A sled initially at rest has a mass of 47.2 kg, including all of its contents. A block with a mass of 14.5 kg is ejected to the left at a speed of 13.5 m/s. What is the speed of the sled and the remaining contents?
To find the speed of the sled and the remaining contents, we can use the law of conservation of momentum. According to this law, the total momentum before the block is ejected is equal to the total momentum after the block is ejected.
The momentum of an object is given by the product of its mass and velocity. Let's denote the initial velocity of the sled and the remaining contents as V_sled and their combined mass as M_sled.
The momentum before the block is ejected is the product of the sled's mass and its initial velocity, which is V_sled * M_sled.
The momentum after the block is ejected is the sum of the momentum of the block and the momentum of the sled and the remaining contents.
The momentum of the block is given by the product of its mass and its speed, which is 14.5 kg * 13.5 m/s.
Therefore, the momentum after the block is ejected is (14.5 kg * 13.5 m/s) + (V_sled * M_sled).
Setting the initial momentum equal to the final momentum, we have:
V_sled * M_sled = (14.5 kg * 13.5 m/s) + (V_sled * M_sled)
Simplifying the equation, we get:
V_sled * M_sled - V_sled * M_sled = 14.5 kg * 13.5 m/s
0 = 14.5 kg * 13.5 m/s
Since the sled was initially at rest, its initial velocity (V_sled) is 0. Therefore, the speed of the sled and the remaining contents after the block is ejected is also 0 m/s.