An object with total mass m total = 8 kg is sitting at rest when it explodes int
ID: 1375105 • Letter: A
Question
An object with total mass mtotal = 8 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 = 44 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 = 0.023 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?
An object with total mass mtotal = 8 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 = 44 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 = 0.023 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
The momentum before the explosion = 0 so the momentum after the explosion is also = 0
mv + 3mV = 0
By the energy given
0.5mv^2 + 0.5(3m)V^2 = 44
solving for V in the momentum equation
V = -mv/3m = -v/3
Plugging back into the energy equation
0.5mv^2 + 0.5(3m)(-v/3)^2 = 44
0.5mv^2 + (1.5/9)mv^2 = 44
v^2 = 44/(2/3)m
4m = 8 kg so m = 2.0 kg
v^2 = 66/2.0
v = 5.74 m/s (1)
Ft = (3m)V
V = 3v = 3(5.74) = 17.23 m/s
F(0.023) = 3(2.0)(17.23)
F = 4495.7 N (2)
change in momentum for smaller> 2.0(5.74) = 11.48 kg m/s (3)
velocity of the center of mass = 0
Again by conservation of momentum
momentum of the system is always 0 the momentum for a system of particles is the total mass of the system
times the velocity of the center of mass, since there is mass velocity of center of mass = 0 m/s