you and a flight attendant toss a ball back and forth in an airplane in flight. Does the kinetic energy of the ball depend on the speed of the airplane? Defend you answer.
KE=mv²/2
“v” is the speed of the ball in the frame of reference “connected with” the airplane
Yes, the kinetic energy of the ball does depend on the speed of the airplane. To understand why, let's consider the definition of kinetic energy first.
Kinetic energy (KE) is the energy possessed by an object due to its motion. It is given by the formula KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity or speed.
In the scenario you described, both you and the flight attendant are tossing the ball back and forth inside the airplane. Now, when the airplane is stationary on the ground, the ball has no kinetic energy because there is no movement.
However, as the airplane takes off and gains speed, the ball also starts moving along with it. As a result, the velocity (v) of the ball increases. Since the kinetic energy is directly proportional to the square of the velocity, an increase in the airplane's speed will lead to an increase in the velocity of the ball, and consequently, its kinetic energy.
Therefore, if the airplane's speed increases, the kinetic energy of the ball will also increase, and if the airplane slows down or comes to a stop, the ball's kinetic energy will decrease accordingly.
In conclusion, the kinetic energy of the ball depends directly on the speed of the airplane because the ball's velocity is directly affected by the airplane's motion.