Special Names for Kinetic Energy (a) A player lobs a mid-court pass with a 624-g basketball, which covers 15 m in 2 s. What is the basketball's horizontal translational kinetic energy while in flight? (b) An average molecule of air, in the basketball in part (a), has a mass of 29 u, and an average speed of 500 m/s, relative to the basketball. There are about 3 Ă— 1023 molecules inside it, moving in random directions, when the ball is properly inflated. What is the average translational kinetic energy of the random motion of all the molecules inside, relative to the basketball? (c) How fast would the basketball have to travel relative to the court, as in part (a), so as to have a kinetic energy equal to the amount in part (b)? Strategy In part (a), first find the horizontal speed of the basketball and then use the definition of kinetic energy in terms of mass and speed, K = mv2. Then in part (b), convert unified units to kilograms and then use K = {mu2 to get the average translational kinetic energy of one molecule, relative to the basketball. Then multiply by the number of molecules to get the total result. Finally, in part (c), we can substitute the amount of kinetic energy in part (b), and the mass of the basketball in part (a), into the definition K = { mu2, and solve for v. Solution 1. The horizontal speed is (15 m)/(2 s), so the horizontal kinetic energy of the basketball is 1 (0.624 kg) (7.5 m/s)2 = 17.6 J. 1 (29 u) (1.66 Ă— 10-27 kg/u) (500 m/s)2 = 6.02 Ă— 10-21 J, 2. The average translational kinetic energy of a molecule is and the total kinetic energy of all the molecules is (3 x 1023) (6.02 Ă— 10-21 J) = 1.80 kJ. 3. v = \/2 (1.8 kJ) / (0.624kg) = 76.0m/s.
Significance In part (a), this kind of kinetic energy can be called the horizontal kinetic energy of an object (the basketball), relative to its surroundings (the court). If the basketball were spinning, all parts of it would have not just the average speed, but it would also have rotational kinetic energy. Part (b) reminds us that this kind of kinetic energy can be called internal or thermal kinetic energy. Notice that this energy is about a hundred times the energy in part (a). How to make use of thermal energy will be the subject of the chapters on thermodynamics. In part (c), since the energy in part (b) is about 100 times that in part (a), the speed should be about 10 times as big, which it is (76 compared to 7.5 m/s). Access for free at https://openstax.org/books/university-physics-volume-1/pages/1-introduction. R6_8 2/2 points (graded) (a) A car and a truck are each moving with the same kinetic energy. Assume that the truck has more mass than the car. Which has the greater speed? The car. The truck. Both have the same kinetic energy. V