Solving Simple Harmonic Motion Problems| Physics HW

[suspenc3]

Homework Statement

http://www.physics.umd.edu/courses/Phys122/Noyes/HW/hw1.pdf (pg 3)

Homework Equations

Im guessing that E = K + U has something to do with it

The Attempt at a Solution

Not really sure where to start..I tried a few approaches but none of them got me anywheres E = 1/2mv^2 + 1/2 kx^2..but I am missing too many things..

Any help?

 

[Ja4Coltrane]

when the bullet colides, it sticks. This means that energy is not conserved but something else is.

 

[Ja4Coltrane]

by the way, the fact that the clay sticks and that the collision is therefore perfectly inelastic is one of those "assumptions"

 

[suspenc3]

conservation of linear momentum?

 

[Ja4Coltrane]

yes. now you can use that in combination with energy.

 

[suspenc3]

so I have $$\frac{mv +Mv_2}{m+M} = v_f$$ where $$Mv_2$$ is going to be 0 since it is at rest?

and $$E=1/2mv^2 + 1/2kx^2$$

Do i let m = m+M? and will 1/2kx^2 be 0 since the block can be considered to be at point x=0?...set it to zero and solve for v?

 

[Ja4Coltrane]

you actually don't need to use energy until you are ready to find the amplitude. You already have enough information to find the velocity.

 

[suspenc3]

So imediately after the collision, the spring has no effect on the velocity?

 

[Ja4Coltrane]

that's correct. two ways to understand that
1) imediately after colision, spring is not compressed and therefore applies no force.

2) even if it were compressed, a force causes an acceleration which only changes velocity of some period of time.

 

[suspenc3]

Solved it..Thanks for the help

 

[Ja4Coltrane]

good job, np