A small toy car with a mass of 0.4 kg and a velocity of 5 m/s crashes into another toy car that was at rest with the same mass. The first toy car stops moving and the second toy car then moves forward and crashes into the third toy car that was at rest with a mass of 0.2 kg.
a) If the system is closed, what is the velocity of the third toy car?
b) Show how you calculated the velocity in the space below.
a) To find the velocity of the third toy car, we can use the principle of conservation of momentum. According to this principle, the total momentum of a closed system remains constant before and after a collision.
In this case, the system consists of the first toy car, second toy car, and third toy car. Initially, only the first toy car is moving, so its momentum is given by the product of its mass (0.4 kg) and velocity (5 m/s):
momentum of first car = mass × velocity = 0.4 kg × 5 m/s = 2 kg·m/s
Since the second toy car was initially at rest, its momentum is zero:
momentum of second car = mass × velocity = 0.4 kg × 0 m/s = 0 kg·m/s
Let's assume the velocity of the third toy car is denoted as "v." After the collision, the first car stops moving and transfers its momentum to the second car, which then collides with the third car. The total momentum of the system after the collision would be the sum of the momentum of the second car and the momentum of the third car:
momentum of system after collision = momentum of second car + momentum of third car
Since the second car had no initial momentum and the third car was initially at rest, we can write:
momentum of system after collision = 0 kg·m/s + (0.2 kg) × v
According to the conservation of momentum principle, this momentum should be equal to the initial momentum of the system (i.e., the momentum of the first car):
momentum of system after collision = momentum of first car
Equating these two expressions, we have:
0 kg·m/s + (0.2 kg) × v = 2 kg·m/s
Now, we can solve for "v" to find the velocity of the third toy car.
b) Calculating the velocity:
0.2 kg × v = 2 kg·m/s
Dividing both sides of the equation by 0.2 kg, we get:
v = 2 kg·m/s / 0.2 kg
v = 10 m/s
Therefore, the velocity of the third toy car is 10 m/s.