two people carry a heavy electric motor by placing it on a light board 2m long.one person lifts at one end with a force of 700N, and the other lifts the opposite end with a force of 400N.Calculate the weight of the motor and determine where its center of Gravity is Located
weight = 700 + 400 = 1,100
x is distance from the strong person
1100 x = 400(2)
x = 8/11 meters from the person lifting with 700 N
To calculate the weight of the motor, we need to use the principle of moments. The principle of moments states that for an object in equilibrium, the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about the same point.
Let's assume that the center of gravity (CG) of the motor is located at a distance of 'x' meters from the person exerting the 700N force.
Now, the force of 700N applied by the first person creates an anticlockwise moment (torque) about the CG, while the force of 400N applied by the second person creates a clockwise moment (torque) about the CG.
The total anticlockwise moment is given by: 700N * (2m - x)
The total clockwise moment is given by: 400N * x
According to the principle of moments, these two moments should be equal when the system is in equilibrium. Therefore, we can set up the equation:
700N * (2m - x) = 400N * x
Simplifying the equation:
1400N - 700N * x = 400N * x
Combining like terms:
700N = 1100N * x
Now, we can solve for 'x':
x = 700N / 1100N
x ≈ 0.6364 meters
So, the CG of the motor is approximately 0.6364 meters from the person exerting the 700N force.
To calculate the weight of the motor, we can use the formula:
Weight = Force * Distance
The weight of the motor is the sum of the forces applied by both people:
Weight = 700N + 400N
Weight = 1100N
Therefore, the weight of the motor is 1100 Newtons.