At what height above the ground must a body of mass 10kg besituated in order to have potentral energy possed by another body of mass 10kg maining with velocity of 10ms
m g h = 1/2 m v²
h = v² / (2 g)
To determine the height at which a body of mass 10kg must be situated in order to have potential energy equal to the kinetic energy possessed by another body of mass 10kg moving with a velocity of 10m/s, we can use the principles of conservation of mechanical energy.
The potential energy of an object at a certain height is given by the formula:
Ep = mgh
Where:
Ep is the potential energy
m is the mass of the object
g is the acceleration due to gravity
h is the height
The kinetic energy of an object is given by the formula:
Ek = 0.5 * m * v^2
Where:
Ek is the kinetic energy
m is the mass of the object
v is the velocity
Based on the conservation of mechanical energy, we can equate these two energies:
Ep = Ek
mgh = 0.5 * m * v^2
Since the mass of both objects is given as 10kg, we can cancel out the "m" terms:
10 * g * h = 0.5 * 10 * 10^2
Simplifying the equation further:
10 * g * h = 0.5 * 10 * 100
10 * g * h = 0.5 * 1000
10 * g * h = 500
Dividing both sides by 10 * g:
h = 500 / (10 * g)
h = 500 / (10 * 9.8)
h ≈ 5.1 meters
Therefore, the body of mass 10kg must be situated at a height of approximately 5.1 meters above the ground to have potential energy equal to the kinetic energy possessed by the other body of the same mass moving at a velocity of 10m/s.