Answer:
a) P = m1v1 + m2v2 P = (0.39 kg)(3.75i m/s) + (0.33 kg)(1.5j m/s) P = 1.4625i kg m/s + 0.495j kg m/s
b) vx = 2.025 m/s.
c) vy = 0.6875 m/s.
Step-by-step explanation:
This is a story about two balls of clay, with masses m1 = 0.39 kg and m2 = 0.33 kg, who were madly in love with each other. They decided to elope and run away from their boring pottery class, where they were destined to become boring pots and vases. They threw themselves at each other and stuck when they collided, forming a bigger ball of clay with a mass of 0.72 kg. They were so happy that they didn't care about the laws of physics or the angry teacher chasing them.
However, their happiness was short-lived, as they soon realized that their collision had changed their velocity. Before they met, mass 1 had a velocity v1 = 3.75i m/s and mass 2 had a velocity of v2 = 1.5j m/s. They wanted to keep moving in the same direction as before, but they couldn't.
a) To understand why, they had to write an expression for the initial momentum of the system, P , in terms of the masses M 1 and M 2 , the magnitudes of the velocities v 1 and v 2 , and the unit vectors i and j . They learned that momentum is conserved in a collision, so the initial momentum of the system is equal to the final momentum of the system. The initial momentum of the system is given by:
P = m1v1 + m2v2
P = (0.39)(3.75i) + (0.33)(1.5j)
P = m1v1 + m2v2 P = (0.39 kg)(3.75i m/s) + (0.33 kg)(1.5j m/s) P = 1.4625i kg m/s + 0.495j kg m/s
P = 1.4625i + 0.495j kg m/s
b) To find the horizontal component of the final velocity v x , in meters per second, after the collision, they had to divide the horizontal component of the initial momentum by the total mass of the system:
v x = P x /m
v x = (1.4625)/(0.72)
vx = 2.025 m/s.
v x = 2.03 m/s
c) To find the vertical component of the final velocity V y , in meters per second, after the collision, they had to divide the vertical component of the initial momentum by the total mass of the system:
V y = P y /m
V y = (0.495)/(0.72)
vy = 0.6875 m/s.
V y = 0.69 m/s
They were shocked to discover that their final velocity was not in the same direction as their initial velocities. They had veered off course and were heading towards a wall. They tried to separate, but it was too late. They smashed into the wall and broke into pieces.
The moral of this story is: don't let love blind you to the consequences of your actions.