Collision with projectile and block attached to spring

[x24759]

Homework Statement

A projectile of mass m = 50g traveling at v0 = 20m/s hits a block of mass M = 450g. The block rests on
a frictionless horizontal surface and is attached to a spring of force constant k = 2000N/m. The projectile
ricochets backward off the block with speed v’ = 0.6v0. The collision lasts for 4ms.
(In the picture, the spring is attached to the block and the wall)
a) What impulse is delivered to the block and what is the average force for the collision?
b) Is the collision elastic? Justify your answer.
c) What is the maximum compression of the spring?
d) Suppose the surface has a “small” coefficient of friction μk = 0.1. Estimate the total distance the block
traverses from the moment it is struck to when it comes finally to rest. Why is this only an estimate? For
such an estimate to be accurate what is the criterion for “small” friction coefficient?

Homework Equations

p=mv
J=Δp
f_av= Δp/Δt
KE=1/2mv²
U_s=1/2kd²
(maybe?) v_rel=-v^'_rel

The Attempt at a Solution

a)
momentum: mv₀=mv^'+Mv₂^'

impulse on block: J=Δp=p2-p1 --> p2= mv₀ - mv^' = .4mv₀ = .4 N⋅s

f_av= Δp/Δt = 100 N

b)
KE= 1/2 m v²
KE^' +1/2mv^'2+1/2Mv₂^'2

KE^'/KE = [m(.6v₀)+M(v₀-.6v₀)²] / mv₀²

=(.6)² + (.450)(.4)²(.05) =>.40 --> 60% KE loss. non- elasticand this is where I am second guessing myself.

 

[x24759]

.

 

[haruspex]

Can't follow your working if you make up variables like p1, p2 etc. and don't define them.
Your answer to a) is wrong. Please explain your working in detail.
For part b), how are you calculating v₂'?

 

[JeremyG]

impulse on block: J=Δp=p2-p1 --> p2= mv0 - mv' = .4mv0 = .4 N⋅s

a) While the idea is not wrong here, you have forgotten to take into account that momentum is a vector quantity, which means that direction is important. Hence, it is important to define what direction you will be taking as positive and stick with that convention throughout your working. A diagram will help you here if you have trouble visualizing.

b) The problem that I mentioned above manifests in your working for part (b) as well. Look through the directions and signs of your vector quantities again.