• Support PF! Buy your school textbooks, materials and every day products Here!

Spring System

  • Thread starter 1831
  • Start date
13
0
[SOLVED] Spring System

1. Homework Statement

You have been asked to design a "ballistic spring system" to measure the speed of bullets. A spring whose spring constant is k is suspended from the ceiling. A block of mass M hangs from the spring. A bullet of mass m is fired vertically upward into the bottom of the block. The spring's maximum compression d is measured.

Find an expression for the bullet's speed.
Express your answer in terms of the variables m, M, k, d, and constant g.


2. Homework Equations

Ki + Ug + Usp = Kf + Ug + Usp

3. The Attempt at a Solution

I used conservation of momentum to find the final velocity of the bullet+block

(m+M)vf=mvi + Mvi

so...

vf=(m/m+M)*vB

where vB is the initial speed of the bullet.

Next, I used:
Ki + Ug + Usp = Kf + Ug + Usp

(1/2)mvi^2 + (1/2)kd^2 + Mgd = (1/2)mvf^2 + (1/2)kd^2 + Mgd
0 + (1/2)kd^2 + 0 = (1/2)(m+M)[(m+M)^2*vB^2] + 0 + Mgd

I found the answer to be:

((kd^2 - Mgd)(m+M))/m^2 = Vb

but this was not correct...please help me.
 

Answers and Replies

13
0
Nevermind, I got it right...finally
 
37
0
Re: [SOLVED] Spring System

wait can you show how you did this because I have the same problem thanks!
 

Related Threads for: Spring System

  • Last Post
Replies
4
Views
8K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
1
Views
8K
  • Last Post
Replies
11
Views
3K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
3
Views
2K
Top