Question

The safety mechanism for an elevator involves a suspension spring at the bottom of the elevator shaft and a safety clamp which applies a constant 17000N frictional force to the elevator. The spring should have a spring constant so that it is able to stop the elevator over a compression distance 2.00m

If the 2000kg elevator is falling at 4m/s when it first comes into contact with the spring what should the force constant of the spring be?

i am not sure if i should consider the Work with regards to gravity or just use energy from kinetic energy to solve.

Answer 1

I think looking at energies is wise. If you take the zero of potential energy to be at the bottom of the motion when the lift falls another 2 m and ends up instantaneously stationary, then:
hitting the spring, energy is kinetic (you have m and v) + potential (where h = 2.0 m).
When lift is stopped, all the lift's energy has gone in two places:
(i) lost to frictional force, 1700 N
(ii) potential energy of compressed SPRING. (Note: potential energy of LIFT is zero, by definition.)
So that's your energy conversion, so your energy conservation equation could be:
E_before = Fric*d + 0.5 k d^2
where:
E_before is kinetic plus potential energies of lift right before it hits the spring;
Fric = Frictional Force = 1700;
d = h = 2.00m;
1/2 k x^2 is the potential energy of a compressed spring: in this case, x = d, when lift finally stops.
Thus you can solve for k, the stiffness.
Really, you're solving for THE MINIMUM k, i.e. the loosest spring, that will JUST stop the lift in 2.0m. (A higher k would stop the lift sooner.)

Answer 2

"If you take the zero of potential energy to be at the bottom of the motion " then it's conventient, I think, but you can take the zero to be anywhere - as long as you don't change your mind during the calculations.

Answer 3

Thanks a lot! I finished the problem after a while. I used:

Energy of the spring + the work of the safety clamp = both the Ep and Ek of the lift.
So:

(1/2kx^2) + (fd) = (mgh) + (1/2mv^2)

Then:

(1/2*k*2^2) + (17000*2) = (2000*9.8*2) + (1/2*2000*4^2)

(2*k) + (34Kj) = (39.2Kj) + (16Kj)

rearrange for k:

k = (39.2 + 16 - 34)/2
k = 10600 N/m

Thanks again for the fast reply!!