Question

a fourth grader exerts 8.4 newtons of force to push a merry-go-round 15 meters in a circle. calculate the work done by the fourth grader.

Explanation:

Step1: Recall Work Formula

Work \( W \) is done when a force \( F \) acts on an object and displaces it in the direction of the force. The formula is \( W = F \times d \times \cos\theta \), where \( \theta \) is the angle between force and displacement.

Step2: Analyze Angle for Merry - go - round

When pushing a merry - go - round in a circle, the force is tangent to the circle, and the displacement (direction of motion) is also tangent. So the angle \( \theta \) between force and displacement is \( 0^{\circ} \), and \( \cos(0^{\circ})=1 \).

Step3: Substitute Values

Given \( F = 8.4\space N \), \( d = 15\space m \), and \( \cos\theta = 1 \). Substitute into the formula: \( W=8.4\times15\times1 \).

Step4: Calculate the Product

\( 8.4\times15 = 126 \). So the work done is \( 126\space J \) (Joules, since \( 1\space N\cdot m=1\space J \)).

Answer:

The work done by the fourth grader is \( \boldsymbol{126}\) Joules.