What is the amount of work required to compress the spring?

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The discussion revolves around calculating work, potential energy, and kinetic energy related to a spring and an object on an inclined plane. The user correctly applied the work-energy principle, finding that the work required to compress the spring and the potential energy acquired by it are both 0.5 Joules. After releasing the mass, they calculated its kinetic energy to also be 0.5 Joules, confirming the conservation of energy. For the inclined plane problem, they determined the speed at the bottom to be 12.65 m/s and calculated the coefficient of kinetic friction on the horizontal surface to be 0.35. The responses indicate that the calculations and understanding of the concepts are accurate.
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Alright I'm having a little trouble with a question. The question is "there is a mass of 1.0 kg that is pushed against a spring with a spring constant of 25N/m. As a result, the spring is compressed by 20.cm. The mass is then released.

What is the amount of work required to compress the spring?

I used the equation WC=1/2kx^2. I then received 0.5 Joules .

Then the second question was,

What is the amount of potential energy acquired by the spring when it is compressed?

I used the same equation as the previous question obviously calculated 0.5 joules.

Then the third question was,

What is the kinetic energy of the mass after the mass is released and it is no longer in contact with the spring?

I used the equatin 1/2mv^2=1/2kx^2, and found the velocity, which i calculated to be 1m/s. and then put the velocity in the equation 1/2mv^2 and calculated the work for kinetic energy to be 0.5 joules also.

I guess my question is, did I do this correct? Can someone give me some feedback?

Thank you!
 
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Indeed it is correct.
 
You got it. Consveration of energy. It turns three problems into one. ;)
 
Thanks for your feedback!
 
Friction problem

Alright, I have another question that I want to make sure I did correct. The question is "an objec of mass m is at rest on a rough inclined plane with height h, length 8 m, and which makes an angle of 30degrees with the horizontal. The object is allowed to move and it stops on a rough horizontal surface, at a distance of 4m from the botton of the inclined plane as shown. The coefficient of kinetic friction on the inclined plane is 0.4 and g=10m/s^2.

What is the speed of the object ast the bottom of the inclined plane?

Alright i used the equation KEfinal -PEfinal = KEinitial -PEinitial, put in the numbers and calculated the velocity to be 12.65 m/s.

The second questin is...

What is the coefficient of kinetic friction for the horizontal surface?

I used the equation Normal force = Force of weight and got

mass*gravity*distance *coefficient of kinetic friction = mass*gravity*distance*coefficient of friction on the incline.

I canceled the mass and the gravity and put in the numbers,

(4m for distance on horizontal0*(uk)= distance of 4 m, (which i obtained from sin30=8/d)*cos30degrees*0.4(the planes coefficient of friction).

I then solved for the coefficient of fricton from the horizontal and calculated 0.35.

(Is this correct?
 

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