An automobile has a mass of 2150 kg and a velocity of +18 m/s. It makes a rear-end
collision with a stationary car whose mass is 1850 kg. The cars lock bumpers and skid
off together with the wheels locked. What is the velocity of the two cars just after the
collision?
momentum is conserved, so
2150*18 + 1850*0 = (2150+1850)v
solve for v
To calculate the velocity of the two cars just 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 of an object is calculated by multiplying its mass by its velocity. Therefore, the momentum before the collision is:
Momentum before collision = (mass of 1st car * velocity of 1st car) + (mass of 2nd car * velocity of 2nd car)
In this case, the 1st car is the moving car and the 2nd car is the stationary car. Let's plug in the given values:
Mass of 1st car = 2150 kg
Velocity of 1st car = +18 m/s (positive sign indicates its direction)
Mass of 2nd car = 1850 kg
Velocity of 2nd car = 0 m/s (since it is stationary)
Momentum before collision = (2150 kg * 18 m/s) + (1850 kg * 0 m/s)
= 38700 kg*m/s + 0 kg*m/s
= 38700 kg*m/s
Now, after the collision, the two cars lock bumpers and skid off together with their wheels locked. This means that the two cars move as a single unit after the collision. Therefore, the mass of the combined cars is the sum of their individual masses:
Total mass after collision = Mass of 1st car + Mass of 2nd car
= 2150 kg + 1850 kg
= 4000 kg
Let's represent the velocity of the combined cars as V. So the momentum after the collision is:
Momentum after collision = Total mass after collision * Velocity of the combined cars
= 4000 kg * V
According to the conservation of momentum principle, the momentum before the collision is equal to the momentum after the collision:
Momentum before collision = Momentum after collision
38700 kg*m/s = 4000 kg * V
Now, we can solve for V by dividing both sides of the equation by 4000 kg:
V = 38700 kg*m/s / 4000 kg
= 9.675 m/s
Therefore, the velocity of the two cars just after the collision is approximately +9.675 m/s (in the direction of the moving car).