Question

Some engineers have developed a device that provides lighting to rural areas with no access to grid electricity. The device is intended for indoor use. It is driven by gravity, and it works as follows: A bag of rock or sand is raised by human power to a higher location. As the bag descends very slowly, it powers a sprocket-wheel which also rotates slowly. A gear train mechanism converts this slow motion to high speed, which drives a DC generator. The electric output from the generator is used to power an LED bulb. Consider a gravity-driven LED bulb that provides 16 lumens of lighting. The device uses a 10-kg sandbag that is raised by human power to a 2-m height. For continuous lighting, the bag needs to be raised every 20 minutes. Using an efficacy of 150 lumens per watt for the LED bulb, determine (a) the velocity of the sandbag as it descends and (b) the overall efficiency of the device

Answer 1

Answer a): velocity of bag = 0.0017m/s

Explanation:

The device is 2m high and it is raised every 20min, this means that it takes 20mins to travel down from the 2m height.

20min = 20x60s = 1200s

Velocity down v = d/t

V = 2/1200 = 0.0017m/s

Answer b): efficiency of device is 65.44% approximately 65%

Explanation:

The work done by gravity to move the 10kg mass down = PE

PE = mgh

where m is mass 10kg,

g is acceleration due to gravity 9.81m/s2

h is the height 2m

PE = 10x9.81x2 = 196.2J

Power P = work done per unit time

P = 196.2J/1200s = 0.1635W

It takes 1W to produce 150lumen of lighting, this device produces 16lumen of lighting, therefore this device uses;

16/150 watt = 0.107W

Efficiency in % = power output over power input

E = 0.107/0.1635 x100% = 65.44%