Question

An elevator is accelerating upward at a rate 6 ft when a bolt from its ceiling falls to the floor of the lift (Distance= 9.5 feet). The time (in seconds) taken by the falling bolt to hit the floor is _____

A)1/√2
B)3/√7
C)1/√3
D)1/2

Answer 1

The tension in the cable supporting the elevator during acceleration is 18820 N, and during constant velocity, it is 16660 N.

Step-by-step explanation:

When an elevator is accelerating upward, the tension in the cable supporting the elevator is greater than its weight. This is because there is an additional force acting on the elevator due to its acceleration. To calculate the tension, we can use Newton's second law, which states that the net force on an object is equal to its mass multiplied by its acceleration. In this case, the net force is equal to the tension minus the weight of the elevator, and the mass is the mass of the elevator. So, we have:

Tension - Weight = Mass x Acceleration

By rearranging the equation to solve for tension, we get:

Tension = Weight + Mass x Acceleration

Using the given values, the weight of the elevator can be calculated using the formula:

Weight = Mass x Acceleration due to gravity

Plugging in the values, we find:

Weight = 1700 kg x 9.8 m/s² = 16660 N

So, the tension in the cable during acceleration is:

Tension = 16660 N + 1700 kg x 1.20 m/s² = 18820 N

During constant velocity, the elevator is not accelerating, so the net force is zero. This means that the tension in the cable is equal to the weight of the elevator:

Tension = Weight = 16660 N