Two balls of mass 4kg and 2 kg are moving in 1-D, answer the following

[Shivam]

Homework Statement

Two balls of mass 4kg and 2kg are moving with speed 10 m/s and 8 m/s, respectively with ball of heavier mass behind the lighter ball. The two balls collide each other elastically. Answer the following questions:
a) The common velocity of the system of balls during collision will be
b) Maximum potential energy stored in the system of two balls during the collision will be about
P.S
Answers- a) 9.3m/s, b) 2.6 J,( according to the book)

Relevant Equations

Conservation of linear Momentum.

My attempt-
a) used equation { MV + mv = (M+m) V' }
and got the right answer.
b) I assumed that potential energy was asked for when the two balls were moving together with velocity 9.3m/s, so
I used that when before the collision K.E( of m) + K.E( of M) will be equal to K.E(of M+m) +P.E( of M+m) or

K.E(m) + K.E(M) = K.E(M+m) +P.E(M+m)

But i got the wrong answer, i got P.E =4.53 , why this is wrong ?

 

[jbriggs444]

Try retaining more digits in the intermediate results. You are computing the difference between two large and nearly equal numbers. Slight errors in those numbers will produce significant errors in the computed result.

Alternately, there is a different way of computing the result that avoids this ill-conditioning problem. What is the initial kinetic energy of each ball in the center-of-mass frame?

Welcome to the world of numerical analysis!

Edit: The rules of significant figures could have been a warning here. The figures for energy would have involved a result of about 260 Joules. The computation would have involved an input, "9.3" which was good to two decimal places. Accordingly, that computed result was good to only 2 significant figures [An uncertainty of plus or minus 10 joules]. When you subtracted, the rule of significant figures is that you discard all insignificant places. None of the digits in the computed result of 4.53 Joules are significant.

 

[Shivam]

Try retaining more digits in the intermediate results. You are computing the difference between two large and nearly equal numbers. Slight errors in those numbers will produce significant errors in the computed result.

Alternately, there is a different way of computing the result that avoids this ill-conditioning problem. What is the initial kinetic energy of each ball in the center-of-mass frame?

Welcome to the world of numerical analysis!

Edit: The rules of significant figures could have been a warning here. The figures for energy would have involved a result of about 260 Joules. The computation would have involved an input, "9.3" which was good to two decimal places. Accordingly, that computed result was good to only 2 significant figures [An uncertainty of plus or minus 10 joules]. When you subtracted, the rule of significant figures is that you discard all insignificant places. None of the digits in the computed result of 4.53 Joules are significant.

Thanx for the Welcome, and you were right, the actual value of speed was 9.33333333 and i got the right answer using that.