LEARNING OBJECTIVES

By the end of this section, you will be able to:

• know the concept of momentum and impulse
• Recall and use the equation: Momentum=Mass X Velocity ; symbollically, p=mv
• Recall and use the equation for impulse: Ft=mv-mu
• Apply the principle of conservation of momentum to solve simple problems in one dimension.

MOMENTUM:

• Every object has mass. So when an object is moving, then it  will obviously have  momentum
•  Momentum depends upon the variables mass and velocity.
• In terms of an equation, the momentum of an object is equal to the mass of the object times the velocity of the object.
• Momentum = mass • velocity.
• In physics, the symbol for the quantity momentum is the lower case p. Thus, the above equation can be rewritten as p = m • vwhere m is the mass and v is the velocity. The equation illustrates that momentum is directly proportional to an object's mass and directly proportional to the object's velocity.

IMPULSE:

• According to Newtons Second Law
• Hence, F = ma
• But a= (v-u)/t.
• Hence F=[ m ( v-u)] /t  
• Or Ft= mv-mu
• Ft is known as impulse. We also know that mv-mu imples change in momentum. 
• Hence, impulse is defined as the change in momentum

SUMS :

1. The following is an example of of a moving object colliding with a stationary object.

Consider Car A  of mass 40 kg   moving  with Car B of mass 45kg . Car B is stationary. Also let  the velocity of Car A =10m/s and that of Car B=0m/s. 

It is observed that the two cars now together move to the right with a velocity of 6m/s as shown below.

Let us find the mass of carB.

Solution:

For a closed system, the   total momentum  is always conserved. Hence it is the same  before and after the collision.

BEFORE COLLISION:

MOMENTUM OF CAR A

= Mass of car A x Velocity of car A

=40 X10 =400 kgm/s

MOMENTUM OF CAR B

= Mass of car B x Velocity of car B

=Mass of car B X 0 = 0 kgm/s

Hence the total momentum before collision= 400kgm/s

AFTER COLLISION:

Total momentum

= Total mass of car A and B x  Velocity of car A and B

=(40+ Mass of car B) x 6

But in a closed system, the total momentum is conserved;

Hence

Total momentum before collision=Total momentum after collision

400= (40+ Mass of car B) x 6

400=(40x6 ) + (Mass of car B)6

400=240 +(Mass of car B)6

400-240=Mass of carB x 6

160=Mass of carB x 6

160/6= Mass of car B

Mass of car B= 26.67 kg

QUESTION:1

CORRECT OPTION:C

Explanation:

• After collision, the direction of velocity changes .
• Kinetic energy= 1/2(mv²). Since it is stated that the molecule rebounds with the same speed, hence it implies that the kinetic energy stays the same.
• The momentum after collision changes . This because before collision, it's momentum is +mv and after collision, the momentum changes to -mv. This is because, the direction of veloicty changes form +v to -v

2.  Gas molecules striking a container wall cause a pressure to be exerted on the wall. Which statement explains this:

A. When a molecule rebounds , there must be a change in energy.

B.When a molecule rebounds there must be a change in it's momentum

C.When a molecule rebounds, there must be a change in its speed.

D.When a molecule rebounds, there must be a change in it's temperature.

CORRECT OPTION: B

EXPLANATION: 

Pressure= Force/Area

= (mass x acceleration)/area

=(mass x (v-u)/time))/area

Pressure={(change in momentum)/time)}/area

Thus a change in momentum will cause a pressure to be exerted on the wall.

3

CORRECT OPTION :C

Explanation:

• According to the principle of conservation of momentum, the total momentum before impact= the total momentum after impact.
• Total momentum before impact= momentum of the ball + momentum of the object
• Total momentum before impact= (3 x 8) + (3 x 0) = 24 kgm/s
• Hence total momentum after impact= 24kg m/s....As momentum is conserved.
• Once again applying the conservation of momentum:"the total momentum before impact= the total momentum after impact.", we get 24= (mass of ball +Object) x combined velocity=> 24= 5 x combined velocity.
• Hence combined velocity= 24/5=4.8m/s