A 3-kg stone is dropped from height of 100 m. Find its kinetic and potential energies when it is halfway to the ground.
Iunderstand that KE=1/2mv^2 and PE=mgh;however, I do I figure the Velocity when only the mass and the height is given...
*How do I figure the Velocity.....
To find the kinetic and potential energies of the stone when it is halfway to the ground, we first need to determine the height at this point.
Given:
Mass (m) = 3 kg
Initial height (h) = 100 m
The midpoint is reached when the stone has fallen half the distance, which is 100 m / 2 = 50 m.
To find the potential energy (PE) at this height, we can use the formula:
PE = m * g * h
where:
m is the mass of the stone
g is the acceleration due to gravity (approximately 9.8 m/s²)
h is the height
Substituting the given values:
PE = 3 kg * 9.8 m/s² * 50 m = 1470 Joules
To find the kinetic energy (KE) at this height, we can use the equation:
KE = 0.5 * m * v²
where:
m is the mass of the stone
v is the velocity of the stone
To determine the velocity at this height, we can use the conservation of energy principle. At the top (initial) height, the potential energy is equal to the kinetic energy. Therefore, we can equate the potential energy at the initial height to the sum of the potential energy and kinetic energy at the midpoint:
PE(initial) = PE(midpoint) + KE
Since PE(initial) = m * g * h, where h = 100 m, and we now know that PE(midpoint) = 1470 J (as calculated previously), we can rearrange the equation to solve for KE:
KE = PE(initial) - PE(midpoint)
Substituting the values:
KE = (3 kg * 9.8 m/s² * 100 m) - 1470 J = 2940 J.
Therefore, when the stone is halfway to the ground, its potential energy is 1470 J and its kinetic energy is 2940 J.