How to Calculate Spring Compression and Body's Launch Height from Falling Mass?

[DEckrich7]

Homework Statement

A falling body has a mass of 15 kg over a height of 135 m onto a spring. The spring has a spring constant of 1.95*10⁵N/m.
a) How far is the spring compressed?
b) At the point where the body's impact on the spring scale the greatest, what is the reading?
c) Assuming all of the elastic potential energy in the compressed spring scale is converted into kinetic energy, what is the body's initial velocity?
d) How high will the body launch?

Homework Equations

F=ma, F=-kx, U_e= .5*k*x², K=.5*m*v², Weight=mg, U_G=mgy

The Attempt at a Solution

Since we're in the metric system, I'm using the gravitational constant of 9.8 m/s². So, with F=ma, I'll do F=15kg*9.8m/s² to give me a force of the body on the scale of 147 N. I'll substitute that value into F=-kx along with the spring constant and solve for x. 147 N/1.95*10⁵N/m yields a displacement of about 7.54*10^-4m. This seems really small however... For letter b, I'm assuming I'll multiply 15kg and 9.8m/s² to find the body's weight in Newtons. For c) and d), I'm just stuck.
Thank you all for your time :).

 

[tiny-tim]

Welcome to PF!

Hi DEckrich7! Welcome to PF!

A falling body has a mass of 15 kg over a height of 135 m onto a spring. The spring has a spring constant of 1.95*10⁵N/m.
a) How far is the spring compressed?
b) At the point where the body's impact on the spring scale the greatest, what is the reading?
c) Assuming all of the elastic potential energy in the compressed spring scale is converted into kinetic energy, what is the body's initial velocity?
d) How high will the body launch?
…
So, with F=ma, I'll do F=15kg*9.8m/s² to give me a force of the body on the scale of 147 N. I'll substitute that value into F=-kx along with the spring constant and solve for x.…

Nooo, that won't work at all

Start again, using conservation of energy …

what do you get? ​

 

[DEckrich7]

Hi DEckrich7! Welcome to PF!



Nooo, that won't work at all

Start again, using conservation of energy …

what do you get? ​

Thank you very much, I am so happy to join the community!
We haven't learned much about the conversation of energy in my class; a similar question to this one was my physics quiz, so we should know how to do this one however (so I should have enough knowledge to solve it!). What I do know however, is that initial Kinetic and potential energy, are equal to the final kinetic and potential energy. I also know that E_total= K+PE+Q. Would that mean the body his bouncing off of the spring with the same velocity it is hitting it with?
Thank you very much, tiny-tim :)

 

[tiny-tim]

Hi DEckrich7!

What I do know however, is that initial Kinetic and potential energy, are equal to the final kinetic and potential energy. I also know that E_total= K+PE+Q. Would that mean the body his bouncing off of the spring with the same velocity it is hitting it with?

That's right, KE + PE = constant.

In this case, the PE is both gravitational PE (=mgh) and spring PE (= 1/2 kx²)

(btw, what's Q? if it's heat, ignore it in problems like this)

So, for a), KE_initial and KE_final are both 0, so that should give you an equation in x …

what do you get? ​

 

[DEckrich7]

Thank you very much for your help tiny-tim, I'll work on the problem, and yes, Q is heat loss.