Two blocks of masses M and 3M are placed on a horizontal, frictionless surface. A light spring is attached to one of them, and the blocks are pushed together with the spring between them as shown in the figure below. A cord initially holding the blocks together is burned; after that happens, the block of mass 3M moves to the right with a speed of 1.85 m/s.
(a) Is the original energy in the spring or in the cord? Explain your asnwer.
(b) Is momentum of the system conserved in the bursting-apart process? How can it be, with large forces acting? How can it be, with no motion beforehand and plenty of motion afterward?
To answer these questions, we need to understand the principles of energy conservation and momentum conservation.
(a) Is the original energy in the spring or in the cord? Explain your answer.
The original energy in the system is stored in the spring. When the blocks are pushed together, potential energy is stored in the compressed spring. This potential energy is eventually converted into kinetic energy when the blocks are released and the spring expands, causing the block of mass 3M to move to the right. So, the energy is initially stored in the spring.
(b) Is momentum of the system conserved in the bursting-apart process? How can it be, with large forces acting? How can it be, with no motion beforehand and plenty of motion afterward?
The momentum of the system is conserved in all interactions, including the bursting-apart process. Although there are large forces acting, the momentum before and after the cord is burned remains the same.
Initially, both blocks are at rest, so the initial momentum of the system is zero. After the cord is burned, the block of mass 3M starts moving to the right with a speed of 1.85 m/s. The smaller block with mass M moves to the left with an unknown velocity v.
Since momentum is conserved, the total momentum before the cord is burned should be equal to the total momentum after. Mathematically, this can be expressed as:
0 = (3M * 1.85) + (M * v)
Solving for v, we can find the velocity of the smaller block. The negative sign indicates that the smaller block moves in the opposite direction to the larger block. So, momentum is conserved in this process, even though the motion of the blocks is different before and after the cord is burned.