Two cars collide head on and stick together. The one moving East was going 20.00 m x sec-1 and had a mass of 1500.0 kg. The one heading West was going 25.00 m x sec-1 and had a mass of 1000.0kg. I n which direction were the two cars moving and how fast were they moving?
Test
To determine the direction and speed at which the two cars move after colliding, we can apply the principles of conservation of momentum.
1. Calculate the total initial momentum of the system:
The initial momentum is given by the sum of the individual momenta of the two cars. Momentum (p) is calculated by multiplying mass (m) with velocity (v).
- For the car moving East:
Momentum1 = mass1 x velocity1 = 1500.0 kg x 20.00 m/s = 30000.0 kg·m/s
- For the car moving West:
Momentum2 = mass2 x velocity2 = 1000.0 kg x (-25.00 m/s) = -25000.0 kg·m/s (negative sign indicates opposite direction)
Total initial momentum = Momentum1 + Momentum2 = 30000.0 kg·m/s + (-25000.0 kg·m/s) = 5000.0 kg·m/s
2. Calculate the total mass of the system:
The total mass of the system is the sum of the masses of the two cars.
Total mass = mass1 + mass2 = 1500.0 kg + 1000.0 kg = 2500.0 kg
3. Calculate the resulting velocity of the system:
Using the principle of conservation of momentum, the total momentum of the system before the collision should be equal to the total momentum after the collision.
After the collision, the two cars stick together and move as one unit. Let's assume their combined velocity is v'.
Total final momentum = Total mass x v'
Since there is no external force acting on the system, we can equate the initial total momentum to the final total momentum:
Total initial momentum = Total final momentum
5000.0 kg·m/s = 2500.0 kg x v'
Divide both sides of the equation by the total mass:
v' = 5000.0 kg·m/s / 2500.0 kg
v' = 2 m/s
The resulting velocity of the two cars, after colliding, is 2 m/s. Since the velocity is positive, they are moving in the East direction.
Therefore, after the collision, the two cars move together in the direction East at a speed of 2 m/s.