Answer to Question #103766 in Classical Mechanics for Joseph Yep

Question

1. Subtracting vectors. What is the direction of North minus West?

2. The Vector A in the (x,y) plane has a magnitude A= 3.2 and makes angle Theta = 125 degrees with the x-axis, where theta is measured in the geometric or anticlockwise sense. What are the components of vector A in the x and y directions? Use the correct number of sig figs.

3. How much of you is not vacuum? Outside of the nucleus, an atom contains mostly empty space. Estimate the fraction of the volume of an atom that is occupied by the nucleus. Assume that a typical atom has a linear dimension of about 0.1 nm and that a typical nuclear dimension is about 1 fm. Give your answer as a power of ten.

4. How many revolutions does the drive shaft of a truck engine make during its lifetime? Inputs: Let's suppose that the truck travels a million km (1 billion m) at an average speed of 80 km per hour. The engine turns at a rate of 2000 revolutions per minute.Give your answer as a number (not a power of ten).

Answer 1

1. The direction of North minus West is North-East.

$$\bold{j-(-i)=i+j}$$

2.

$$A_x=3.2\cos{125}=-1.8$$

$$A_y=3.2\sin{125}=2.6$$

3.

$$\frac{V_n}{V_a}=\frac{a_n^3}{a_a^3}$$

$$\frac{V_n}{V_a}=\frac{(10^{-15})^3}{(0.1\cdot10^{-9})^3}=10^{-15}$$

4.

$$t=\frac{s}{v}=\frac{1000000}{80}=12500\ h$$

$$N=(2000)(12500)(60)=1500000000$$