A 1100-kg elevator is lifted at a constant speed of 1.5 m/s through a height of 20 m.
a)How much work is done by the tension in the elevator cable?How much work is done by gravity?
b)How much work is done by gravity?
answered above.
To determine the work done by the tension in the elevator cable and the work done by gravity, we can use the formulas:
Work = Force x Distance
a) Work done by the tension in the elevator cable:
In this case, the elevator is being lifted at a constant speed, so there is no change in its kinetic energy. Therefore, the net force acting on the elevator is zero, which means the tension force in the cable should be equal to and opposite to the force due to gravity.
To calculate the work done by the tension in the elevator cable, we need to find the force exerted by the tension.
Using Newton's second law, Force = mass x acceleration, since the elevator is moving at a constant speed, the acceleration is zero, so the force due to gravity is the force exerted by the tension. F = m x g, where m is the mass of the elevator (1100 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
The work done by the tension in the elevator cable is given by:
Work = Force x Distance = (m x g) x Distance
Substituting the given values:
Work = (1100 kg x 9.8 m/s^2) x 20 m
b) Work done by gravity:
The work done by gravity can be calculated using the formula:
Work = Force x Distance
In this case, the force due to gravity is acting in the opposite direction to the displacement of the elevator (lifting upward), so the angle between the force and displacement is 180 degrees. Therefore, the work done by gravity is negative.
The work done by gravity is given by:
Work = (m x g x cos(theta)) x Distance
Since cos(180 degrees) = -1, the equation becomes:
Work = - (m x g) x Distance
Substituting the given values:
Work = - (1100 kg x 9.8 m/s^2) x 20 m
By substituting the values into the above equations, you can calculate the values for the work done by the tension in the elevator cable and the work done by gravity.