Answer:
We can solve this problem by using the law of conservation of momentum, which states that the total momentum of a system remains constant if no external forces act on it.
At the moment when the cord is burned, the spring exerts a force on both blocks, causing them to move in opposite directions. Let's assume that the block of mass 7 kg moves to the left with a velocity of v m/s.
According to the law of conservation of momentum, the initial momentum of the system (before the cord is burned) is equal to the final momentum of the system (after the cord is burned). The initial momentum of the system is zero, since both blocks are initially at rest. The final momentum of the system can be calculated as follows:
final momentum = (mass of 7 kg block) x (velocity of 7 kg block) + (mass of 25 kg block) x (velocity of 25 kg block)
We know that the mass of the 25 kg block moves to the right with a velocity of 12 m/s. Therefore, the final momentum of the system can be written as:
final momentum = (7 kg)(v) + (25 kg)(12 m/s)
Setting the initial momentum equal to the final momentum and solving for v, we get:
0 = (7 kg)(v) + (25 kg)(12 m/s)
v = -50.4 m/s
Therefore, the block of mass 7 kg moves to the left with a velocity of 50.4 m/s. However, it's important to note that this answer is negative, indicating that the block moves in the opposite direction to the positive direction we assumed. If we consider the positive direction to be the direction in which the 25 kg block moves, then the velocity of the 7 kg block is:
v = -50.4 m/s (in the negative direction)
If we take the absolute value of the velocity, we get:
|v| = 50.4 m/s
Therefore, the velocity of the block of mass 7 kg is 50.4 m/s in the opposite direction to the motion of the 25 kg block.
Step-by-step explanation:
Certainly!
This problem involves the law of conservation of momentum, which states that the total momentum of a closed system remains constant if no external forces act on it. This means that the initial momentum of the system is equal to the final momentum of the system.
Initially, the two blocks are at rest on a frictionless surface, so their initial momentum is zero. When the blocks are pushed together with the spring between them, the spring exerts a force on both blocks, causing them to move in opposite directions. This is because the force of the spring is equal and opposite on both blocks, due to Newton's third law of motion.
At the moment when the cord is burned, the spring is no longer exerting a force on the blocks, so the momentum of the system is conserved. The final momentum of the system can be calculated using the formula:
final momentum = (mass of 7 kg block) x (velocity of 7 kg block) + (mass of 25 kg block) x (velocity of 25 kg block)
We know that the mass of the 25 kg block moves to the right with a velocity of 12 m/s, so we can substitute this value into the formula. However, we don't know the velocity of the 7 kg block, so we can assume that it moves to the left with a velocity of v m/s. Since the two blocks move in opposite directions, we take the velocity of the 7 kg block to be negative.
Setting the initial momentum equal to the final momentum and solving for v gives us the velocity of the 7 kg block. However, it's important to note that the answer we get is negative, indicating that the block moves in the opposite direction to the positive direction we assumed. If we consider the positive direction to be the direction in which the 25 kg block moves, then the velocity of the 7 kg block is equal to the magnitude of the negative value we obtained.