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------------------------------------------------ On a frictionless surface, two blocks, one weighing 4oz the other weighing 12oz, are placed on either side of a spring, and the spring is compressed by 2in. The system is held in place by a string. When the string is cut, the heavier block moves away at 2ft/s.

a. What is the speed of the lighter block?

b. How much energy is stored in the system before the string is cut?

c. Is the energy stored in the string or spring? Explain why.

-6ft/s the negative sign indicates that the lighter block moves in the opposite direction to the heavier block, and Potential Energy (spring) is 0.83 ft-lb, and The energy in the spring is what propels the blocks forward when the string is cut, as the potential energy is converted into kinetic energy of the blocks.

a. We can use the conservation of momentum to find the speed of the lighter block. Since there are no external forces acting on the system after the string is cut, the total momentum of the system remains constant. The initial momentum of the system is zero because both blocks are at rest. The final momentum is given by:

Final Momentum = Mass of Heavier Block * Speed of Heavier Block + Mass of Lighter Block * Speed of Lighter Block

Since the final momentum is zero (both blocks come to rest after separation), we can write the equation as:

0 = 12 oz * 2 ft/s + 4 oz * Speed of Lighter Block

Now, let's solve for the speed of the lighter block:

Speed of Lighter Block = - (12 oz * 2 ft/s) / 4 oz ≈ -6 ft/s

The negative sign indicates that the lighter block moves in the opposite direction to the heavier block.

b. The system consists of two blocks and a compressed spring. The energy stored in the spring when it is compressed can be calculated using the formula for potential energy in a spring:

Potential Energy (spring) = 0.5 * k * x^2

Where:

k = spring constant

x = compression of the spring (2 inches = 2/12 ft)

The spring constant (k) depends on the properties of the spring and can be given or measured. Let's assume the spring constant is 50 lb/ft (pounds per foot) for demonstration purposes:

Potential Energy (spring) = 0.5 * 50 lb/ft * (2/12 ft)^2 ≈ 0.83 ft-lb

c. The energy is stored in the spring, not the string. When the spring is compressed, it gains potential energy due to its ability to exert a restoring force when released. The string is only holding the system in place, preventing the spring from expanding and the blocks from moving. The energy in the spring is what propels the blocks forward when the string is cut, as the potential energy is converted into kinetic energy of the blocks.

To know more about momentum please refer:

https://brainly.com/question/18798405

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