Change in the Kinetic Energy of a System

[drewcila]

The question is to find the change in kinetic energy of a system. the system in use is a pully system with a wooden block on a flat surface attached to a 100g mass. I have calculated force of friction between the block and desk, and using a ticker timer, I have individual speeds at every 0.1 of a second. Additionally, the distance it travels is 45cm. We have to prove that the change in Kinetic energy is = work done in the system, so I can't use work as my answer.

I know that the equation for kinetic energy is Ek= 1/2mv²
Change in Kinetic energy is represented by the final Ek - initial Ek

I was thinking something like Ek_f = 1/2(0.100)v₂²
then subtract Ek_i= 1/2(0.100)v₁²
I do not know what variables to use in this situation. do I use the mass of the block or the 100g mass apply force? and which velocity should I use? the speed at 0.1 seconds and 0.6 seconds? Does friction play into kinetic energy?

 

[kuruman]

We have to prove that the change in Kinetic energy is = work done in the system, so I can't use work as my answer.

I am not sure what this means. It looks like you are asked to prove the work-energy theorem, $\Delta K = W_{net}$ so you do need to calculate work. Also, is your wooden block pulled by a hanging mass through a string over a pulley? If so, the change in kinetic energy is the difference in kinetic energy between two points in space. Your system has two moving masses, so you need to calculate the kinetic energy of each. Note that they are moving at the same speed at all times. So the left side of the equation is $\Delta K=\Delta K_{wood}+\Delta K_{mass}$. You can calculate this and get a number.

The right side of the equation is the total work done by all the forces acting on the system. You need to figure out what forces do how much work on what parts of the system, calculate the numbers and add them all up. This number you get for the right side of the equation should be equal to the first number you got for the left side of the equation, $\Delta K$.

 

[Chandra Prayaga]

A diagram would be helpful