A 2.0 kg mass is moving to the right at 3.0 m/s . A 4.0 kg mass is moving to the left at 2.0 m/s.
A) If after the collision the two masses join together what is their velocity after the collision?
3.0 X 2.0 = 6m/s. Is this correct?
B)Is this a elastic or inelastic collision?
Elastic. Is this correct?
3.0 X 2.0 = 6m/s. Is this correct?
The unit is not correct: 3 kg * 2 m/s gives 6 kg-m/s.
This is not the answer, but the momentum of the left mass.
Calculate the momentum of the right mass and add to that of the left (watch the sign) to get the total momentum.
Divide the total momentum by the total mass to get the velocity after the inelastic impact.
An elastic impact is like bouncing a superball on the wall, and an inelastic impact is like dropping mashed potatoes on the floor. Hope you get the idea.
A) To find the velocity after the collision, we need to apply the principle of conservation of momentum. The total momentum before the collision is given by the sum of the individual momenta:
Momentum before collision = (mass1 * velocity1) + (mass2 * velocity2)
= (2.0 kg * 3.0 m/s) + (4.0 kg * (-2.0 m/s))
= 6.0 kg·m/s - 8.0 kg·m/s
= -2.0 kg·m/s
Since the masses join together and move as a single body after the collision, the total mass is now equal to the sum of the two masses:
Total mass after collision = mass1 + mass2
= 2.0 kg + 4.0 kg
= 6.0 kg
Using the principle of conservation of momentum, the total momentum after the collision is equal to the momentum before the collision:
Momentum after collision = Total mass after collision * velocity after collision
= 6.0 kg * velocity after collision
Setting the momentum before and after the collision equal to each other, we can solve for the velocity after the collision:
-2.0 kg·m/s = 6.0 kg * velocity after collision
velocity after collision = (-2.0 kg·m/s) / 6.0 kg
= -0.33 m/s
Therefore, the velocity of the masses after the collision is approximately -0.33 m/s.
B) This collision can be classified as an inelastic collision. In an elastic collision, both momentum and kinetic energy are conserved, meaning the total kinetic energy before the collision is equal to the total kinetic energy after the collision. However, in this case, the masses join together and move as one body after the collision. This implies that some kinetic energy is lost during the collision and the collision is not perfectly elastic. Therefore, it is an inelastic collision.
To determine the velocity of the masses after the collision, we can use the principle of conservation of momentum. In an isolated system (where no external forces act upon the objects), the total momentum before the collision is equal to the total momentum after the collision.
A) Firstly, let's calculate the total momentum before the collision:
Total momentum before collision = (mass 1 * velocity 1) + (mass 2 * velocity 2)
Given:
mass 1 = 2.0 kg (moving to the right)
mass 2 = 4.0 kg (moving to the left)
velocity 1 = 3.0 m/s (to the right)
velocity 2 = -2.0 m/s (to the left, negative sign indicates opposite direction)
Total momentum before collision = (2.0 kg * 3.0 m/s) + (4.0 kg * -2.0 m/s)
= 6.0 kg·m/s - 8.0 kg·m/s
= -2.0 kg·m/s
So, the total momentum before the collision is -2.0 kg·m/s.
Now, for two masses to join together after the collision, the total momentum after the collision will also be equal to -2.0 kg·m/s.
Total momentum after collision = -2.0 kg·m/s
To find the final velocity, we need to divide this total momentum by the combined mass of the two masses:
mass after collision = mass 1 + mass 2 = 2.0 kg + 4.0 kg = 6.0 kg
Final velocity after collision = Total momentum after collision / mass after collision
= (-2.0 kg·m/s) / (6.0 kg)
= -0.33 m/s
Therefore, the combined mass will move to the left with a velocity of -0.33 m/s after the collision.
B) In this case, since kinetic energy is not conserved but momentum is conserved, this is an inelastic collision. In an elastic collision, both momentum and kinetic energy would be conserved.