My question states that an elevator is falling on springs that are supposed to absorb the residual energy if the brakes fail to stop the elevator. They are asking how many springs are needed so that the elevator does not compress the springs by more than 0.2m?
mass of elevator is 4000 kg
the distance the elevator falls is 15 m
the sum of frictional forces of the breaks is 5000N
and the spring constant of each spring is 5.0x10^6 N/m with a maximum compression of 0.3 m
3. The Attempt at a Solution [/B]
I found the work done by the frictional forces by multiplying the frictional forces by the distance, and subtracted that by the potential energy of the elevator so obtain the total energy of the elevator.
This gave me:
Wf=(Ff)(d)=(-5000N)(15m)= -75,000 J
Ep =mgh=(4000kg)(9.8N/m)(15m)= 588,000 J
Etotal= 513,000 J
I then found the elastic potential energy of each spring by using the compression of 0.2 m
Ep=(0.5)(5.0x10^6N/m)(0.2m^2)= 100,000 J
To find how many springs I need, would I just have to divide the total energy of the elevator by the potential energy of the springs? I'm not sure what the next step should be