A ball of mass 8kg falls from rest from height of 100m. Neglecting air resistance, calculate its kinetic energy after falling of a distance of 30m/s^2
I assume you mean it fell 30 meters
m g h = 8 * 9.81 * 30 Joules
P.E.= Mgh = 8*9.8*100 = 7840 J.
P.E. = Mgh = 8*9.8*(100-30) = 5488 J. = P.E. after falling 30 m.
K.E. = 7840-5488 = 2352 J.
2400j
To calculate the kinetic energy of the ball, we need to consider the work-energy principle. According to this principle, the work done on an object is equal to the change in its kinetic energy.
First, let's find the work done on the ball as it falls a distance of 30 meters. The work done by gravity can be calculated using the formula:
Work = force * distance * cosine(angle)
Since the ball is falling vertically and the force of gravity is acting straight downward, the angle between the force of gravity and the direction of motion is 0 degrees. Therefore, the cosine of 0 degrees is 1.
Now, let's calculate the force of gravity acting on the ball. The force of gravity can be calculated using Newton's second law:
Force = mass * acceleration
The mass of the ball is given as 8 kg, and the acceleration is given as 30 m/s^2.
Force = 8 kg * 30 m/s^2 = 240 N (Newton)
Now that we know the force and distance, we can calculate the work done on the ball:
Work = 240 N * 30 m = 7200 J (Joules)
Since work done is equal to the change in kinetic energy, the ball's kinetic energy after falling a distance of 30 meters is 7200 Joules.