## THIS USER ASKED 👇

**A heavy lab cart moves with kinetic energy Ko on a track and collides with a lighter lab cart that is initially at rest. The carts bounce off each other but the collision is not perfectly elastic, causing the two-cart system to lose kinetic energy Klost. A student wonders if the fraction of kinetic energy lost from the two-cart system during the collision (Klost/Ko) depends on the speed of the first cart before the collision and plans to perform an experiment.**

**Design an experimental procedure that could be used to test the student’s hypothesis. Assume equipment usually found in a school physics laboratory is available. In the table below, list the quantities that would be measured and the equipment that would be used to measure each quantity. Also, define a symbol to represent each quantity. You do not need to use every row and may add additional rows as needed. Describe the overall procedure to be used, referring to the table above. Provide enough detail so that another student could replicate the experiment. As needed, use the symbols defined in the table and/or include a simple diagram of the setup. Be sure to address how experimental uncertainty could be reduced.**

## THIS IS THE BEST ANSWER 👇

(a, b) see the input matrices in the calculator image below

(c) see the output matrix in the calculator image below

Laura should use Supermarket II.

Step by step explanation:

(a) Your details are not clearly identifiable, so we assume that the costs of a commodity are listed for one supermarket before being listed for the next. Then your A matrix will …

__

(b) The column of maturities is the purchase quantities …

__

(c) Matrix multiplication is a neat thing to do by hand, so let’s do a calculator. Some calculators offer easier data entry than others, and some insist that data be entered into tables before any calculation can be made. We have chosen this one (attached), not because it is the easiest to use, but because we can post a picture of the entry and the result.

Supermarket II has at least Laura’s full bill.

_____

As you know, the result of the consecutive column of product matrix multiplication is element by element of the ‘row’ of the left matrix with the ‘column’ of the right matrix. Here, this means that the second column of the first row of output is calculated from the 2nd row of A and the 1st (only) column of B:

2.99 · 2 + 2.89 · 3 + 2.79 · 2 + 3.29 · 3 = 5.98 +8.67 +5.58 +9.87

= 30.10

## Leave a Reply