Two balls are connected to 60-cm-long light strings and the other ends of the st
ID: 2278446 • Letter: T
Question
Two balls are connected to 60-cm-long light strings and the other ends of the
strings are fixed together as shown in the figure. One of the balls has a mass of 2.0 kg and is raised up and to the right until it is 12.0 cm higher than the other ball, which has a mass of 3.0 kg. The upper ball is released from rest and sticks to the lower ball when they collide. Find the (a) frequency, (b) max angular displacement, (c) max height, and (d) max speed of the subsequent motion.
Two balls are connected to 60 - cm - long light strings and the other ends of the strings are fixed together as shown in the figure. One of the balls has a mass of 2.0 kg and is raised up and to the right until it is 12.0 cm higher than the other ball, which has a mass of 3.0 kg. The upper ball is released from rest and sticks to the lower ball when they collide. Find the (a) frequency, (b) max angular displacement, (c) max height, and (d) max speed of the subsequent motion.Explanation / Answer
a. Frequency of pendulum = sqrt( g/L)/2pi = sqrt( 9.81/0.6) /2 * 3.14 = 0.6438 Hz ( cycles per second)
b. maximum height reached = 4.8 cm ( using conservation of energy principle)
Maximum angular displacement= cos-1 ( (60-4.8)/60) = cos-1( 55.2/60) = 23.07 degrees
c.let Maximum height reached be 'h',
At when masses are at maximum height their velocity will be zero just like initial moment. So potential energy for two instants will be same, ( Potential engery assumed zero at lowest point)
2* 9.81* 12 = 5 * 9.81 * h
this gives h= 4.8 cm
d. Speed will be maximum when potential energy is minimum, that is when masses are at lowest point in their trajectory.
decrease in potential energy = rise in kinetic energy
2* 9.81* 0.12 = 5* (speed2)
Maximum speed = 0.686 m/s