stuck on a momentum question?

Question

a 20g pellet is fired into a 200g wooden block initially at rest on a horizontal surface.
the block slides 5.1m before stopping.
the friction coefficient μ is 0.7 between block and surface.
what was the pellet's speed just before impact?

im having trouble with this because the only momentum questions i have ever done are the ones where at least one velocity is given, so i'm struggling here.

my thoughts on it are its something to do with kinetic energy, energy lost due to friction etc, and i worked out the pellet's speed on impact is 11x that of the pellet-block combination when it moves off after impact.

i dont care about the final answer really, just the method of finding it.
cheers.

Answer 1

In this case you have to find both the velocities

You have the friction so you can use

v^2 = u^2 - 2*a*S

v= final velocity =0
u = initial velocity of (block + bullet)(still unknown)
S = distance =5.1m
a = ( friction coeff * g )

here you can find the value of u

now by conservation of momentum

M(bullet)*V(bullet)= M(bullet+block) * u

substitute and find V (bullet).....

Answer 2

First we have to make some simplifying assumption. The collision of bullet and the block is inelastic and lasts for very short time. Of course some kinetic energy is lost, to result into the movement of a total composite mass of block and pellet that is 220 g. Momentum has to be conserved for we assume that there is no exernal force acting on the two for such a short time. Let the velocity of pellet be v. Conservation of mommentum gives us: 20 v = 220 v' where v' is the initial velocity of the [block+pellet]. v' = v/11.


The net frictional force, f acting on the composite system is 0.7x0.220x9.8 N and the acceleration of the system is negative = 0.7x9.8. Using kinematic equation v'^2 = 2x0.7x9.8 x 5.1 = 69.96 or v' = 8.36, so v = 11 x 8.36 = 92.0 m/s. If you hav eany difficulty ask pointed question. I shall try to answer.

Answer 3

Sure, use conservation of energy.

How much energy was converted to heat by friction?

F = 0.7 x (Total mass 220g x 9.8N/kg)

Work = Force x distance.

Energy of pellet = 1/2 m v^2