Question

Calculate the final speed of an object if its initial speed is 10 m / s. The object has a mass of 5 kg. Initially it has a height of 20 meters, and it goes down to a height of 15 m. There are no dissipative forces on the object.

Answer 1

By work-energy theorem, change in potential energy U = change in kinetic energy K

change in potential energy U = mgh

where m is mass, g is acceleration due to gravity and h is height difference between final position and

initial position

change in kinetic energy K = (1/2)m( v_f² - v_i² )

where v_f is final speed and v_i is initial speed

mgh = (1/2)m ( v_f² - v_i² )     or   ( v_f² - v_i² ) = ( 2 g h ) = ( 2 9.8 5 ) = 98 m²s^-2

v_f² = v_i² + 98 = 100 + 98 = 198

hence final speed v_f = = 14.07 m/s