Question

A football coach sits on a sled while two of his players build their strength by dragging the sled across the field with ropes. the friction force on the sled is 1140 n and the angle between the two ropes is 25.0 ∘. how hard must each player pull to drag the coach at a steady 2.30 m/s ? assume both players pull with the same force.

Answer 1

To drag the coach at a constant speed, each player needs to apply a force of approximately 583.89 N to counteract the friction force of 1140 N on the sled, calculated using trigonometry and Newton's Second Law of Motion.

Step-by-step explanation:

The key concept in this question involves Newton's Second Law of Motion and the dynamics of forces acting at angles. The friction force on the sled is given as 1140 N, and since the football coach is moving at a steady speed, we can infer that the net force is zero, implying that the pulling forces balance out the friction force.

To find the force each player must exert, we first determine the total force needed to overcome friction. Since the rope's angle is 25.0° (half the angle between the ropes), the total horizontal force exerted by the two players (F-total) needs to match the friction force. Using trigonometry, the force each player exerts (F-player) can be expressed as:

F-player = F-total / (2 × cos(25.0°/2)) = 1140 N / (2 × cos(12.5°))

So, we calculate the force:

F-player = 1140 N / (2 × cos(12.5°)) = 1140 N / (2 × 0.9763) = 1140 N / 1.9526 = 583.89 N

Therefore, each player needs to exert approximately 583.89 N to drag the coach at a steady speed of 2.30 m/s.

Answer 2

Refer to the diagram below, which provides a plan view of the problem

Because each player applies the same force, F, the angle between the force and the direction of motion is (1/2)*25° = 12.5°.

Because the sled moves with constant velocity, the sled is in dynamic equilibrium, and
2F cos(12.5°) = 1140 N
1.9526 F = 1140
F = 583.84 N

Answer: 583.8 N (nearest tenth)