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 1000 N, the players have equal pulls, and the angle between the two ropes is 20°. How hard must each player pull to drag the coach at a steady 2.0 m/s?

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Step 1: Analyze the forces acting on the sled. The sled is being pulled by two players with equal forces (T₁ and T₂) at an angle of 20° between the ropes. The friction force opposing the motion is 1000 N. Since the sled is moving at a steady speed, the net force in the horizontal direction is zero (Newton's First Law).

Step 2: Break down the tension forces into their horizontal and vertical components. Each player's pull contributes a horizontal component (T₁cosθ and T₂cosθ) and a vertical component (T₁sinθ and T₂sinθ). Here, θ is half the angle between the ropes, which is 10° (since the total angle is 20°).

Step 3: Write the equation for the horizontal force balance. The sum of the horizontal components of the tension forces must equal the friction force: 2Tcosθ = 1000 N. Solve for T, the tension in each rope.

Step 4: Consider the vertical components of the tension forces. These components do not affect the horizontal motion but may contribute to lifting the sled slightly, reducing the normal force and friction. However, since the problem specifies steady motion, we focus only on the horizontal forces.

Step 5: Substitute θ = 10° into the equation from Step 3 and solve for T. Use trigonometric values for cosθ to find the magnitude of the pull required by each player.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Friction Force

Friction force is the resistance that one surface or object encounters when moving over another. In this scenario, the friction force acting on the sled is 1000 N, which must be overcome by the players' pulling forces to maintain a constant velocity. The frictional force depends on the nature of the surfaces in contact and the normal force acting between them.

Tension in Ropes

Tension is the force transmitted through a rope or string when it is pulled tight by forces acting from opposite ends. In this problem, two players are pulling the sled with equal tension forces (T1 and T2) at an angle of 20 degrees between them. The resultant tension must be calculated to determine how hard each player must pull to overcome the friction and maintain a steady speed.

Equilibrium of Forces

An object is in equilibrium when the net force acting on it is zero, meaning it does not accelerate. In this case, the sled is being pulled at a constant speed of 2.0 m/s, indicating that the total horizontal forces (the horizontal components of T1 and T2) must equal the friction force. This principle allows us to set up equations to solve for the tension in the ropes.

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