Question

1 formula 1 point a yo-yo on a string has a mass of 0.6 kilograms. a student spins the yo-yo around in a circle with a speed of 7 m/s. the yo-yo’s string is 0.7 meters long. calculate the tension force in the string. answer next

Explanation:

Step1: Identify the formula

For an object moving in a circular path, the centripetal force \( F_c \) (which in this case is provided by the tension \( T \) in the string) is given by the formula \( F_c = T=\frac{mv^2}{r} \), where \( m \) is the mass, \( v \) is the velocity, and \( r \) is the radius of the circular path.

Step2: Substitute the given values

We are given \( m = 0.6 \, \text{kg} \), \( v = 7 \, \text{m/s} \), and \( r = 0.7 \, \text{m} \). Substituting these values into the formula:

\( T=\frac{0.6\times(7)^2}{0.7} \)

First, calculate \( 7^2 = 49 \). Then, \( 0.6\times49 = 29.4 \). Now, divide by \( 0.7 \): \( \frac{29.4}{0.7}=42 \).

Answer:

The tension force in the string is \( 42 \, \text{N} \) (Newtons).