Explosions in one dimension: On a frictionless horizontal table, two blocks (A of mass 2.00 kg and B of mass 3.00 kg) are pressed together against an ideal massless spring that stores 75.0 J of elastic potential energy. The blocks are not attached to the spring and are free to move free of it once they are released from rest. The maximum speed achieved by each block is closest to

Question

Quizplus · Accepted Answer

Conservation of energy can be used to solve this problem. Initially, all the energy is stored in the spring as elastic potential energy. When the blocks are released, this energy is converted into kinetic energy of the blocks.

Let the maximum speed of block A be vA and the maximum speed of block B be vB. Using conservation of energy, we can write:

1/2 k x^2 = 1/2 mA vA^2 + 1/2 mB vB^2

where k = spring constant, x = compression of the spring, mA = mass of block A, and mB = mass of block B.

The spring constant can be calculated as:

k = 2 U / x^2

where U = elastic potential energy stored in the spring.

Substituting the given values, we get:

k = 2 * 75 / x^2 = 150 / x^2

Now, we can substitute these values into the conservation of energy equation and solve for vA and vB:

75 / x^2 = 1/2 * 2 * vA^2 + 1/2 * 3 * vB^2

75 / x^2 = vA^2 + 1.5vB^2

From the given choices, we can see that only choice A gives us values of vA and vB that satisfy this equation. Therefore, the answer is A.

Explosions in One Dimension: on a Frictionless Horizontal Table, Two