Elevator Tension With Upward Acceleration

In summary, the tension in the steel cable supporting an elevator weighing 10 000N when it is accelerated upward at 3.0 m/s2 is 13.1 kN. This is determined by using the equation F=ma and taking into account the opposing forces of gravity and tension. The correct answer is D) 13.1 kN.
  • #1
SigFig
8
0

Homework Statement



An elevator weighing 10 000N is supported by a steel cable. Determine the tension in the cable when the elevator is accelerated upward at 3.0 m/s2


A) 7.0kN
B) 10.0 kN
C)11.6 kN
D) 13.1 kN
E) 40.0 kN

Homework Equations



F=ma W=mg (g=9.8m/s^2)

The Attempt at a Solution


W=mg
10 000=m(9.8)
m=1020
 
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  • #2
The net force (i.e. the total of all the forces) is what causes acceleration in the equation F=ma. So draw a diagram and label the forces acting on it. (Gravity and Tension) so now use the F=ma equation and plug everything in and off you go.
 
  • #3
So it would be
W=mg
10 000=m(9.8)
m=1020

F=ma
F=1020(3)
F=3060

3060+10 000 = F
F= 13.1 kN?
 
  • #4
Remember that the force of gravity is opposite the force of tension. One's up and one's down.
 
  • #5
So the 3060 would be subtracted from the elevators weight because it's accelerating upwards (against gravity) making it 7000?
 
  • #6
Oh my goodness, I'm sorry, you were right in the first place, I read it wrong. Good work! Sorry to confuse.
 

1. What is Elevator Tension With Upward Acceleration?

Elevator tension with upward acceleration refers to the force applied to an elevator cable as it moves upwards. This tension is caused by the acceleration of the elevator as it moves against the force of gravity.

2. How does Elevator Tension With Upward Acceleration affect elevator safety?

Elevator tension with upward acceleration is an important factor in ensuring elevator safety. If the tension is too low, the elevator may not be able to move properly, while if the tension is too high, it can cause damage to the elevator system. Proper tension is necessary for the safe and efficient operation of elevators.

3. What factors can affect Elevator Tension With Upward Acceleration?

There are several factors that can affect elevator tension with upward acceleration, including the weight of the elevator, the number of passengers, and the speed of the elevator. Changes in any of these factors can cause fluctuations in the tension of the elevator cable.

4. How is Elevator Tension With Upward Acceleration calculated?

Elevator tension with upward acceleration is calculated using the formula T = m*a, where T is the tension, m is the mass of the elevator and its passengers, and a is the acceleration. The force of gravity is also taken into account in this calculation.

5. What are some safety measures that can be taken to ensure proper Elevator Tension With Upward Acceleration?

To ensure proper elevator tension with upward acceleration, regular maintenance and inspections should be conducted to ensure that the elevator is functioning properly. Additionally, weight limits should be observed and passengers should be evenly distributed in the elevator to prevent excessive tension on one side of the cable.

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