Blocks on Spring without Friction

In summary, a spring with a relaxed length of xo is stretched to a distance of Dx = 40 cm by a force of F = 20 N. An attached block with mass m = 12 kg rests on a frictionless surface. After the force is removed, the potential energy of the block due to the spring is calculated using PE=(mgh) and is equal to 47.04 J. The total mechanical energy of the block in the stretched position is equal to the potential energy, but when it returns to its unstretched position, the total mechanical energy is zero. When the spring returns to its unstretched length, the speed of the block is also zero. However, when the spring has only returned halfway (20 cm
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A spring is stretched a distance of Dx = 40 cm beyond its relaxed length of xo by a force, F = 20 N. Attached to the end of the spring is an block of mass m = 12 kg, which rests on a horizontal frictionless surface.
After a moment, the force is removed.

a) What is the potential energy of the block due to the spring when it is held in the stretched position?

For this question, I did PE=(mgh). So, PE= (12)(9.8)(0.4m) and got 47.04 J, but that's not the right answer.

b) What is the total mechanical energy of the block when it is held in the stretched position?

c) What is the total mechanical energy of the block when it returns to its unstretched position?

d) When the spring again returns to its unstretched length, what is the speed of the block?

e) What is the total mechanical energy of the block when it has returned only halfway (20 cm) to its unstretched position?

f) When the spring has returned only halfway (20 cm), what is the speed of the block?
 
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1. How does the absence of friction affect the motion of blocks on a spring?

Without friction, the blocks will experience a smooth and continuous motion as they slide back and forth on the spring. This is because there is no force acting against the motion of the blocks, allowing them to move freely without any resistance.

2. Can the blocks continue to oscillate indefinitely without friction?

No, the blocks will eventually come to a stop due to the loss of energy through other forms of friction, such as air resistance or internal friction within the spring itself. However, in a hypothetical scenario where there is absolutely no friction at all, the blocks will continue to oscillate indefinitely.

3. How does the mass of the blocks affect the amplitude of the oscillations?

The mass of the blocks does not directly affect the amplitude of the oscillations. However, a heavier block will require more force to set it in motion and will have a slower velocity compared to a lighter block.

4. What happens if the spring is compressed or stretched beyond its natural length?

If the spring is compressed or stretched beyond its natural length, the blocks will experience a restoring force that will push them back towards the equilibrium position. This will result in the blocks oscillating with a larger amplitude.

5. Can the blocks reach a state of equilibrium without friction?

Yes, the blocks can reach a state of equilibrium without friction. This is because the restoring force of the spring will always act to bring the blocks back to their equilibrium position, regardless of the absence of friction. However, in a real-world scenario, there will always be some form of friction present which will prevent the blocks from ever truly reaching a state of perfect equilibrium.

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