The boy pulls the sled by the rope with a force of 50 N. Having passed 100 m with the sled, he completed

The boy pulls the sled by the rope with a force of 50 N. Having passed 100 m with the sled, he completed the work of 2500 J. What is the angle between the rope and the road?

F = 50 N.

A = 2500 J.

S = 100 m.

∠α -?

When moving the sled through the snow, the boy performs mechanical work A, the value of which is determined by the formula: A = F * S * cosα, where F is the force with which the boy pulls the rope, S is the distance the sled has moved when moving, ∠α – the angle between the direction of the boy’s force F and the movement of the sled S.

We express сosα from the formula.

cosα = A / F * S.

cosα = 2500 J / 50 N * 100 m = 0.5.

We know that according to the cosine table, cos60 ° = 0.5.

Since the boy’s force is directed along the rope for which he pulls the sled, the rope is directed towards the horizon at an angle ∠α = 60 °.

Answer: the angle between the rope and the road is ∠α = 60 °.