Calculate Forces on Elevator: Tension, Mass & Velocity

In summary, when the elevator is at rest, the forces acting on it are the force of gravity, which is 29400N downwards, and the tension of the cable, which is 29400N upwards. When the elevator is ascending at a constant speed of 3.0 m/s, the forces are the same as when it is at rest. However, when it is ascending at an acceleration of 3.0 m/s^2, the tension of the cable increases to 20400N upwards and the force of gravity remains the same at 29400N downwards.
  • #1
pinkyjoshi65
260
0
A stationary elevator and its contents have a combined mass of 3000Kg. The elevator is suspended by a single cable. (Assume three significant digits.)
Draw a free-body diagram of the elevator and calculate the values of all the forces that are acting on it when at rest.
If the elevator is ascending at a speed of 3.0 m/s, what are the values of the forces acting at this point?
If the elevator is descending at 3.0 m/s2, what are the values of all the forces acting at this point?

For a i did---F_g=mg = 3000*9.8=29400N (Down)
F_g=〖-F〗_T
F_T=29400 N (Up)

For c i did---Net Force downwards=mg-T
downward acceleration= Net force/m= (mg-T)/m
a = g-T/m
T= (g-a)m
= (9.8-3)3000= 20400N(Up)
Net Force acting upwards= mg= 3000*9.8= 29400N(Down)

how to do part b?what equation should i use?
 
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  • #2
While the elevator is ascending, it's acceleration (i'm assuming) is constant, which means that the force is not changing. F=ma
For part b, just substitute in -3.0m/s^2 for the a, and you have your F
 
  • #3
so tht means tension will b 9000N (up) and F_g will me 29400N (down)? also is the rest of the solution (including direction) right?
 

FAQ: Calculate Forces on Elevator: Tension, Mass & Velocity

1. What is the formula for calculating the tension on an elevator?

The formula for calculating the tension on an elevator is T = mg + ma, where T is the tension, m is the mass of the elevator, g is the acceleration due to gravity, and a is the acceleration of the elevator.

2. How do you calculate the mass of an elevator?

The mass of an elevator can be calculated by dividing the force of gravity acting on the elevator by the acceleration due to gravity. This can be represented as m = F/g, where m is the mass, F is the force of gravity, and g is the acceleration due to gravity.

3. What is the relationship between the velocity and the tension on an elevator?

The relationship between the velocity and the tension on an elevator is directly proportional. This means that as the velocity of the elevator increases, the tension also increases. This is because a higher velocity requires a greater force to keep the elevator moving.

4. How does the mass of an elevator affect the tension?

The mass of an elevator directly affects the tension. As the mass of the elevator increases, the tension also increases. This is because a heavier elevator requires a greater force to lift it, which results in a higher tension on the elevator's cables.

5. What are the units used to measure tension, mass, and velocity in the context of calculating forces on an elevator?

Tension is typically measured in Newtons (N), mass is measured in kilograms (kg), and velocity is measured in meters per second (m/s) in the context of calculating forces on an elevator.

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