A ball tossed upward will return to the same point with the same initial speed when air resistance is negligible. When air resistance is not negligible, how does the return speed compare with its initial speed?
Solution 39E Introduction In this problem we will use the concept conservation of energy to answer and the fact that due to air resistance the ball will lose some energy to whether the ball will have same velocity or not. Solution Step 1: Explanation. When I am tossing some ball upwards, I am throwing the ball with some velocity. That means, initially I am giving some kinetic energy to the ball. Now if there is no air resistance, as the ball goes up, the kinetic energy will be converted to potential energy and at the top of the flight, the all the kinetic energy will be converted to potential energy and the ball have only potential energy. And when, now when the ball is coming down, the potential energy will now, again, be converted to kinetic energy and at the starting point all the potential energy will be converted to kinetic energy again. Since, since the gravity is a conservative force, the total energy of the ball will remain always conserved. And since the kinetic energy of the ball depends on the velocity and the mass of the ball, the velocity will be same. Now when there is air resistance, which is not a conservative force, the ball will loose some energy during it’s flight due to friction. Now when the ball returns to the initial position, the ball will have only kinetic energy, but the ball has already lost some energy due to air resistance. So at this point the kinetic energy is less than the initial energy. Hence the velocity will be less than the initial velocity.