00:01
Here in this question, the kinetic energy can be calculated using the formula, can be calculated using the formula half mgh, where m is the mass, g is acceleration due to gravity and h is the height.
00:13
So the kinetic energy is calculated as 0 .5 into mass, that is 80 kg into acceleration due to gravity, that is 9 .8 meter per second square into height, that is 0 .032 meters and this comes out to be 12 .57 joules.
00:31
Now the strain energy in the bar can be calculated using the formula the strain energy strain energy that is represented by s e is 0 .5 sigma square v by e where sigma is the stress v is the volume is the young's modulus the volume of the bar can be calculated using the formula v is equals to pi r square l where r is the radius and l is the length so volume v is equals to pi into 0 .008 sorry 0 .008 meter square into 3 .2 meters and this comes out to be 0 .00064 meter cube now substituting the values into the strain energy formula and solve for sigma.
01:22
Sigma is equals to square root of 2 into se into e by v and that is equals to square root of 2 into 12 .57 into 205 upon volume that is 0 .00064.
01:41
So sigma is equals equals to 365 .5 mega pascals.
01:46
Now if the bar is turned down to half the diameter along its length, the volume will be half and the stress will increase by a factor of square root of 2...