Final answer:
To find the force the child exerted to do 7355 J of work while moving 135 m up the hill, we use the work formula. With the assumption of no angle between force and displacement, the force is approximately 54.5 N.
Step-by-step explanation:
To determine the size of the force that the child must exert to move the sled 135 m up the hill with 7355 J of work done, we can use the work formula, which is the product of force, distance, and the cosine of the angle between the force and displacement vectors. In this case, because the child is walking up the hill and we can assume the force is exerted parallel to the displacement, the angle is 0 degrees and the cosine of 0 degrees is 1. Hence, the work done is simply the force multiplied by the distance. The formula to calculate the force is:
Work = Force × Distance × cos(θ)
Since Work is 7355 J and the Distance is 135 m, we can rearrange the formula to solve for Force:
Force = Work / Distance
So, the force exerted by the child is:
Force = 7355 J / 135 m ≈ 54.5 N