Mechanics | Relativity Answers

A clown at a birthday party has brought along a helium cylinder, with which he intends to fill balloons. When full, each balloon contains 0.00210 m3 of helium at an absolute pressure of 1.20 x 10^5 Pa. The cylinder contains helium at an absolute pressure of 2.30 x 10^7 Pa and has a volume of 0.00360 m3. The temperature of the helium in the tank and in the balloons is the same and remains constant. What is the maximum number of people who will get a balloon?

An ideal gas at 10.3 °C and a pressure of 2.48 x 10^5 Pa occupies a volume of 3.12 m3. (a) How many moles of gas are present? (b) If the volume is raised to 5.45 m3 and the temperature raised to 25.6 °C, what will be the pressure of the gas?

A cylindrical glass of water (H2O) has a radius of 5.66 cm and a height of 15.8 cm. The density of water is 1.00 g/cm3. How many moles of water are contained in the glass?

In an old house, the heating system uses radiators, which are hollow metal devices through which hot water or steam circulates. In one room the radiator has a dark color (emissitivity = 0.820). It has a temperature of 60.4 oC. The new owner of the house paints the radiator a lighter color (emissitivity = 0.491). Assuming that it emits the same radiant power as it did before being painted, what is the temperature (in degrees Celsius) of the newly painted radiator?

A cubical piece of heat-shield-tile from the space shuttle measures 0.15 m on a side and has a thermal conductivity of 0.065 J/(s·m·C°). The outer surface of the tile is heated to a temperature of 1300°C, while the inner surface is maintained at a temperature of 22°C. (a) How much heat flows from the outer to the inner surface of the tile in 5.0 minutes? (b) If this amount of heat were transferred to 3.0 liters (3.0 kg) of liquid water, by how many Celsius degrees would the temperature of the water rise?

For his early morning exercises, Andee jogged 12 times around a circular track of a radius 5.0 m. Find total distance traveled and his displacement.

If the magnitude of the resultant force is to be 9kN directed along the positive x axis, determine the magnitude of force T acting on the eyebolt and its angle delta.

During a baseball game, a batter hits a high
pop-up.
If the ball remains in the air for 4.72 s, how
high above the point where it hits the bat
does it rise? Assume when it hits the ground
it hits at exactly the level of the bat. The
acceleration of gravity is 9.8 m/s
2
.
Answer in units of m.

1. Suppose you wish to invest N$2,000 today so that you have N$6,000 six years from now. What must the annual interest rate be to achieve your goal if interest is compounded monthly? [4]

2. Assume that the current rate of inflation on housing is estimated at 10% per annum. Lydia's house is currently valued at N$ 450 000.
(a) How much could you expect to sell it for in 5 years? [3]
(b) Is it worthwhile to sell your house now or in five years, justify your answer? [2]

3. You want to buy a cellphone at the end of the year which will cost you N$ 4500. Assume on 1 January 2020 you open up a Unit trust which pays 6.5% interest per month. How much should you invest (starting from January) to yield N$4500 in December 2020? [4]

4. According to a survey carried out in 2019, the biomass of crabs in a particular region was estimated to be 5 350 MT. In 2014, the biomass was estimated to be 3 897 MT. Calculate the annual rate of growth of the crab’s population? [4]