An object of mass 26 kg is thrown straight upwards from the ground at 27 m/s. Due to air resistance (a non-conservative force), the object loses some of its initial energy during its trip to reach maximum height and only travels to a height above the ground of 16.3 meters. What percentage of its initial energy is lost to air resistance during its flight to maximum height?
Without air resistance
KE=PE
mv²/2=mgh
h=v²/2g =27²/2•9.8 = 37.2 m
(mgh-mgh1)/mgh = (h-h1)/h= (37.2-16.3)/37.2=0.56
56%
To find the percentage of initial energy lost to air resistance during the flight to maximum height, we need to calculate the initial energy and the final energy at maximum height.
1. Calculate the initial energy:
The initial energy is given by the equation for kinetic energy:
Kinetic Energy = (1/2) * mass * velocity^2
Given:
Mass (m) = 26 kg
Velocity (v) = 27 m/s
Kinetic Energy (initial) = (1/2) * 26 kg * (27 m/s)^2
2. Calculate the final energy at maximum height:
At maximum height, the only energy the object has is its potential energy. Potential energy is given by the equation:
Potential Energy = mass * gravitational acceleration * height
Given:
Mass (m) = 26 kg
Gravitational acceleration (g) = 9.8 m/s^2
Height (h) = 16.3 m
Potential Energy (final) = 26 kg * 9.8 m/s^2 * 16.3 m
3. Calculate the percentage of energy lost:
Percentage of energy lost = ((initial energy - final energy) / initial energy) * 100
Percentage of energy lost = ((Kinetic Energy (initial) - Potential Energy (final)) / Kinetic Energy (initial)) * 100
Now, plug in the values we calculated earlier and solve for the percentage:
Percentage of energy lost = ((0.5 * 26 kg * (27 m/s)^2) - (26 kg * 9.8 m/s^2 * 16.3 m)) / (0.5 * 26 kg * (27 m/s)^2) * 100
Evaluating this equation will give you the percentage of energy lost to air resistance during the flight to maximum height.