Question

A lift of mass 400kg is hung by a wire calculate the tension in the wire when the lift is (a) at rest (b) moving upward with a constant velocity of 2.0m/s (c) moving upward with an acceleration of 2.0m/s square

Answer 1

Weight of the lift = mg = (400)(10) = 4000 newton

Now,
When, the lift is at rest
The only forces acting in the vertical direction resulting in equillibrium are weight in the downwards direction and tension in the upward direction
So,
Tension = Weight
Therefore,
Tension = 4000 Newton
Now,
(b) Again there is no acceleration in the vertical direction because, the lift is just moving at constant velocity.
Therefore, again Tension = Weight = 4000 N
(c)
Here,
Because, the net acceleration is upwards therefore, Tension has to be the greater force than weight for net upward force.
So,
Tension = Weight + Mass*Net Acceleration
Tension = (4000) + (400)(2) = 4800 Newton

Hope this helps you !

Answer 2

Answer:

When the lift is at rest,

T = mg = 400 * 10 = 4000N

When it is moving upward with a constant velocity,

T = mg = 4000N

When it is moving upward with an acceleration of 2m/s²,

T = mg + ma = 4000 + 400*2 = 4800N