Another alternative representation — Energy bar charts

Example problem — Box on an incline

Here’s a problem that I once gave on an in-class assessment:

A 2.6-kg block slides down a frictionless incline from point A to point B. A force (magnitude P = 3.4 N) acts on the block between A and B, as shown in the above figure. Points A and B are 2.2 m apart. If the kinetic energy of the block at A is 10 J, what is the kinetic energy of the block at B?

This problem was copied out of a test bank and I believe that I changed all the values for everything except the initial kinetic energy. Like all the problems I’m going to show here, the solutions are easily googleable. Here’s my solution:

Solution to the above problem.

But, I don’t like this. I mean, there’s nothing wrong with it, but if the solution is already on the internet, then it’s not really a very interesting problem.

The best alternative representation for this type of question is an energy bar chart. (Some classes modify this representation and called them LOL charts.) Here’s my take on this one:

I was trying to scale the bar heights to be 10 J per division. It’s not perfect, but it is close.

What about a free-body diagram and the force vectors added together? Here’s what that looks like:

Again, the vectors are reasonably close to being drawn to scale. Notice that when the vectors are drawn to scale, the sum of all the vectors is a vector that points down the ramp — this makes sense, as the box is accelerating down the ramp.

What would the graphs of the velocity and acceleration of the box look like? Here’s my drawings of the graphs:

I like the variety of representations here for this problem. My realization as I was putting this together was that after the bar charts, the emphasis is no longer on applying Work-KE theorem (or conservation of energy.) I may need to think more about that.