Help Please!
Two cars in opposite directions were going at 50 mph before a collision. They had a head on inelastic collision, i.e. the two cars stuck together afterward. The common speed of the combined piece right after the collision is 20 mph. The mass of Car 1 was 2,000 lb. Car 2 was heavier. The mass of Car 2 was ____ lb.
To find the mass of Car 2, we can use the law of conservation of momentum. According to this law, in the absence of external forces, the total momentum of a system remains constant before and after a collision.
The momentum of an object is given by the product of its mass and velocity. Therefore, we can write the momentum equation for the two cars before the collision as:
Momentum before = Momentum after
To solve for the mass of Car 2, let's first calculate the initial momentum of each car before the collision.
The initial momentum of Car 1 (m1) is given by the product of its mass (m1) and velocity (v1):
Momentum of Car 1 before = m1 * v1
Given:
Mass of Car 1 (m1) = 2,000 lb
Velocity of Car 1 (v1) = 50 mph
Momentum of Car 1 before = 2,000 lb * 50 mph
Now, let's consider Car 2:
Since the two cars are moving in opposite directions, the velocity of Car 2 (v2) would be negative to indicate its direction. The negative sign is not needed for the masses. Hence, the velocity of Car 2 can be written as -v2.
The momentum of Car 2 (m2) before the collision would be given by:
Momentum of Car 2 before = m2 * (-v2)
Now, let's consider the combined piece after the collision. The momentum of the combined piece is given by the mass of the combined piece (m1 + m2) multiplied by its velocity (20 mph).
Momentum of combined piece after = (m1 + m2) * 20 mph
Since it is an inelastic collision and the cars stick together, we know that the common velocity of the combined piece is 20 mph.
Now, using the law of conservation of momentum, we can equate the momentum before and after the collision:
Momentum of Car 1 before + Momentum of Car 2 before = Momentum of combined piece after
(2,000 lb * 50 mph) + (m2 * (-v2)) = (m1 + m2) * 20 mph
Now, substitute the given values and solve the equation for the mass of Car 2 (m2).