is
   `75` cm. We need to convert this to meters.
3. Calculate the Centripetal Acceleration (
   `a_c`): Centripetal acceleration is given by the formula
   `a_c=rw^2`.

Let's calculate each of these step by step.

Step 1: Calculate the Angular Velocity (
`w`)

Given:

• Period of revolution,
  `T=0.80` seconds.

The formula for angular velocity is:

`w=(2\pi )/(T)`

Substituting the given values:

`w=(2\pi )/(0.80)`

`w\approx(6.2832)/(0.80)`

`w\approx7.854` rad/s

Step 2: Radius of the Circle (
`r`)

Given:

• Length of string
  `=75` cm
  `=0.75` m (after converting from cm to m).

Step 3: Calculate the Centripetal Acceleration (
`a_c`)

The formula for centripetal acceleration is:

`a_c=rw^2`

Substituting the values:

`a_c=0.75\cdot(7.854)^2`

`a_c\approx0.75\cdot61.725`

`a_c\approx46.26` m/s²

So, the centripetal acceleration is approximately
`46.26` m/s².