- #1
Leomar
- 3
- 0
Hi, hope you can help me with finding out what I am doing wrong on this problem.
It goes as follows:
A massless, vertical spring of force konstant k is attached at the bottom to a platform of mass mp, and at the top to a massless cup.
The platform rests on a scale. A ball of mass mb is dropped into the cup fro a negligible height. What is the reading on the scale a) when the ball momentarily comes to a rest with the spring compressed.
And b) same as a), but with the ball dropped from a height h.
For problem a), I set that the ball would have potentional energy=0 when at rest, and thus that the work done by the spring must equal mbgx.
1/2kx^2=mbgx
=>
x=2mbg/k
Using Hookes law, the force exerted by the spring on the ball is 2mbg.
So the spring exerts the same force on the platform, and the scale should show F=mpg+2mbg
Which according to the solutionsguide is correct. (Though I might have made a mistake here anyway)
For problem b), I tried using the same method, setting that
1/2kx^2=mbg(x´+h) (Where x`=2mbg/k, from problem a))
=>
x=(2mbg(2mbg/k+h)/k)^(1/2)
rearranging
x=2mbg/k(1+hk/2mbg)^(1/2)
Which gives the solution
F=mpg+2mbg(1+hk/2mbg)^(1/2)
This is where the solutionsguide is disagreeing with me.
A hint or two would be very much appreciated.
It goes as follows:
A massless, vertical spring of force konstant k is attached at the bottom to a platform of mass mp, and at the top to a massless cup.
The platform rests on a scale. A ball of mass mb is dropped into the cup fro a negligible height. What is the reading on the scale a) when the ball momentarily comes to a rest with the spring compressed.
And b) same as a), but with the ball dropped from a height h.
For problem a), I set that the ball would have potentional energy=0 when at rest, and thus that the work done by the spring must equal mbgx.
1/2kx^2=mbgx
=>
x=2mbg/k
Using Hookes law, the force exerted by the spring on the ball is 2mbg.
So the spring exerts the same force on the platform, and the scale should show F=mpg+2mbg
Which according to the solutionsguide is correct. (Though I might have made a mistake here anyway)
For problem b), I tried using the same method, setting that
1/2kx^2=mbg(x´+h) (Where x`=2mbg/k, from problem a))
=>
x=(2mbg(2mbg/k+h)/k)^(1/2)
rearranging
x=2mbg/k(1+hk/2mbg)^(1/2)
Which gives the solution
F=mpg+2mbg(1+hk/2mbg)^(1/2)
This is where the solutionsguide is disagreeing with me.
A hint or two would be very much appreciated.