An Akron falls from a tree it starting height was 12 m off the ground. at what height is the acorn’s potential energy equal to the acorn’s kinetic energy
To determine the height at which the acorn's potential energy is equal to its kinetic energy, we can use the principle of conservation of energy.
The potential energy (PE) of an object at a certain height is given by the formula PE = m * g * h, where m is the mass of the object, g is the acceleration due to gravity, and h is the height.
The kinetic energy (KE) of an object is given by the formula KE = (1/2) * m * v^2, where m is the mass of the object and v is the velocity.
Since we are assuming the acorn falls from rest, its initial velocity is zero, so its initial kinetic energy is also zero.
At the starting height of 12 m, the potential energy of the acorn is given by PE = m * g * h = m * 9.8 * 12 = 117.6 * m.
Now, we need to find the height at which the acorn's potential energy is equal to its kinetic energy (which is zero initially). Let's call this height H.
At height H, the potential energy is given by PE = m * g * H = 9.8 * H * m.
Since the kinetic energy is initially zero, we can equate the potential energy at height H to zero:
117.6 * m = 9.8 * H * m
Simplifying the equation by cancelling out the mass:
117.6 = 9.8 * H
Dividing both sides by 9.8:
H = 117.6 / 9.8
H ≈ 12 m
Therefore, the acorn's potential energy is equal to its kinetic energy at a height of approximately 12 meters.