A 3400 kg truck moving at 17 m/s collides with a stationary 950 kg passenger car, and the two stick together. Assuming that they are free to move afterward, what is the momentum of the truck+car object after the collision?
a) 13 kg m/s
To solve this problem, 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. Let's calculate the momentum of the truck before the collision:
Momentum of truck = mass of truck * velocity of truck
= 3400 kg * 17 m/s
= 57800 kg m/s
Since the car is stationary, its velocity before the collision is 0. Therefore, the momentum of the car before the collision is:
Momentum of car = mass of car * velocity of car
= 950 kg * 0 m/s
= 0 kg m/s
After the collision, the truck and car stick together and move as a single object. Let's denote the final velocity of the truck+car object as v.
The total momentum after the collision is:
Total momentum after collision = (mass of truck + mass of car) * final velocity
= (3400 kg + 950 kg) * v
= 4350 kg * v
According to the conservation of momentum principle, the total momentum before the collision is equal to the total momentum after the collision. Therefore:
Total momentum before collision = Total momentum after collision
57800 kg m/s + 0 kg m/s = 4350 kg * v
Simplifying this equation gives:
57800 kg m/s = 4350 kg * v
Now, let's solve for v:
v = 57800 kg m/s / 4350 kg
v ≈ 13.29 m/s
Therefore, the momentum of the truck+car object after the collision is approximately:
Total momentum after collision = (3400 kg + 950 kg) * 13.29 m/s
Total momentum after collision ≈ 4350 kg * 13.29 m/s
Total momentum after collision ≈ 57836.5 kg m/s
Therefore, the answer is 57836.5 kg m/s, which is closest to option a) 13 kg m/s.