Question

An elevator supported by a single cable descends a shaft at a constant speed. The only forces acting on the elevator are the tension in the cable and the gravity. Which one of the following statements is correct? Group of answer choices
A. The work done by the gravity is zero joules.
B. The tension force does positive work.
C. The net work done by the two forces is zero joules.
D. The work done by the tension force is zero joules.
E. The gravitational force does negative work.

Answer 1

Answer:

C. The net work done by the two forces is zero joules.

Explanation:

Work (W) is defined as the product of force F) by the distance (d)the body travels due to this force.  

W= F*d Formula ( 1)

The work is positive (W+) if the force has the same direction of movement of the object.  

The work is negative (W-) if the force has the opposite direction of the movement of the object.

The component of the force that performs work must be parallel to the displacement.  

Calculation of the forces

We apply Newton's second law:

∑F = m*a

∑F : algebraic sum of the forces in Newton (N)

m : mass in kilograms (kg)

a : acceleration in meters over second square (m/s²)

∑F = m*a  

a = 0 because the elevator moves at constant speed.

∑F=0

T-W = 0

T = W  

Calculation of work done by the forces

W₁ :  work done by the gravity= (+ W*d ) J

W₂ : work done by the tension force=( -T*d) J

Net work done by the two forces(W₁-W₂):

W₁= W₂ .because T = W  

W₁-W₂ =0