Question

1. What is the circumference of a circle with a radius of 2.1 cm? your answer as a number; do not include units. You must use the appropriate number of significant figures.

2. Density is defined as mass per unit volume. A solid cylinder has a diameter of 17.4 mm and a length of 50.3 mm. Its mass is 49 g. What is its density? Give your answer in metric tonnes per cubic metre. (The metric tonne is 1000 kg.) Write your answer as a number, using the appropriate number of significant figures.

3. A solar racing car* typically has a power of about 1.2 kW (1.2 kilowatts). What is this in horsepower (hp)? (Use the conversion 1 hp = 745.7 watts). Give your final answer as a number, with the appropriate number of sig figs.

4. Absolute value of vector A = Absolute value of vector B = Absolute value of vector C. Further, Vector A+ Vector B +Vector C = 0. What is the angle between vector A and Vector B?
Express your answer in degrees.

Answer 1

1. The circumference is

$$C=2\pi R=2\cdot3.14\cdot2.1=13.$$

2. The density is

$$\rho=\frac{m}{V}=\frac{m}{[\pi d^2/4]\cdot L}=\\=\frac{49\cdot10^{-3}}{[3.14\cdot (17.4\cdot10^{-3})^2/4]\cdot 50.3\cdot10^{-3}}=4097\text{ kg/m}^3.$$

Or 4.08 tonnes/cubic meter.

3. 1.2 kW is 1200 W. Power in horse powers:

$$P=\frac{1200\text{ W}}{745.7\text{ W/hp}}=1.609\text{ hp}.$$

4. 120° because the system of three equal vectors can be balanced only if the angle between each pair of vectors is 120 degrees.