Use the Law of conservation of energy to predict the final speed of a bowling ball dropped from the top of a 25.0 m tall building just before hitting the ground. ignore air resistance.
the gravitational potential energy becomes kinetic energy
m g h = 1/2 m v^2
v = √(2 g h)
22.1
To predict the final speed of the bowling ball, we can use the Law of Conservation of Energy. According to this law, the total mechanical energy of a system remains constant if no external forces, such as air resistance, are acting on it.
In this case, the initial mechanical energy of the bowling ball is solely in the form of potential energy because it is at rest at the top of the building. As it falls, this potential energy is converted into kinetic energy, and at the bottom of the building, all the potential energy is transformed into kinetic energy.
The equation for potential energy is given by:
Potential Energy (PE) = m * g * h
Where:
m is the mass of the object (bowling ball)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
h is the height or vertical distance (25.0 m in this case)
The equation for kinetic energy is given by:
Kinetic Energy (KE) = (1/2) * m * v^2
Where:
m is the mass of the object (bowling ball)
v is the final velocity (speed) of the object
Since the total mechanical energy of the system is conserved, we can set the initial potential energy equal to the final kinetic energy:
PE = KE
m * g * h = (1/2) * m * v^2
Simplifying the equation:
g * h = (1/2) * v^2
Now, plug in the given values:
9.8 m/s^2 * 25.0 m = (1/2) * v^2
245 = (1/2) * v^2
Multiply both sides by 2:
490 = v^2
Taking the square root of both sides:
v = √490
v ≈ 22.1 m/s
Therefore, the predicted final speed of the bowling ball just before hitting the ground is approximately 22.1 m/s.