# Firefighter sliding down pole onto spring

## Homework Statement

A 80.5 kg firefighter slides down a pole while a constant frictional force of 300 N retards her motion. A horizontal 20.0 kg platform is supported by a spring at the bottom of the pole to cushion the fall. The firefighter starts from rest 3.25 m above the platform, and the spring constant is 4000 N/m.

(a) Find the firefighter's speed just before she collides with the platform.

(b) Find the maximum distance the spring is compressed. (Assume the frictional force acts during the entire motion, and the spring is not compressed before the collision.)

U=mgh
K=1/2mv^2
Wspr=1/2kx^2

## The Attempt at a Solution

I easily found (a), the answer is 6.28 m/s. I cannot understand why (b) isn't right, though. I found the speed of the combined platform and firefighter after collision (5.03 m/s) through conservation of momentum. However, I try to plug this into another conservation of energy equation and it just doesn't work.

## Answers and Replies

gneill
Mentor
I easily found (a), the answer is 6.28 m/s. I cannot understand why (b) isn't right, though. I found the speed of the combined platform and firefighter after collision (5.03 m/s) through conservation of momentum. However, I try to plug this into another conservation of energy equation and it just doesn't work.

We're not psychic, we can't find errors if you don't show us precisely what you've done. Please show your your work in detail.

We're not psychic, we can't find errors if you don't show us precisely what you've done. Please show your your work in detail.
Haha, sorry, trying to study for a midterm and so I just quickly wrote this post before moving to the next problem.

My answer to part (a) is correct, and the velocity right before impact is 6.28 m/s. I applied conservation of momentum to find the combined velocities.

m1v1 + (0) = (m1v)f + (m2v)f [f = final, the velocities after are exactly the same because they "stick"]
m1v1/(m1+m2) = v = 5.03 m/s

Then I applied conservation of mechanical energy, because there are no non-conservative forces.
KEi + PEi = KEf + PEf
There is no initial potential energy, and there is no final kinetic energy.
KEi = PEf
(1/2)mv^2 = (1/2)kx^2
From this I get x = .7 something, but the answer is 0.987 m.

Why is this wrong? I'm getting the feeling it's the spring force part.

gneill
Mentor
I don't see where you've taken into account the friction that's still acting, nor the change in gravitational potential energy as the mass descends while the spring compresses.

Biker
I don't see where you've taken into account the friction that's still acting, nor the change in gravitational potential energy as the mass descends while the spring compresses.
Oh, I'm an idiot. I forgot gravity, and in addition I misread the problem. I thought that it was saying the friction didn't apply at all for part B. Whoops.