Describe Motion of lift or an Elevator. How do we calculate tension in the cable supporting the lift/elevator?
Consider a lift (elevator or cage) carrying some mass and moving with uniform acceleration.
Let
m = Mass carried by the lift in kg,
a = Uniform acceleration of the lift in m/s2, and
R = Reaction of the lift or tension in the cable supporting the lift in newtons.
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)
When the lift is moving upwards as shown in Fig. 1.24 (a), then
R – m.g = m.a or R = m.g + m.a = m (g + a)
When the lift is moving downwards as shown in Fig. 1.24 (b), then
m.g – R = m.a or R = m.g – m.a = m (g – a)
Consider a lift (elevator or cage) carrying some mass and moving with uniform acceleration.
Let
m = Mass carried by the lift in kg,
a = Uniform acceleration of the lift in m/s2, and
R = Reaction of the lift or tension in the cable supporting the lift in newtons.
When the lift is moving upwards as shown in Fig. 1.24 (a), then
R – m.g = m.a or R = m.g + m.a = m (g + a)
When the lift is moving downwards as shown in Fig. 1.24 (b), then
m.g – R = m.a or R = m.g – m.a = m (g – a)
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