A man carries 20 tiles from the ground to the roof of a house. Each tile has a mass of 1.2 kg. The roof of the house is 15 m above the ground.How much work does the man do against gravity on the tiles in carrying them to the roof?
Answers
Answer: W = - n m g h
Given data states that a laborer carries n bricks to a height h each of mass m. Therefore the work done will be given by the expression that is,
W = - Potential Energy ( P. E. )
Thereby, Potential energy is given by,
P. E. = m g h
\Rightarrow For each brick, we have P. E. = m g h and thereby for n bricks will be P. E. = n m g h
\Rightarrow Therefore, the work done is W = - n m g h,
where negative indicates work done against gravity, n is the number of bricks, m is the mass of each brick, g is the acceleration due to gravity and h is the height of the roof of the house.
Explanation:
Gravitational potential energy
When an object is lifted in a gravitational field, energy is transferred to a gravity store. This store is called gravitational potential energy.
gravitational potential energy = mass × height × gravitational field strength (g)
This is when:
gravitational potential energy is measured in joules (J)
mass is measured in kilograms (kg)
height is measured in metres (m)
gravitational field strength (g) is measured in newtons per kilogram (N/kg)
Example
Calculate the energy transferred to the gravity store when a woman of mass 60 kg climbs 4 rungs up a ladder. Each rung is 15 cm high.
First calculate the distance climbed in metres:
15 cm is 0.15 m
0.15 × 4 = 0.6 m
Then calculate the gravity store increase (the gravitational potential energy), remembering that g is 10 N/kg on Earth:
gravitational potential energy = mass × height × gravitational field strength (g)
gravitational potential energy = 60 × 0.6 × 10
gravitational potential energy = 360 J