A projectile of mass mA=20g is shot towards a block of mass MB= 5kg with a veloc
ID: 2207915 • Letter: A
Question
A projectile of mass mA=20g is shot towards a block of mass MB= 5kg with a velocity of vA=400m/s. The block is at rest, attached to a horizontal massless spring (at equilibrium) with k=500N/m. :
(a) (6 pts) If the collision between the projectile and the mass is perfectly elastic, what are the velocities of the two masses immediately following the collision?
(b) (6 pts) For the collision in (a), how far does the spring compress, assuming the surface to be frictionless?
(c) (5 pts) For the collision in (a), if the projectile is in contact with the mass for 0.5ms, what is the average force exerted on the block by the projectile during the collision?
d) (8pts) Now, assume the collision is perfectly inelastic and the surface has a coefficient of kinetic friction of ?
k=0.15. What is the velocity of the projectile and block following the perfectly inelastic collision?
e) (10pts) For the situation described in (d), how far does the spring compress?
Explanation / Answer
mA*vA=mA*v1+mB*v2 v2-v1=vA so .02*400=.02*v1+5*v2 v2-v1=400 so v1=-396.8 m/s v2=3.2 m/s a)v(block)=3.2 m/s v(proj)=-396.8 m/s b).5*m*v^2=.5*k*x^2 so .5*5*3.2^2=.5*500*x^2 so x=.32 m c)F=mv*t=.02*400*.0005=4*10^(-3) N d).02*400=(.02+5)*v so v=1.6 m/s e).5*5.02*1.6^2=.5*k*x^2+u(M+m)g*x so .5*5.02*1.6^2=.5*500*x^2+7.38x so x=.15 m