A worker has to move a rock with mass 50 kg on a stairway from the first floor to the second floor of a house. The second floor is 4.6 m above the first floor and the stairway has 18 steps. The rock is lifted from step to step. How much energy (in Joule) has to be spend to move the rock up the stairway.
Energy = mgh
h=difference in elevations between floors.
The number of steps is irrelevant because it's the total difference in elevations that counts.
If m is in kg, g in m/s², and h in metres, the result mgh is in joules.
To calculate the energy required to move the rock up the stairway, we need to consider the work done against gravity.
The work done against gravity is given by the formula:
Work = Force × Distance × cos(θ)
Where,
Force = Mass × Acceleration due to gravity
Distance = Vertical displacement (height) of the rock
θ = Angle between the force and displacement (in this case, the angle is 0 degrees as the force and displacement are in the same direction)
First, let's calculate the force acting on the rock:
Force = Mass × Acceleration due to gravity
Force = 50 kg × 9.8 m/s² (standard acceleration due to gravity)
Force = 490 N
Next, let's calculate the vertical displacement (height) of the rock:
Vertical Displacement = Number of steps × Height of each step
Vertical Displacement = 18 steps × 4.6 m/step (height of each step)
Vertical Displacement = 82.8 m
Now, we have all the values we need to calculate the work done:
Work = Force × Distance × cos(θ)
Work = 490 N × 82.8 m × cos(0°)
Work = 40452 Joules
Therefore, the worker would need to spend approximately 40452 Joules of energy to move the rock up the stairway.