An object with total mass m total = 6.4 kg is sitting at rest when it explodes i
ID: 2034406 • Letter: A
Question
An object with total mass mtotal = 6.4 kg is sitting at rest when it explodes into two pieces. The two pieces, after the explosion, have masses of m and 3m. During the explosion, the pieces are given a total energy of E = 45 J.
1) What is the speed of the smaller piece after the collision?
2) What is the speed of the larger piece after the collision?
3) If the explosion lasted for a time t = 0.029 s, what was the average force on the larger piece?
4) What is the magnitude of the change in momentum of the smaller piece?
5) What is the magnitude of the velocity of the center of mass of the pieces after the collision?
Explanation / Answer
Mass of smaller piece m = 1.6 kg
mass of larger piece = 3*1.6 = 4.8 kg
let the velocity of objects be v1 and v2
By the conservation of momentum we have
0 = mv1 + 3mv2
v1 + 3v2 = 0 --------(1)
E = 0.5mv1^2 + 0.5*3m*v2^2
45 = 0.5*6.4(v1^2 + 3v2^2)
v1^2 + 3v2^2 = 14.0625
(-3v2)^2 + 3v2^2 = 14.0625
12v2^2 = 14.0625
v2 = 1.08 m/s
v1 = -3v2 = -3*1.08 = -3.25 m/s
a) speed of the smaller piece = 3.25 m/s
b) speed of the larger piece = 1.08 m/s
3) average force = rate of change of momentum
= dp/dt = 4.8*1.08 / 0.029
= 179.17 N
4) magnitude of change in momentum of smaller piece = 1.6*(0 - (-3.25) ) = 5.2 kg m/s
5) Vcm = m1v1 + m2v2 / m1 + m2
= m*-3.25 + 3m * 1.087 / m + 3m
= 0
so the velocity of center of mass is zero