Mechanical Engineering Principles

138 MECHANICAL ENGINEERING PRINCIPLES

from which,common velocity,v=

0. 30

0. 050

=

6 m/s in the direction that the 30 g mass is

initially travelling.

Problem 6. A ball of mass 50 g is moving

with a velocity of 4 m/s when it strikes a

stationary ball of mass 25 g. The velocity of

the 50 g ball after impact is 2.5 m/s in the

same direction as before impact. Determine

the velocity of the 25 g ball after impact.

Massm 1 =50 g= 0 .050 kg,
m 2 =25 g= 0 .025 kg. Initial velocityu 1 =4 m/s,
u 2 =0; final velocityv 1 = 2 .5 m/s,v 2 is unknown.

Total momentum before impact

=m 1 u 1 +m 2 u 2

=( 0. 050 × 4 )+( 0. 025 × 0 )

= 0 .20 kg m/s

Total momentum after impact

=m 1 v 1 +m 2 v 2

=( 0. 050 × 2. 5 )+( 0. 025 v 2 )

= 0. 125 + 0. 025 v 2

Total momentum before impact=total momentum
after impact, hence

0. 20 = 0. 125 + 0. 025 v 2

from which,velocity of 25 g ball after impact,

v 2 =

0. 20 − 0. 125

0. 025

=3m/s

Problem 7. Three masses,P,QandRlie

in a straight line.Phas a mass of 5 kg and

is moving towardsQat 8 m/s.Qhas a mass

of 7 kg and a velocity of 4 m/s, and is

moving towardsR.MassRis stationary.P

collides withQ,andPandQthen collide

withR. Determine the mass ofRassuming

all three masses have a common velocity of

2 m/s after the collision ofP andQwith R.

MassmP=5 kg,mQ=7 kg, velocityuP=8m/s
anduQ=4 m/s.

Total momentum beforePcollides with

Q=mPuP+mQuQ

=( 5 × 8 )+( 7 × 4 )=68 kg m/s

LetP andQhave a common velocity ofv 1 m/s

after impact.

Total momentum afterP andQcollide

=mPv 1 +mQv 1

=v 1 (mP+mQ)= 12 v 1

Total momentum before impact=total momentum

after impact, i.e. 68= 12 v 1 , from which, common

velocity ofP andQ,

v 1 =

68

12

= 5

2

3

m/s.

Total momentum afterP andQcollide withR

=(mP+Q× 2 )+(mR× 2 )(since the common

velocity after impact=2m/s)

=( 12 × 2 )+( 2 mR)

Total momentum beforePandQcollide withR=

total momentum afterPandQcollide withR,

i.e.

(

mP+Q× (^523)
)
=( 12 × 2 )+ 2 mR
i.e. 12 × 523 = 24 + 2 mR
68 − 24 = 2 mR
from which, mass ofR, mR=^442 =22 kg.
Now try the following exercise
Exercise 59 Further problems on linear
momentum
(Where necessary, takegas 9.81 m/s^2 )

1. Determine the momentum in a mass of
   50 kg having a velocity of 5 m/s.
   [250 kg m/s]


2. A milling machine and its component
   have a combined mass of 400 kg.
   Determine the momentum of the table
   and component when the feed rate is
   360 mm/min. [2.4 kg m/s]


3. The momentum of a body is 160 kg m/s
   when the velocity is 2.5 m/s. Determine
   the mass of the body. [64 kg]