Determine the mechanical energy of a bird of mass 200g flying at 12m/s at a height of 50m above the ground
We need to find the mechanical energy of the bird which is equal to the sum of its kinetic energy (due to its motion) and potential energy (due to its height above the ground).
Kinetic energy = 1/2 * mass * velocity^2
Potential energy = mass * gravity * height
where mass is in kilograms, velocity in meters per second, height in meters and gravity is 9.81 m/s^2.
Converting the mass of the bird from grams to kilograms:
mass = 200g = 0.2 kg
Kinetic energy = 1/2 * 0.2 kg * (12 m/s)^2 = 14.4 joules
Potential energy = 0.2 kg * 9.81 m/s^2 * 50 m = 98.1 joules
Mechanical energy = Kinetic energy + Potential energy
Mechanical energy = 14.4 J + 98.1 J = 112.5 J
Therefore, the mechanical energy of the bird is 112.5 joules.
To determine the mechanical energy of the bird, we need to consider both its kinetic energy and potential energy.
1. Calculate the kinetic energy:
The kinetic energy (KE) of an object is given by the equation:
KE = (1/2) * mass * velocity^2
Given:
Mass of the bird = 200g = 0.2kg
Velocity of the bird = 12m/s
Plugging these values into the formula:
KE = (1/2) * 0.2kg * (12m/s)^2
= (1/2) * 0.2kg * 144m^2/s^2
= 14.4 Joules
2. Calculate the potential energy:
The potential energy (PE) of an object at a height above the ground is given by the equation:
PE = mass * gravitational acceleration * height
Given:
Mass of the bird = 0.2kg
Gravitational acceleration (g) = 9.8m/s^2 (approximate value)
Height of the bird = 50m
Plugging these values into the formula:
PE = 0.2kg * 9.8m/s^2 * 50m
= 98 Joules
3. Calculate the total mechanical energy:
The total mechanical energy (ME) of the bird is the sum of its kinetic energy and potential energy:
ME = KE + PE
= 14.4 Joules + 98 Joules
= 112.4 Joules
Therefore, the mechanical energy of the bird is 112.4 Joules.
To determine the mechanical energy of the bird, we need to consider two forms of energy: kinetic energy and potential energy.
Kinetic Energy:
The kinetic energy of an object can be calculated using the formula:
KE = (1/2) * m * v^2,
where KE is the kinetic energy, m is the mass, and v is the velocity.
Given:
m = 200g = 0.2 kg (since 1 kg = 1000 g)
v = 12 m/s
Plugging in the values, we can calculate the kinetic energy:
KE = (1/2) * 0.2 kg * (12 m/s)^2
= 0.2 kg * 144 m^2/s^2
= 28.8 Joules
Potential Energy:
The potential energy of an object in a gravitational field can be calculated using the formula:
PE = m * g * h,
where PE is the potential energy, m is the mass, g is the acceleration due to gravity, and h is the height.
Given:
m = 200g = 0.2 kg
g = 9.8 m/s^2 (standard gravity)
h = 50 m
Plugging in the values, we can calculate the potential energy:
PE = 0.2 kg * 9.8 m/s^2 * 50 m
= 98 Joules
Mechanical Energy:
The mechanical energy of an object is the sum of its kinetic energy and potential energy:
ME = KE + PE
Plugging in the values we calculated earlier:
ME = 28.8 Joules + 98 Joules
= 126.8 Joules
Therefore, the mechanical energy of the bird is approximately 126.8 Joules.