Question

You are standing in an elevator with a 20.0 kg child on your shoulders. The elevator is traveling upward at a velocity of 2.00 m/s and an acceleration of -1.00 m/s2 . Your mass is 60.0 kg; the elevator mass is 1200.0 kg.

1) What is the tension in the cable that supports the elevator?

For this question, I found that the tension was smaller than the downward force. How can this be possible with the elevator having an upward velocity? Shouldn't the tension be causing the elevator to be going up?

Answer 1

Remember that it is a case of uniformly retarded motion , just as the elevator is about to come to rest on approaching any upper floor of a building.

Mathematical treatment of the problem is as follows:

Answer 2

Solution: Tension in the Elevator Cable

Given:

• Mass of child ($m_c$) = 20.0 kg

• Your mass ($m_y$) = 60.0 kg

• Elevator mass ($m_e$) = 1200.0 kg

• Total mass ($M$) = $m_c+m_y+m_e=20+60+1200=1280\text{kg}$

• Upward velocity ($v$) = +2.00 m/s

• 
  

• 
  

• Acceleration ($a$) = -1.00 m/s² (negative sign indicates deceleration, i.e., slowing down while moving upward).

• 
  

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Step 1: Identify Forces

1. Total weight ($W$) acting downward:

   $$W=M\times g=1280\text{kg}\times 9.81{\text{m/s}}^2=12,556.8\text{N}$$

2. Tension ($T$) in the cable acts upward.

3. 
   

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Step 2: Apply Newton’s Second Law

The elevator is decelerating upward ($a=-1.00{\text{m/s}}^2$), so the net force is:

$$\sum F=T-W=M\times a$$$$T-12,556.8=1280\times (-1.00)$$$$T=12,556.8-1280=11,276.8\text{N}$$

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Final Answer:

The tension in the cable is 11,276.8 N.