Distinguish between gravitational potential energy and electric potential energy.

Question 41

(a) Distinguish between gravitational potential energy and electric potential energy. [2]

(b) A body of mass m moves vertically through a distance h near the Earth’s surface. Use the defining equation for work done to derive an expression for the gravitational potential energy change of the body. [2]

(c) Water flows down a stream from a reservoir and then causes a water wheel to rotate, as shown in Fig. 4.1.

Fig. 4.1

As the water falls through a vertical height of 120 m, gravitational potential energy is converted to different forms of energy, including kinetic energy of the water. At the water wheel, the kinetic energy of the water is only 10% of its gravitational potential energy at the reservoir.

(i) Show that the speed of the water as it reaches the wheel is 15 m s^-1. [2]

(ii) The rotating water wheel is used to produce 110 kW of electrical power. Calculate

the mass of water flowing per second through the wheel, assuming that the production of electric energy from the kinetic energy of the water is 25% efficient. [3]

Reference: Past Exam Paper – November 2011 Paper 21 Q4

Solution:

(a) Electric potential energy is the energy (stored) when a charge is moved due to work done in an electric field while gravitational potential energy is the energy (stored) when a mass is moved due to work done in gravitational field.

(b)

Work done = Force × distance moved (in the direction of force)

and Force = mg                                                                                  

(GPE =) mg × h                      OR mg × Δh                                       

(c)

(i)

{As the water falls, GPE is converted into KE of the water.

However, the process is only 10% efficient. That is, only 10% (= 0.1) of the GPE is converted into KE.

0.1 × Gravitational potential energy = Kinetic energy}

0.1 × mgh = ½ mv²                

0.1 × m × 9.81 × 120 = ½ mv²

{m can be eliminated.

Speed v = √(2×0.1×9.81×120) }

Speed of water, v = 15.3 m s^-1

(ii)

Power, P = ½ mv² / t                                                              

{Power = energy / time

The falling water has kinetic energy

Kinetic energy = ½ mv²

Power = (½ mv²) / t = ½ × (m/t) × v²  

where m/t is the mass of water flowing per second}

{Only 25% of the kinetic energy produces electric energy.

Electrical power = 0.25 × ½ × (m/t) × v² = 110×10³ W

0.25 × ½ × (m/t) × v² = 110×10³

(m/t) = 110×10³ / (0.25×0.5×15.3²)}

Mass of water flowing per second: m/t = (110×10³) / (0.25×0.5×15.3²)

m/t = 3760 kg s^-1