An object with total mass m total = 17.6 kg is sitting at rest when it explodes
ID: 1360912 • Letter: A
Question
An object with total mass mtotal = 17.6 kg is sitting at rest when it explodes into three pieces. One piece with mass m1= 4.5 kg moves up and to the left at an angle of 1 = 24° above the –x axis with a speed of v1 = 26.9 m/s. A second piece with mass m2 = 5.2 kg moves down and to the right an angle of 2 = 29° to the right of the -y axis at a speed of v2 = 22.7 m/s.
1)
What is the magnitude of the final momentum of the system (all three pieces)?
kg-m/s
2)
What is the mass of the third piece?
kg
3)
What is the x-component of the velocity of the third piece?
m/s
4)
What is the y-component of the velocity of the third piece?
m/s
5)
What is the magnitude of the velocity of the center of mass of the pieces after the collision?
m/s
6)
Calculate the increase in kinetic energy of the pieces during the explosion.
J
Explanation / Answer
given,
total mass = 17.6 kg
m1 = 4.5 kg
1 = 24°
v1 = 26.9 m/s
m2 = 5.2 kg
2 = 29°
v2 = 22.7 m/s
initial momentum of the system = 0 kg.m/s (since the system was in rest)
by conservation of momentum
initial momentum = final momentum
final momentum = 0 kg m/s
magnitude of the final momentum of the system = 0 kg.m/s
total mass = m1 + m2 + m3
17.6 = 4.5 + 5.2 + m3
m3 = 7.9 kg
mass of third piece = 7.9 kg
final horizontal momentum = m1 * v1 * cos(theta1) + m2 * sin(theta2) + m3 * v
0 = 4.5 * 26.9 * cos(24) - 5.2 * 22.7 * sin(29) + 7.9 * v
v = -6.754 m/s
x-component of the velocity of the third piece = -6.754 m/s
final vertical momentum = m1 * v1 * sin(theta1) + m2 * cos(theta2) + m3 * v
0 = 4.5 * 26.9 * sin(24) - 5.2 * 22.7 * cos(29) + 7.9 * v
v = 6.836 m/s
y-component of the velocity of the third piece = 6.836 m/s