into usable mechanical energy, would the chocolate give her the energy required to climb up a 1000 ft hill?

Solution

First let us calculate the energy content of the chocolate. This is 0.05 × 4700 × 4.1868 kJ 984 kJ. Note that the energy content of foods are usually measured in kilocalories but the prefix kilo is very often dropped and the units are loosely referred to as ‘Calories’. The average person's daily intake is from 2000 to 4000 kcal. The energy used up in climbing the hill is not easy to assess. Some will be used in overcoming friction (converted into heat energy) but we can assume that the largest part will go into the increase in gravitational potential energy which is given by mass × g × height = (8 × 14 × 0.4536) × 9.807 × (1000 × 0.3048) J 151.9 kJ. We conclude that the chocolate gives ample energy for the climb.

Exercises

4.18A man is walking along a road at a speed of 4 miles h −1 . Calculate his speed in metres per second (m s −1 ).

Alternative units of force which are sometimes used are the poundal (symbol, pdl) (defined as the

4.19force which gives a 1 lb mass an acceleration of 1 ft s −2 ) and the dyne (symbol, dyn) (defined as the force which gives a 1 g mass an acceleration of 1 cm s −2 ). Calculate the number of poundals equivalent to 1 N and the number of dynes equivalent to 1 pdl.

4.20In a high-pressure gas flow, the flow rate is sometimes quoted in ‘millions of cubic feet per day’ and at other times in ‘cubic metres per second’. Calculate the conversion factors.

4.21One athletics track has a perimeter of 400 m while another has a perimeter of 440 yd. Which is longer?

4.22Calculate the Earth's rotational speed in radians per second (rad s −1 ) and its speed in orbit (mph) taking our mean distance from the sun to be 93 million miles.

4.9 Dimensions

In mechanics, all quantities can be expressed in terms of the fundamental quantities mass, length and time, denoted by the symbols M, L and T. Any other physical quantity will be a combination of these three and the particular combination is referred to as the ‘dimensions’ of that physical quantity. For example, the dimensions of area are L 2 and the dimensions of density are ML −3 (or M/L 3 ). Note that dimensions are independent of the units used. For example, speed has dimensions LT −1 (or L/T) but could be measured in miles

per hour or metres per second. It is convenient to use square brackets [ ] to denote ‘the dimensions of …’ so that

Note that some quantities are dimensionless, in other words pure numbers, e.g. [angle] = LL −1 = L°. From Newton's second law of motion, force = mass × acceleration; so the dimensions of force are MLT