At car (1140-kg)traveling at 76.04 m/s and truck (12600-kg)traveling 6.88 m/s have a head-on collision and then stick together. What is their final common velocity (m/s)? (assume the car is going in the positive direction)
What is the cars' change in momentum in the above question (kg m/s)?
When I calculate the velocity of the truck, I get 22.9 m/s which is correct.
The formula that I am using to find the common velocity is
pi= (velocity car)(mass car) - (velocity truck)(mass truck)
I then take the pi calculated and use it to find the final velocity
vf = pi/(mc+mt)
I get close to the right answer (-4.36) but should have been -4.42.
For the last question. I believe that I am using the wrong formula.
mc*(vf-vc)
The correct answer was -31100 but I get nowhere near this number.
Am I missing some key steps here?
To find the final common velocity of the car and truck after the collision, you can use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.
The total momentum before the collision is given by the formula:
initial momentum = (mass car) * (velocity car) + (mass truck) * (velocity truck)
Substituting the given values:
initial momentum = (1140 kg) * (76.04 m/s) + (12600 kg) * (6.88 m/s) = 1033380 kg*m/s + 86688 kg*m/s = 1120068 kg*m/s
Since the car is traveling in the positive direction, and the truck is traveling in the negative direction, their velocities have opposite signs.
The total momentum after the collision is given by the formula:
final momentum = (mass combined) * (final velocity)
Since the car and truck stick together after the collision, their masses are combined:
mass combined = (mass car) + (mass truck) = 1140 kg + 12600 kg = 13740 kg
Rearranging the formula, we get:
final velocity = final momentum / mass combined
Substituting the values:
final velocity = 1120068 kg*m/s / 13740 kg = 81.49 m/s (approximately)
So, the final common velocity of the car and truck after the collision is approximately 81.49 m/s.
To find the change in momentum of the car, you can use the formula:
change in momentum = mass car * (final velocity - initial velocity)
Substituting the values:
change in momentum = (1140 kg) * (81.49 m/s - 76.04 m/s) = 6174 kg*m/s (approximately)
Therefore, the change in momentum of the car is approximately 6174 kg*m/s.