An elevator has a loading capacity of 300% of its mass and weighs 0.5tonnes. When accelerating, the elevator gains its maximum speed of 2m/s in 1.5sec and decelerates with equal parameters. So:
a) What is the tension in each of the 3 ropes when moving the fully occupied elevator up and down?
b) The steel ropes have a dimeter of 2cm and run each over a wheel of 1m radius. What percentage compression and expansion does the wire experience when being moved over the wheel?
2006-12-01 11:53:46 · 3 answers · asked by susiebondi 1 in Science & Mathematics ➔ Physics
The total weight fully loaded is the weight of the elevator plus 3x its weight in the load or 4x its weight. Its acceleration going up is 2m/s divided by 1.5sec = 1.33m/sec^2. The tension force on all three ropes while acceterating upwards is the weight + mass*a. The mass is weight/g, so the total force is total wt*(1+a/g). Going down the force is reduced by the same amount F = total wt*(1-a/g). The tension on each rope is one-third the total.
The stress in each rope is the force divided by the area, or F/πr^2. The strain (% change in length) is proportional to the stress. I'm not clear on what the action of the wheel is in this case. A diagram would help.
2006-12-01 12:28:10 · answer #1 · answered by gp4rts 7 · 0⤊ 0⤋
The % compression & expansion, known to we engineering types as strain, is 1%, or .01. In this case it is simply the rope radius divided by the wheel radius.
2006-12-01 21:59:27 · answer #2 · answered by Steve 7 · 0⤊ 0⤋
a is .5 tons i think
and b ???
2006-12-01 19:55:51 · answer #3 · answered by Anonymous · 0⤊ 0⤋