Question

1. Which of the following equations are dimensionally correct? (Select all that are correct.) a) vf = vi + ax b) y = (2 m)cos(kx), where k = 2 m-1

2. One gallon of paint (volume = 3.78 10-3 m3) covers an area of 16.0 m2. What is the thickness of the fresh paint on the wall?

3. Compute
(a) the order of magnitude of the mass of a bathtub half full of water. (Bathtub. Assume the tub measures 1.3 m by 0.5 m by 0.3 m.)
(b) the order of magnitude of the mass of a bathtub half full of pennies. (Assume the pennies are made entirely of copper.)[103kg]

Answer 1

1) The only equation which dimensionally correct? b) y = (2 m)cos(kx), where k = 2 m-1
Here is an explanation for my choice : vf = vi + ax is wrong because index '' x '' should be replaced with t, only in that case it will be dimensionally right.

2y = (2 m)cos(kx) is definitely correct as a lenght = lenghth * any number that is placed between -1 and +1.

2) The thing which will lead us to the answer and help to get the thickness of the paint on the wall : remember that Volume = Area * Depth.
Then we obtain simle equation in which you just need to solve for Depth :

`3.78 x 10-3 m^3= 34m^2 * depth` and that's all!

3) To solve these two you just need to know the dencity.
So, density of water = 1000 kg/m^3 and density of copper = 9000 kg/m^3
Then we can easily get the answer :
We already know the volume of tub which is 1.3 x 0.5 x 0.≈ 0.2m³ after that we can get the volof water half filling tub ≈ 0.2/2 ≈ 0.1m³.
And then we just compute for both : 10^2kg and 10^3kg respectively.