A cyclist comes to a skidding stop in 10 m, the force on the cycle due to the road is 200 N and opposite to the motion. How much work does the road do on the cycle?

Explanation

The work done by a force on an object is given: W = F x d x cosθ where: W = work done by the force (in joules, J) F = magnitude of the force (in newtons, N) d = displacement of the object (in meters, m) θ = angle between the force and displacement vectors (in degrees) In this case, the force on the cycle due to the road is opposite to the motion of the cycle, so the angle between the force and the displacement vectors is 180 degrees. Putting the values, we get: W = 200 N x 10 m x cos(180°) The cosine of 180 degrees is -1, so we can simplify the expression as follows: W = -200 N x 10 m = -2000 J Therefore, the work done by the road on the cycle is -2000 J, which means that the road does negative work on the cycle. This is because the force on the cycle is opposite to the displacement of the cycle, and so the work done by the force is negative.