# 0.3 Gravity and mechanical energy  (Page 5/9)

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If the suitcase falls off the cupboard, it will lose its potential energy. Halfway down the cupboard, the suitcase will have lost half its potential energy and will have only $9,8\phantom{\rule{2pt}{0ex}}J$ left. At the bottom of the cupboard the suitcase will have lost all it's potential energy and it's potential energy will be equal to zero.

Objects have maximum potential energy at a maximum height and will lose their potential energy as they fall.

A brick with a mass of $1\phantom{\rule{2pt}{0ex}}\mathrm{kg}$ is lifted to the top of a $4\phantom{\rule{2pt}{0ex}}m$ high roof. It slips off the roof and falls to the ground. Calculate the potential energy of the brick at the top of the roof and on the ground once it has fallen.

• The mass of the brick is $m=1\phantom{\rule{2pt}{0ex}}\mathrm{kg}$
• The height lifted is $h=4\phantom{\rule{2pt}{0ex}}m$

All quantities are in SI units.

• We are asked to find the gain in potential energy of the brick as it is lifted onto the roof.
• We also need to calculate the potential energy once the brick is on the ground again.
1. Since the block is being lifted we are dealing with gravitational potential energy. To work out $PE$ , we need to know the mass of the object and the height lifted. As both of these are given, we just substitute them into the equation for $PE$ .

2. $\begin{array}{ccc}\hfill PE& =& mgh\hfill \\ & =& \left(1\right)\left(9,8\right)\left(4\right)\hfill \\ & =& 39,2\phantom{\rule{0.166667em}{0ex}}\mathrm{J}\hfill \end{array}$

## Gravitational potential energy

1. Describe the relationship between an object's gravitational potential energy and its:
1. mass and
2. height above a reference point.
2. A boy, of mass $30\phantom{\rule{2pt}{0ex}}\mathrm{kg}$ , climbs onto the roof of a garage. The roof is $2,5\phantom{\rule{2pt}{0ex}}m$ from the ground. He now jumps off the roof and lands on the ground.
1. How much potential energy has the boy gained by climbing on the roof?
2. The boy now jumps down. What is the potential energy of the boy when he is $1\phantom{\rule{2pt}{0ex}}m$ from the ground?
3. What is the potential energy of the boy when he lands on the ground?
3. A hiker walks up a mountain, $800\phantom{\rule{2pt}{0ex}}m$ above sea level, to spend the night at the top in the first overnight hut. The second day he walks to the second overnight hut, $500\phantom{\rule{2pt}{0ex}}m$ above sea level. The third day he returns to his starting point, $200\phantom{\rule{2pt}{0ex}}m$ above sea level.
1. What is the potential energy of the hiker at the first hut (relative to sea level)?
2. How much potential energy has the hiker lost during the second day?
3. How much potential energy did the hiker have when he started his journey (relative to sea level)?
4. How much potential energy did the hiker have at the end of his journey?

## Kinetic energy

Kinetic Energy

Kinetic energy is the energy an object has due to its motion.

Kinetic energy is the energy an object has because of its motion. This means that any moving object has kinetic energy. The faster it moves, the more kinetic energy it has. Kinetic energy ( $KE$ ) is therefore dependent on the velocity of the object. The mass of the object also plays a role. A truck of $2 000\phantom{\rule{2pt}{0ex}}\mathrm{kg}$ , moving at $100\phantom{\rule{2pt}{0ex}}\mathrm{km}·\mathrm{hr}{}^{-1}$ , will have more kinetic energy than a car of $500\phantom{\rule{2pt}{0ex}}\mathrm{kg}$ , also moving at $100\phantom{\rule{2pt}{0ex}}\mathrm{km}·\mathrm{hr}{}^{-1}$ . Kinetic energy is defined as:

If potatoes cost Jane $1 per kilogram and she has$5 that could possibly spend on potatoes or other items. If she feels that the first kilogram of potatoes is worth $1.50, the second kilogram is worth$1.14, the third is worth $1.05 and subsequent kilograms are worth$0.30, how many kilograms of potatoes will she purchase? What if she only had $2 to spend? Susan Reply cause of poverty in urban DAVY Reply QI: (A) Asume the following cost data are for a purely competitive producer: At a product price Of$56. will this firm produce in the short run? Why Why not? If it is preferable to produce, what will be the profit-maximizing Or loss-minimizing Output? Explain. What economic profit or loss will the
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