Energy

1. How much energy would your body need to provide for climbing a hill 500m high

(use your own mass as 70kg and g = 10/kg)

Energy needed by the body is equal to the gain in Potential Energy E_p

E_p = mgh

E_p = 10 x 70 x 500

E_p = 350 000 J

2. A catapult is used to fire a stone of mass 50g vertically to a height of 4.05m. Calculate the

i) potential energy gained by the stone.

E_p = mgh

m = 50 g = 50 / 1000 = 0.05 kg

E_p = 0.05 x 10 x 4.05

E_p = 2.025 J

ii) The speed of the stone as it leaves the catapult.

From the conservation of energy all the potential gained = all the kinetic energy lost

2.025 = 1/2 mv²

v² = [2 x 2.025] / m

v² = 4.05 / 0.05

v² = 81

v = sqrt 81 = 9 m/s

3. The sun's source of energy is nuclear fusion reaction in which mass is converted to energy. The energy E

converted by a loss of mass m is given by the Einstein equation

E = mc²

where c is the speed of light in a vacuum (3 x 10 ⁸ m/s). The sun is losing mass at a rate of 2 x 10 ⁹ kg

every second.

i) Calculate the energy released every second

E = 2 x 10 ⁹ x (3 x 10 ⁸)²

E = 18 x 10 ²⁵ J