How much power is required to lift a 25kg box to the top of a 4 meter flight of stairs in 3.5 seconds
To determine the power required to lift a 25kg box to the top of a 4-meter flight of stairs in 3.5 seconds, we need to first understand the concept of power.
Power is the rate at which work is done or energy is transferred. It is calculated by dividing the work done by the time taken. Mathematically, power (P) is expressed as:
P = W/t
Where:
P = Power (in watts)
W = Work done (in joules)
t = Time taken (in seconds)
In our scenario, the work done is equal to the gravitational potential energy gained by lifting the box to the top of the stairs. Gravitational potential energy is calculated using the formula:
PE = mgh
Where:
PE = Potential energy (in joules)
m = Mass of the object (in kilograms)
g = Acceleration due to gravity (approximately 9.8 m/s^2)
h = Height (in meters)
Substituting the given values, we have:
PE = (25 kg) x (9.8 m/s^2) x (4 m)
PE = 980 joules
Since the work done is equal to the potential energy, W = PE, we have:
W = 980 joules
Now, let's calculate the power using the formula mentioned earlier:
P = W/t
P = (980 joules) / (3.5 seconds)
Calculating this, we get:
P ≈ 280 watts
Therefore, approximately 280 watts of power is required to lift a 25kg box to the top of a 4-meter flight of stairs in 3.5 seconds.