A child pushes a merry-go-round with a force of 55.0 N at an angle tangent to the circle (that is, perpendicular to a radius). If the child pushes it through exactly one full circle, and the merry-go-round has a radius of 1.15 m, how much work does she do?
? Please explain!
W=M•φ =F•R•φ =55•1.15•2•π =518.4 J
To find the work done by the child, we can use the formula for work:
Work = Force × Distance × Cosine(θ),
where:
- Force is the applied force by the child (55.0 N),
- Distance is the distance traveled by the merry-go-round in one full circle (the circumference of the circle),
- Cosine(θ) is the cosine of the angle between the applied force and the direction of the displacement (which is 0 degrees in this case, since the applied force is perpendicular to the radius).
The first step is to find the distance traveled by the merry-go-round in one full circle. The distance traveled in one full circle is equal to the circumference of the circle, which is given by the formula:
Circumference = 2 × π × radius.
In this case, the radius of the merry-go-round is 1.15 m. Plugging the radius into the formula, we get:
Circumference = 2 × 3.14 × 1.15.
Next, calculate the cosine of 0 degrees, which is equal to 1.
Finally, substitute the values into the work formula:
Work = 55.0 × (2 × 3.14 × 1.15) × 1.
The final step is to calculate the result to find the work done by the child.