Question

A 2,000-kg elevator is being accelerated upward at a rate of 3.0 m/s2. what is the tension in the cable?

O 25,600 N
O 20,000 N
O 23,100 N
O none of the above
O 13,900 N

Answer 1

The tension in a 2,000-kg elevator cable when accelerating upward at 3.0 m/s2 can be found using Newton's second law. The tension is calculated by adding the product of the mass of the elevator and the acceleration due to gravity with the product of the mass and the additional acceleration. The tension in the cable is 25,620 N.

Step-by-step explanation:

To calculate the tension in the cable of an elevator, we use Newton's second law, which states that Force equals mass times acceleration (F = ma). For an elevator, the total force exerted by the cable is not just to overcome gravity but also to provide the additional force for the upward acceleration. Therefore, the formula to calculate tension (T) in the elevator cable is:

T = m(g + a)

where:

• T is the tension in the cable,
  
• m is the mass of the elevator (2,000 kg),
  
• g is the acceleration due to gravity (9.81 m/s2),
  
• a is the acceleration of the elevator (3.0 m/s2).
  

Plugging in the numbers:

T = 2000 kg * (9.81 m/s2 + 3.0 m/s2)

T = 2000 kg * 12.81 m/s2

T = 25,620 N

Therefore, the tension in the cable is 25,620 N.