have a look at the diagram(adsbygoogle = window.adsbygoogle || []).push({});

A physical system consists of wood block B and mass M. B is at rest on frictionless horizontal table. A small vertical wall W is place near one of the ends of B. The wall is fastened to B.A spring with spring constant k is attached to the wall and is connected tp a block C. of mass m.

No friction between C and B. A bullet of mass mu [itex] \mu [/itex] is shot is shot into block C. The velocity v is parallel to the table. The spring does not bend.

Assume that the bullet is stopped in such a short time taht t is negligible. The spring mass and the wall mas are neglected

a) find the maximum compression d of the spring, in terms of v, k, M , m and [itex] \mu [/itex]

bullet goes into the block inelastically so

[tex] \mu v = (\mu + m) v_{f} [/tex]

and [tex] v_{f} = \frac{\mu v}{\mu + m} [/tex]

this vf (kinetic energy) is converted to spring energy

[tex] \frac{1}{2} (\mu + m) (\frac{\mu v}{\mu + m})^2 = \frac{1}{2} kx^2 [/tex]

and thus [tex] x = \mu v \sqrt{\frac{1}{k(\mu + m)}} [/tex]

this is assuming that [tex] x = \Delta L + D [/tex]

and D is converted to the enrgy that makes this thing go forward

so [tex] \frac{1}{2} k D^2 = \frac{1}{2} ( \mu + m + M ) v_{f}^2 [/tex]

[tex] D = v_{f} \sqrt{\frac{\mu + m + M}{k}} [/tex]

now here's the dilemma, what is v?? i cannot find D without using some unknown velocity

how would i use the conservation of momentum here?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Bullet shot into a box

**Physics Forums | Science Articles, Homework Help, Discussion**