Two trucks that appear to be identical collide on an icy road. One was originally at rest. The trucks stick together and move off at more than half the original speed of the moving truck. What can you conclude about the contents of the two trucks?
The law of conservation of linear momentum for inelastic collision
m1•v = (m1+ m2)•u =(m1+ m2)•(v/2)
Consenquently, m2=m1
To analyze the situation, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision, assuming no external forces act on the system.
Let's denote the mass of the initially moving truck as m1 and its initial velocity as v1. Since the other truck was initially at rest, its mass will be denoted as m2, and its initial velocity will be 0.
After the collision, the trucks stick together and move off at more than half the original speed of the moving truck. Let's denote their final velocity as vf.
Using the principle of conservation of momentum:
Total momentum before collision = Total momentum after collision
(m1 * v1) + (m2 * 0) = (m1 + m2) * vf
Since the trucks stick together, we can rewrite the equation as:
(m1 * v1) = (m1 + m2) * vf
Now, we can conclude about the contents of the two trucks based on the given information.
If the final velocity (vf) is more than half the original speed of the moving truck (v1/2), it means that the overall mass of the trucks (m1 + m2) is less than the initial mass of the moving truck (m1).
Therefore, we can conclude that the truck that was initially at rest (m2) must have contained something with a lower mass compared to the initial truck (m1), as the total final mass is less than the initial mass of the moving truck.
In simpler terms, the contents of the two trucks can be understood as follows: The truck initially at rest contained something lighter, while the moving truck (which caused the collision) contained something heavier.