A slingshot will shoot a 10-g pebble 22.0 m straight up. (a) How much potential energy is stored in the slingshot’s rubber band? (b) With the same potential energy stored in the rubber band, how high can the slingshot shoot a 25-g pebble? (c) What physical effects did you ignore in solving this problem?
Solution 18E a) Mass of the pebble is 10 g. It can reach a height of 22 meters by a slingshot. The gravitational potential energy it would acquire there is, G.P.E = mgh = 0.01 × 9.8 × 22 = 2.156 J . As we know the conservation of mechanical energy, the potential energy stored in the rubber band must have converted into the kinetic energy of the pebble and then again would have converted to gravitational potential energy by reaching the height of 22 meters. So, the potential energy stored in the rubber band must be 2.156 J. b) With the same potential energy, a 25 g pebble would reach a height of, 2.156 J = mgh 2.156 = 0.025 × 9.8 × h h = 2.156 / (0.025 × 9.8) = 2.156 / 0.245 = 8.8 meters. It would reach a height of 8.8 meters. c) Here we have ignored the air resistance for which the mechanical energy could not have conserved. The total energy is always conserved, but the air friction would have increased the heat energy which would have been a decrease in mechanical energy.