Velocity problem (only distances are given)?

[driftk]

I've been trying a lot of methods but none of them get me the right answer. Can anyone help?

The brothers of Iota Eta Pi fraternity build a platform, supported at all four corners by vertical springs, in the basement of their frat house. A brave fraternity brother wearing a football helmet stands in the middle of the platform; his weight compresses the springs by a distance of 0.18 m . Then four of his fraternity brothers, pushing down at the corners of the platform, compress the springs another distance 0.53 m until the top of the brave brother's helmet is a distance 0.90 m below the basement ceiling. They then simultaneously release the platform. You can ignore the masses of the springs and platform.

1. When the dust clears, the fraternity asks you to calculate their fraternity brother's speed just before his helmet hit the flimsy ceiling?

 

[LowlyPion]

Welcome to PF.

Well they give you a way to get k in terms of the pledge's dumb weight.

Then they give you total displacement that get's stored in the spring.

From release to the unloaded point then you can figure his kinetic energy can't you? (Don't forget his gravitational potential increase until the platform releases him.)

His kinetic energy happily gives you Vo and then g acts over the short remaining distance until impact and his brain is no longer any good for doing physics problems. So I guess it's Toga Party time for him.

 

[driftk]

I still can't figure it out.

 

[turin]

You can ignore the masses of the springs and platform.

I doubt that.

 

[HallsofIvy]

If we let the mass of the one person be m, then F= mg= k(0.18) so k= mg/0.18. Calculate the stored energy when the spring is compressed a total of 0.18+ 0.54= 0.72 m. This will be a function of "m".

Then calculate the person's gravitational potential energy when relative to his initial position when he has moved up 0.9 meter. That will also depend on "m". That plus his kinetic energy must equal the stored energy of the spring. All the "m"s will cancel and you will have an equation to solve for v.

 

[LowlyPion]

Focus for a moment on the pledge's mass and the distance he depresses the platform.

m*g = -k*x

That means that -k = m*g/x = m*g/.18

Now write an equation that reflects the Spring Potential Energy when it's fully depressed by his mates, less whatever gain in gravitational potential energy to the ceiling .9 m away when he's released and that should give you his Kinetic Energy at impact.