Question

The bird perched on the swing shown below has a mass of 54.3 g, and the base of the swing, y = 7.65 cm below the hook, has a mass of 140 g. The swing and bird are originally at rest, and then the bird takes off horizontally at 2.10 m/s. How high will the base of the swing rise above its original level? Disregard friction.

Answer 1

Since no external force acts on the system (bird+swing), the momentum must remain conserved

initial velocities of both the bird and the swing is zero. Let their final velocities be denoted by 'u' and 'v' respectively.

Using, conservation of momentum,

54.3*0 + 140*0 = 54.3*u + 140*v

v = -0.8145 m/s

This is the horizontal velocity of the swing just as the bird leaves the swing

-ve sign represents that the velocity of the swing is in the opposite direction from the bird

Now the kinetic energy of the swing will be converted to its potential energy

0.5mv² = mgh

h = 0.5v² = 0.5*0.8145*0.8145

h = 0.3317 meters