Two people are carrying a uniform wooden board that is 3.00 m long and weighs 160 N. If one person applies an upward force equal to 60 N at one end, at what point does the other person lift? Begin with a free-body diagram of the board.

Verified step by step guidance

1. Begin by drawing a free-body diagram of the board. Represent the board as a horizontal line. Mark the center of the board, which is the point where the weight of the board (160 N) acts downward. This point is at the midpoint of the board, 1.50 m from either end.
2. Identify the forces acting on the board. There are three forces: the weight of the board (160 N) acting downward at the center, the upward force of 60 N applied by one person at one end, and the upward force applied by the other person at an unknown point along the board.
3. Apply the principle of equilibrium. For the board to be in equilibrium, the sum of the vertical forces must be zero, and the sum of the torques about any point must also be zero.
4. Choose a pivot point to calculate the torques. A convenient choice is the point where the 60 N force is applied. Calculate the torque due to the weight of the board: Torque = Force x Distance from pivot. The distance from the pivot to the center of the board is 1.50 m.
5. Set up the torque equilibrium equation: The torque due to the weight of the board (160 N) should be balanced by the torque due to the unknown force applied by the other person. Solve this equation to find the distance from the pivot to the point where the other person lifts the board.

Key Concepts

Free-Body Diagram

A free-body diagram is a graphical representation used to visualize the forces acting on an object. In this scenario, it helps identify the forces applied by the two people and the weight of the board. By representing these forces, we can better understand how they interact and determine the point where the second person must apply their force to balance the board.

Torque and Equilibrium

Torque is the rotational equivalent of force, calculated as the product of force and the distance from the pivot point. For the board to be in equilibrium, the sum of torques around any point must be zero. This principle allows us to set up an equation to find the position where the second person must apply their force to balance the board, considering the torques produced by the weight of the board and the force applied by the first person.

Center of Mass

The center of mass is the point at which the mass of an object is considered to be concentrated. For a uniform board, it is located at its midpoint. Understanding the center of mass is crucial in this problem because it helps determine the distribution of weight along the board, which affects the calculation of torques and the position where the second person should apply their force to maintain equilibrium.