Physics for Scientists and Engineers
Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 8, Problem 65P

(a)

To determine

The proof that v1f=v2i and v2f=v1i when two masses are equal.

(a)

Expert Solution
Check Mark

Answer to Problem 65P

It is proved that v1f=v2i and v2f=v1i when two masses are equal.

Explanation of Solution

Formula used:

The expression for the final velocity of first object is given by,

  v1f=m1m2m1+m2v1i+2m2m1+m2v2i

The expression for the final velocity of second object is given by,

  v2f=2m1m1+m2v1i+m2m1m1+m2v2i

Calculation:

The expression for the final velocity of first object is calculated as,

  v1f=m1m2m1+m2v1i+2m2m1+m2v2i=m1m1m1+m1v1i+2m1m1+m1v2i=2m12m1v2i=v2i

The expression for the final velocity of second object is given by,

  v2f=2m1m1+m2v1i+m2m1m1+m2v2i=2m1m1+m1v1i+m1m1m1+m2v2i=2m12m1v1i=v1i

Conclusion:

Therefore, It is proved that v1f=v2i and v2f=v1i when two masses are equal.

(b)

To determine

The proof that v1fv1i and v2f0 when m2>>m1 and v2i=0 .

(b)

Expert Solution
Check Mark

Answer to Problem 65P

It is proved that v1fv1i and v2f0 when m2>>m1 and v2i=0 .

Explanation of Solution

Calculation:

The expression for the final velocity of first object is calculated as,

  v1f=m1m2m1+m2v1i+2m2m1+m2v2i=m1m2m1+m2v1i+2m2m1+m2(0)= m 1 m 2 1 m 1 m 2 +1v1i010+1v1i

Further simplify the above,

  v1fv1i

The expression for the final velocity of second object is given by,

  v2f=2m1m1+m2v1i+m2m1m1+m2v2i=2m1m1+m2v1i+m2m1m1+m2(0)=2( m 1 m 2 )( m 1 m 2 )+1v1i2(0)(0)+1v1i

Further simplify the above,

  v2f0

Conclusion:

Therefore, it is proved that v1fv1i and v2f0 when m2>>m1 and v2i=0 .

(c)

To determine

The proof that v1fv1i and v2f2v1i when m1>>m2 and v2i=0 .

(c)

Expert Solution
Check Mark

Answer to Problem 65P

It is proved that v1fv1i and v2f2v1i when m1>>m2 and v2i=0 .

Explanation of Solution

Calculation:

The expression for the final velocity of first object is calculated as,

  v1f=m1m2m1+m2v1i+2m2m1+m2v2i=m1m2m1+m2v1i+2m2m1+m2(0)=1 m 2 m 1 1+ m 2 m 1 v1i101+0v1i

Further simplify the above,

  v1fv1i

The expression for the final velocity of second object is given by,

  v2f=2m1m1+m2v1i+m2m1m1+m2v2i=2m1m1+m2v1i+m2m1m1+m2(0)=2( m 1 m 1 )1+( m 2 m 1 )v1i21+0v1i

Further simplify the above,

  v2f2v1i

Conclusion:

Therefore, it is proved that v1fv1i and v2f2v1i when m1>>m2 and v2i=0 .

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Chapter 8 Solutions

Physics for Scientists and Engineers

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