Questions: The young rider on a playground merry-go-round must hold on with a force of 121 N . If the rider's mass is 15.9 kg and the radius of the merry-go-round is 2.33 m , what is the speed of the rider? Hint•

The young rider on a playground merry-go-round must hold on with a force of 121 N . If the rider's mass is 15.9 kg and the radius of the merry-go-round is 2.33 m , what is the speed of the rider?
Hint•

Transcript text: The young rider on a playground merry-go-round must hold on with a force of 121 N . If the rider's mass is 15.9 kg and the radius of the merry-go-round is 2.33 m , what is the speed of the rider? Hint•

Solution

Solution Steps

Step 1: Identify the Given Values

We are given the following values:

Force (\( F \)) = 121 N
Mass (\( m \)) = 15.9 kg
Radius (\( r \)) = 2.33 m

Step 2: Understand the Relationship

The force that the rider must hold on with is the centripetal force, which is given by the formula: \[ F = \frac{mv^2}{r} \] where \( v \) is the speed of the rider.

Step 3: Solve for Speed

Rearrange the formula to solve for \( v \): \[ v = \sqrt{\frac{Fr}{m}} \]

Step 4: Substitute the Given Values

Substitute the given values into the equation: \[ v = \sqrt{\frac{121 \, \text{N} \times 2.33 \, \text{m}}{15.9 \, \text{kg}}} \]

Step 5: Calculate the Speed

Perform the calculation: \[ v = \sqrt{\frac{282.93}{15.9}} \] \[ v = \sqrt{17.7994} \] \[ v \approx 4.2165 \, \text{m/s} \]