Firefighter sliding down pole onto spring

• doneky
In summary: 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.

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.

doneky said:
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.

gneill said:
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.

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
gneill said:
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.

1. What is the purpose of a firefighter sliding down a pole onto a spring?

The purpose of this maneuver is to quickly and safely transport firefighters from their living quarters on the upper floors of a fire station to the ground level, where they can quickly respond to emergency calls.

2. How does the pole sliding mechanism work?

The pole is typically made of metal and is mounted vertically between two floors. Firefighters hold onto the pole with their hands and use friction to control their descent. The spring at the bottom of the pole helps to cushion their landing and reduce the impact on their bodies.

3. Is sliding down a pole onto a spring safe for firefighters?

Yes, when done correctly, this maneuver is a safe and efficient way for firefighters to quickly respond to emergency calls. Fire stations have strict safety protocols in place and provide training to ensure that firefighters know how to properly slide down the pole.

4. How do firefighters prevent injuries while sliding down the pole?

Firefighters are trained to keep their arms and legs close to the pole while sliding down to minimize the risk of injury. They also wear specialized gloves to protect their hands from friction burns and maintain a controlled descent to prevent any sudden impacts at the bottom.

5. Can firefighters slide down the pole in all types of emergency situations?

In most cases, firefighters will use the pole sliding method to quickly respond to emergency calls. However, in situations where they may be carrying heavy equipment or dealing with physical injuries, they may use the stairs instead to safely reach the ground level.