An elevator has a mass of 1000 kg. What is the tension force on its cables when it is stationary?

Question

A. What is the tension force on its cables when it is stationary?

B. What force is needed to accelerate it upward at a rate of 2m/sec/sec?

C.What force is needed to accelerate it downward at a rate of 2m/sec/sec?

Answer 1

First, consider an FBD of the elevator with positive as upward

The forces on the elevator are
gravity
-m*g
tension of the cables
T

for A
T-m*g=0
T=m*g
or
T=9.81*1000

B

for B
T-m*g=m*a
T=m*(g+a)
T=1000*(9.81+2)

C

for C, same as B
only the acceleration is negative (Downward)
T=m*(g+a)
T=m*(9.81-2)

j

Answer 2

A. What is the tension force on its cables when it is stationary?

Well F=ma so the force acting by gravity is

F=1000kg x 9.8 m/s^2 = 9800 N
So the tension in the cable is -9800 N (assuming it is empty)


B. What force is needed to accelerate it upward at a rate of 2m/sec/sec?

Gravity pulling down at 9.8 and we want to overcome and go -2 m/s (neg because we are in the oposit direction)..so we need to go 11.8

F= 1000(11.8) = 11800 N

C.What force is needed to accelerate it downward at a rate of 2m/sec/sec?

N= 10000(7.8) = 7800N...so we need tension of -7800 N to counter the 9800 N exerted by gravity

Answer 3

whilst it is table sure, the great upward rigidity is comparable to the great downward rigidity. for this reason, the downward rigidity is the load of the elevator, and the rigidity that's helping this elevator is named rigidity interior the cables. weight of the elevator = 1000 kg * 9.8 m/s^2 = 9800 N so, the rigidity interior the cables could be 9800 N. wish this clears you.