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

• Shivam
In summary, the conversation discusses the use of an equation and assumptions to solve for potential energy in a collision scenario. The speaker initially gets the wrong answer due to a problem with significant figures, but eventually solves it by using a more precise value for speed. The conversation also touches on the importance of numerical analysis and the rules of significant figures.
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' }
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 ?

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.

Last edited:
jbriggs444 said:
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.

## 1. What is the total mass of the two balls?

The total mass of the two balls is 6kg.

## 2. What is the velocity of the balls?

The velocity of the balls is not specified in the question, so it cannot be determined.

## 3. What is the direction of motion for the balls?

The direction of motion for the balls is not specified in the question, so it cannot be determined. It could be moving in the same direction or opposite directions.

## 4. What is the momentum of each ball?

The momentum of each ball can be calculated using the formula p = mv, where p is momentum, m is mass, and v is velocity. However, since the velocity is not specified, the momentum cannot be determined.

## 5. What is the kinetic energy of the system?

The kinetic energy of the system can be calculated using the formula KE = 1/2mv^2, where KE is kinetic energy, m is mass, and v is velocity. However, since the velocity is not specified, the kinetic energy cannot be determined.

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