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

Conservation of Energy bullet of mass

  • #1

Homework Statement


A bullet of mass m is fired with a velocity of 50m/s at an angle x. At the top of its trajectory it hits a bob of mass 3m hanging by a string 3.3 m long and gets imbedded in it. The string rotates by an angle of 120 degrees.

Find x and the coordinates of the bob wrt the projectile.


The Attempt at a Solution



The bullet hits the bob with velocite 50 cosx. The kinetic energy of the bullet gets converted into the gravitational potential energy of the bob and the bullet.

[tex]0.5m(50cosx)^2= 4mg*3.3*(1+sin30)[/tex]
cosx=0.4

The answer, however, is 30 degrees. I used cosx=0.4 to solve the second part, but needless to say, that answer didnt match either.

What did I do wrong? Or is the given answer incorrect?
 

Answers and Replies

  • #2
1,860
0
I have no idea what "bob wrt the projectile" means, and so I am not really sure what you did wrong or what you were trying to solve. However, in your energy equation it looks like you are doing
[tex]E_i = E_f[/tex]
[tex]K_i + U_i = K_f + U_f[/tex]
[tex]K_i = U_f[/tex]

I agree with the initial kinetic, but it looks to me like you calculated the height the wrong for your potential.
 
  • #3
Doc Al
Mentor
44,892
1,144
The bullet hits the bob with velocite 50 cosx.
Good.
The kinetic energy of the bullet gets converted into the gravitational potential energy of the bob and the bullet.
Careful! Is energy conserved during the collision of bullet with bob?
 
  • #4
Isnt the energy conserved? And bob wrt projectile means that the origin is at the point where the projectile was launched. We have to find the position of the bob w.r.t that origin.
 
  • #5
1,357
0
  • #6
Doc Al
Mentor
44,892
1,144
Isnt the energy conserved?
As e(ho0n3 has stated, during the collision only momentum is conserved. But after the collision, the mechanical energy of the "bullet+bob" system is conserved. Both parts are needed to solve this problem.
 

Related Threads on Conservation of Energy bullet of mass

  • Last Post
Replies
2
Views
3K
Replies
9
Views
5K
Replies
2
Views
2K
Replies
10
Views
3K
Replies
7
Views
14K
Replies
12
Views
2K
Replies
3
Views
3K
Replies
5
Views
5K
Top