Question

1. a yo - yo swings in a horizontal circle of radius 0.80 m at 2.5 m/s. find the centripetal acceleration.

Explanation:

Step1: Recall centripetal acceleration formula

The formula for centripetal acceleration \( a_c \) is \( a_c = \frac{v^2}{r} \), where \( v \) is the velocity and \( r \) is the radius of the circular path.

Step2: Substitute given values

We are given \( v = 2.5 \, \text{m/s} \) and \( r = 0.80 \, \text{m} \). Substituting these into the formula: \( a_c = \frac{(2.5)^2}{0.80} \).

Step3: Calculate the numerator

First, calculate \( (2.5)^2 = 6.25 \).

Step4: Divide to find acceleration

Now, divide \( 6.25 \) by \( 0.80 \): \( \frac{6.25}{0.80} = 7.8125 \, \text{m/s}^2 \).

Answer:

The centripetal acceleration is \( 7.8125 \, \text{m/s}^2 \) (or approximately \( 7.8 \, \text{m/s}^2 \) or \( 7.81 \, \text{m/s}^2 \) depending on significant figures).