An object of a mass 50kg released from a height of 60m what energy does the body strike the ground (take g=10m/s
initial PE = mgh = final KE
To find the energy with which the object strikes the ground, we need to calculate the potential energy and convert it into kinetic energy.
1. Calculate the potential energy:
Potential Energy = mass * gravity * height
Potential Energy = 50 kg * 10 m/s² * 60 m
Potential Energy = 30,000 Joules (J)
2. Since we assume there is no energy lost due to air resistance, the potential energy will be completely converted into kinetic energy as the object falls.
3. Therefore, the kinetic energy is equal to the potential energy:
Kinetic Energy = 30,000 Joules (J)
Hence, the object will strike the ground with 30,000 Joules of energy.
To determine the energy that the object strikes the ground with, we need to calculate its potential energy when it was at the initial height and then convert it into kinetic energy when it reaches the ground.
The potential energy (PE) of an object is given by the formula: PE = m * g * h, where m is the mass, g is the acceleration due to gravity, and h is the height.
Given:
Mass (m) = 50 kg
Height (h) = 60 m
Acceleration due to gravity (g) = 10 m/s^2
First, we calculate the potential energy at the initial height:
PE = m * g * h
PE = 50 kg * 10 m/s^2 * 60 m
PE = 30,000 J (joules)
Since energy is conserved, this potential energy will be converted into kinetic energy when the object reaches the ground.
The kinetic energy (KE) of an object is given by the formula: KE = (1/2) * m * v^2, where m is the mass and v is the velocity.
At the moment of impact, the object's potential energy is completely converted into kinetic energy (assuming no other energy losses like air resistance).
Therefore, to calculate the velocity (v), we can equate the potential energy to the kinetic energy:
KE = (1/2) * m * v^2
PE = KE
30,000 J = (1/2) * 50 kg * v^2
Simplifying the equation:
v^2 = (2 * PE) / m
v^2 = (2 * 30,000 J) / 50 kg
v^2 = 1,200 m^2/s^2
Taking the square root of both sides to solve for v:
v = √(1,200 m^2/s^2)
v ≈ 34.64 m/s
So, the object will strike the ground with a velocity of approximately 34.64 m/s.
To calculate the kinetic energy (KE), we substitute the velocity (v) back into the equation:
KE = (1/2) * m * v^2
KE = (1/2) * 50 kg * (34.64 m/s)^2
KE ≈ 34,640 J (joules)
Therefore, the object will strike the ground with approximately 34,640 joules of kinetic energy.