Two cars of the same mass collide head -on and become tangled so that they move on together. If the engines of both were stopped at the moment of impact and the speeds of the cars impact were 120m/s ,find the joint velocity immediately after collision
same mass, same velocity opposite direction? Joint velocity=zero
To find the joint velocity immediately after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum (p) of an object is given by the product of its mass (m) and velocity (v). Since the two cars have the same mass, we can simplify the equation as follows:
Total momentum before collision = Total momentum after collision
(mass of car 1 × velocity of car 1) + (mass of car 2 × velocity of car 2) = (total mass × joint velocity)
Let's assume the mass of each car is "m", and the joint velocity after the collision is "V".
(2m × 120 m/s) = (2m × V)
240m²/s = 2mV
Divide both sides of the equation by 2m:
120 m/s = V
Therefore, the joint velocity immediately after the collision is 120 m/s.
To find the joint velocity immediately after the collision, we can use the principle of conservation of momentum. The momentum is a measure of an object's motion and is calculated by multiplying the mass of an object by its velocity.
Given that the two cars have the same mass (let's call it "m") and are moving with velocities of -120 m/s and 0 m/s at the moment of impact, we can calculate their momenta before the collision.
The momentum of the first car (car 1) is given by:
Momentum1 = mass x velocity = m x (-120) = -120m
The momentum of the second car (car 2) is given by:
Momentum2 = mass x velocity = m x 0 = 0
Since there are no external forces acting on the system of the two cars, the total momentum before the collision should be equal to the total momentum after the collision.
Total initial momentum = Total final momentum
Therefore,
Momentum1 + Momentum2 = (Mass of both cars) x (Joint velocity after collision)
Substituting the calculated momenta:
(-120m) + 0 = (2m) x (Joint velocity after collision)
Simplifying the equation:
-120m = 2m x (Joint velocity after collision)
Dividing both sides by 2m:
-60 = Joint velocity after collision
Therefore, the joint velocity immediately after the collision is -60 m/s.