Question

An elevator car has two equa masses, m, attached to the ceiling as shown. the elevator ascends with an acceleration of magnitude a.

a. what are the tensions in the two cords in terms of m, a, and g?
b. If a is increased until one cord breaks will it be the upper or lower cord? c. What are tensions if the cable attached to the top of the elevator car snaps? (Use the following as necessary: m and g.)

Answer 1

To find the tensions in the two cords attached to the ceiling of the elevator, we need to analyze the forces acting on the masses. The tension in the upper cord is greater than the tension in the lower cord. If the cable attached to the top of the elevator car snaps, the tension in the remaining cord will be equal to the weight of the masses.

Step-by-step explanation:

To find the tensions in the two cords, we need to analyze the forces acting on the masses attached to the ceiling of the elevator.

Let's denote the tensions in the upper and lower cords as T1 and T2 respectively. The gravitational force acting on each mass is mg, where m is the mass and g is the acceleration due to gravity.

When the elevator is accelerating upward, the tension in the upper cord is T1 = m(a + g) and the tension in the lower cord is T2 = mg.

If the acceleration is increased until one cord breaks, it will be the upper cord that breaks first. This is because the tension in the upper cord is greater than the tension in the lower cord.

If the cable attached to the top of the elevator car snaps, the tension in the remaining cord will be equal to the weight of the masses, T = mg.