Answer:
The complete question is:
A 2.0-kg block is attached to one end of a spring with a spring constant of 100 N/m and a 4.0-kg block is attached to the other end. The blocks are placed on a horizontal frictionless surface and set into motion. At one instant the 2.0-kg block is observed to be traveling to the right with a speed of 0.50 m/s and the 4.0-kg block is observed to be traveling to the left with a speed of 0.30 m/s. Since the only forces on the blocks are the force of gravity, the normal force of the surface, and the force of the spring, we conclude that: A) the spring is compressed at the time of the observation B) the spring is not compressed at the time of observation C) the motion was started with the masses at rest D) the motion was started with at least one of masses moving E) the motion was started by compressing the spring.
Answer: D) The motion was started with at least one of masses moving.
Explanation:
A) the spring is compressed at the time of the observation
This situation is not true because if the spring is compressed, both the blocks will move with equal velocity.
B) the spring is not compressed at the time of observation
This situation is not true because if the spring is not compressed then the blocks will be in equilibrium position and in static position.
C) the motion was started with the masses at rest
This situation is not true because the blocks will then move either with same velocity or the blocks will be in static position.
E) the motion was started by compressing the spring
This situation is not true because the blocks will then move with same velocity since, both blocks are tied with the same string.
D) the motion was started with at least one of masses moving
This situation is true since, both the blocks are moving in opposite direction i.e. 2 kg block is moving in right direction and 4 kg block is moving in left direction so, in this situation:
m1 = 2 kg
m2 = 4 kg
v1 = 0.5 m/s
v2 = -0.3 m/s (because 4 kg block is moving in opposite direction as compare to 2 kg block)
m1 x v1 = m2 x v2
2 x 0.5 = 4 x (-0.3)
1 ≠ -1.2
Since, m1 x v1 is not equal to m2 x v2 which means that only one block (i.e. 2 kg block) is moving in right direction which makes the other block (4 kg block) move in opposite direction.
