At what height above ground must a body of mass 20kg be situated in order to have P.E= K.E by another body of mass 10kg moving with a velocity of 15m/s
20gh = 1/2 * 10 * 15^2
To find the height above the ground at which the potential energy (PE) of a body of mass 20 kg is equal to the kinetic energy (KE) of another body of mass 10 kg moving at a velocity of 15 m/s, we need to apply the conservation of mechanical energy.
The total mechanical energy of a system remains constant if no external forces, other than gravity, are acting on it. This means that the sum of potential energy and kinetic energy is constant.
In this scenario, the potential energy (PE) 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.
The kinetic energy (KE) is given by the formula:
KE = 0.5 * m * v^2
where m is the mass and v is the velocity.
Since we want the potential energy to be equal to the kinetic energy, we can set them equal to each other:
m * g * h = 0.5 * m * v^2
Now we can cancel out the mass on both sides of the equation:
g * h = 0.5 * v^2
Next, we can solve for h by isolating it:
h = (0.5 * v^2) / g
Plugging in the given values:
h = (0.5 * (15 m/s)^2) / 9.8 m/s^2
Simplifying:
h = (0.5 * 225 m^2/s^2) / 9.8 m/s^2
h = 112.5 m^2/s^2 / 9.8 m/s^2
h ≈ 11.48 meters
Therefore, the body of mass 20 kg must be situated at a height of approximately 11.48 meters above the ground in order for its potential energy to be equal to the kinetic energy of the 10 kg body moving with a velocity of 15 m/s.