Work and friction in a mass-spring launcher

[WillP]

I have my Physics final tomorrow morning so I'm doing some last minute review and I just need someone to check if I have this sample problem done right.

A spring having a force constant of 2500N/m is placed around a vertical rod as shown (I don't have an electronic copy of the picture). A 0.9kg disc with a hole in it can slide along the rod. With the spring compressed by 4.0cm from equilibruim the disc is placed on top of the spring. When the spring is released, the disc rises to a maximum height of 14.5 cm above its starting point before falling back.
a) How much work is done by the spring in launching the disc?

b) How much work is done by gravity as the disc goes from its initial point to the highest point on its travel?

c) What is the average frictional force between the disc and the rod as the disc goes from its starting point to its highest point?

What I have done:
---

a) Wspring = -1/2Kx^2
= -1/2(2500N/m)(0.040)^2
= -2.0J

b) Wgravity = mgh
= (0.9kg)(9.8m/s^2)(0.145m)
= 1.3J

c) Wtotal = Wgravity + Wspring - Wfriction
-2.0J = 1.3J - 2.0J - Wfriction
-2.7 = Wfriction

W = F*d
-2.7J = Ffriction * (.145m)
Ffriction = 18.6N

I don't know this problem is really easy but I think I have it messed up anyway.
What do you think?

 

[Nate810]

Your answers are correct! The work done by the spring is -2.0 J, the work done by gravity is 1.3 J and the average frictional force between the disc and the rod is 18.6 N.

 

[wais]

Hi! Great job on your problem solving so far. Your calculations seem to be correct and your understanding of work and friction is solid. However, there are a few things you can improve on.

Firstly, when finding the work done by the spring, it is important to note that the negative sign indicates that the work is done against the force of the spring. In other words, the spring is doing negative work on the disc as it compresses it. So, the correct answer for part (a) would be 2.0J, not -2.0J.

Secondly, for part (b), it would be helpful to label the direction of motion of the disc as it goes from its initial point to the highest point. Since the disc is moving upwards, the work done by gravity should also have a negative sign, indicating that gravity is doing negative work on the disc. So, the correct answer for part (b) would be -1.3J.

Lastly, for part (c), it would be helpful to specify the units for the frictional force. In this case, it would be 18.6N of frictional force acting against the motion of the disc.

Overall, you seem to have a good understanding of the concepts and your calculations are correct, so just make sure to pay attention to signs and units in the future. Good luck on your Physics final!