A child pushes a merry-go-round with a force of 80.0 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?

If you could please show some work so that I may actually learn. Thank you

W=M•ö =F•R•ö =80•1.15•2•ð =578.05 J

To find the work done by the child in pushing the merry-go-round, we can use the formula:

Work = Force × Distance × cos(θ)

Where:
- Force is the amount of force applied by the child, which is 80.0 N in this case.
- Distance is the distance traveled along the circular path, which is the circumference of the circle. The formula for circumference is:
Circumference = 2πr
In this case, the radius of the merry-go-round is 1.15 m, so the circumference would be:
Circumference = 2π × 1.15 = 7.23 m.
- θ represents the angle between the direction of the applied force and the direction of the displacement. In this case, since the force is tangential to the circle, it is perpendicular to the radius. Therefore, θ = 90 degrees.

Now let's substitute the values into the formula:

Work = 80.0 N × 7.23 m × cos(90°)

The cosine of 90 degrees is 0, since the cosine of a right angle is always 0. So the equation becomes:

Work = 80.0 N × 7.23 m × 0

Multiplying any number by 0 results in 0, so the work done by the child is 0 Joules.

Therefore, the child does no work in pushing the merry-go-round in a full circle.