Two people carry a heavy electric motor by placing it on a light board 2.00 m long. One person lifts at one end with a force of 400 N, and the other lifts the opposite end with a force of 600 N. What is the weight of the motor, and where along the board is its center of gravity located?

검증된 단계별 안내

Understand that the board is in static equilibrium, meaning the sum of forces and the sum of torques (moments) around any point must be zero.

Calculate the total weight of the motor by summing the forces exerted by the two people: 400 N + 600 N. This is because the upward forces must balance the downward force of the motor's weight.

Choose a pivot point to calculate the torques. A convenient choice is one end of the board, say where the 400 N force is applied, to simplify calculations.

Set up the torque equation around the chosen pivot point. The torque due to the 600 N force is 600 N multiplied by the full length of the board (2.00 m). The torque due to the motor's weight is its weight (W) multiplied by the distance (d) from the pivot to the center of gravity.

Solve the torque equation for the distance (d) to find the center of gravity: 600 N * 2.00 m = W * d. Use the previously calculated weight of the motor to find d.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Equilibrium of Forces

In physics, equilibrium refers to a state where all forces acting on an object are balanced, resulting in no net force and no acceleration. For the motor to be in equilibrium on the board, the sum of the upward forces (400 N and 600 N) must equal the weight of the motor. This ensures that the motor remains stationary and does not move vertically.

Center of Gravity

The center of gravity of an object is the point where its entire weight is considered to be concentrated. It is crucial for determining how the weight is distributed along the board. In this problem, the center of gravity can be found by setting the torques about any point to zero, ensuring rotational equilibrium, and solving for the position where the torques due to the lifting forces balance.

Torque and Rotational Equilibrium

Torque is the rotational equivalent of force, calculated as the product of force and the perpendicular distance from the pivot point. For rotational equilibrium, the sum of the torques around any point must be zero. In this scenario, calculating torques about one end of the board helps determine the position of the motor's center of gravity by ensuring the clockwise and counterclockwise torques balance.