Determine Min Work & Final Velocity of Masses in Massless Spring Exp

• edud8
In summary, a massless spring is used in an experiment where a 1 kilogram and 3 kilogram mass are on a frictionless table. The 3 kilogram mass is compressed by pushing on the 1 kilogram mass, resulting in a velocity of 10 meters per second. The minimum work needed to compress the spring is 150 J. In a second experiment, both masses are released simultaneously and the final velocity of each mass relative to the table can be determined by remembering that energy is conserved. The final answer will be an integer.
edud8
1981B2. A massless spring is between a 1 kilogram mass and a 3 kilogram mass as shown above, but is not attached to either mass. Both masses are on a horizontal frictionless table. In an experiment, the 1 kilogram mass is held in place and the spring is compressed by pushing on the 3 kilogram mass. The 3 kilogram mass is then released and moves off with a speed of 10 meters per second.
a. Determine the minimum work needed to compress the spring in this experiment.

The spring is compressed again exactly as above, but this time both masses are released simultaneously.
b. Determine the final velocity of each mass relative to the table after the masses are released.

attempt:
1/2mv^2=1/2kx^2
1/2mv^2=150, but idk how to solve for k or x

edud8 said:
1/2mv^2=1/2kx^2
1/2mv^2=150, but idk how to solve for k or x
You don't need to. You only need to know the amount of energy stored in the spring, which is the 150 J you found.

This is the total KE of both masses in part 2, and you also need to remember something else that is conserved.

.

I would approach this problem by first identifying the known values and variables. The known values in this experiment are the masses (1 kg and 3 kg), the final velocity of the 3 kg mass (10 m/s), and the acceleration due to gravity (9.8 m/s^2). The variables are the spring constant (k), the displacement of the spring (x), and the final velocity of the 1 kg mass (v).

To determine the minimum work needed to compress the spring, we can use the formula for work done by a spring, which is W = 1/2kx^2. Rearranging this equation, we can solve for the spring constant (k) by dividing both sides by x^2. This gives us k = 2W/x^2.

Since we know the final velocity of the 3 kg mass (v = 10 m/s), we can use the formula for kinetic energy to solve for the displacement of the spring (x). This gives us 1/2mv^2 = 1/2kx^2. Rearranging this equation, we get x = √(mv^2/k).

Substituting the values for mass and velocity, we get x = √(3 kg * (10 m/s)^2 / k). We can then use this value of x to solve for the spring constant (k) using the formula k = 2W/x^2.

For part b, we can use the law of conservation of momentum to determine the final velocity of each mass. Since the masses are released simultaneously, the total momentum before and after the release will be the same. This means that the sum of the momenta of the two masses before the release will be equal to the sum of the momenta after the release.

Before the release, the 1 kg mass is at rest, so its momentum is 0. The momentum of the 3 kg mass can be calculated using the formula p = mv, where m is the mass and v is the final velocity (10 m/s). This gives us a momentum of 30 kg*m/s.

After the release, the 1 kg mass will have a final velocity (v1) and the 3 kg mass will have a final velocity (v2). Using the law of conservation of momentum, we can set up the equation 0 + 30 kg*m/s = 1

1. How do you determine the minimum work in a massless spring experiment?

The minimum work in a massless spring experiment can be determined by calculating the change in potential energy of the spring. This can be done by multiplying the spring constant (k) by the square of the displacement of the spring (x). This will give you the minimum work required to compress or stretch the spring.

2. What is the final velocity of the masses in a massless spring experiment?

The final velocity of the masses in a massless spring experiment can be calculated using the conservation of energy principle. This states that the initial energy of the system (spring potential energy) is equal to the final energy of the system (kinetic energy of the masses). By equating these energies, you can solve for the final velocity.

3. How does the mass of the masses affect the final velocity in a massless spring experiment?

The mass of the masses does not have a direct effect on the final velocity in a massless spring experiment. However, it does affect the amount of work required to compress or stretch the spring. A heavier mass will require more work to reach the same displacement as a lighter mass.

4. Can a massless spring have a non-zero final velocity?

No, a massless spring cannot have a non-zero final velocity. This is because a massless spring has no inertia and therefore cannot store any kinetic energy. Any energy put into the spring will immediately be transferred to the masses, resulting in a zero final velocity for the spring itself.

5. How does the spring constant affect the minimum work and final velocity in a massless spring experiment?

The spring constant (k) has a direct effect on both the minimum work and final velocity in a massless spring experiment. A higher spring constant will result in a stiffer spring, requiring more work to compress or stretch it. This will also result in a higher final velocity for the masses. Conversely, a lower spring constant will result in less work and a lower final velocity.

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