Question

Object A has a mass of 3 kg and is moving at 4 m/s. Object B has a mass of 2 kg and is at rest.a. What is the initial momentum of object A and object B?B. What is the total initial momentum of object A and B?C. Object A and B collide. After the collision object A has a velocity of 1 m/s.i. What is the momentum of object A and object B after the collision?ii. What is the velocity of object B after the collision?

Answer 1

Question A)

For Object A

`p=12` kg*m/s

For Object B

`p=0` kg*m/s

Question B)

12 kg*m/s

Question C)

4.5 m/s

Step-by-step explanation:

The principle of conservation of momentum states that in a system make out of objects that react (collide or explode), the total momentum is constant if no external force is acted upon the system.

Sum of Momentum Before Reaction = Sum of Momentum After Reaction

Here is the formula

`m_(1) u_(1) + m_(2) u_(2)=m_(1) v_(1)+m_(2) u_(2)`

Note the following.

`m_(1)` = mass of first object

`m_(2)` = mass of second object

`u_(1)` = initial velocity of first object

`u_(2)` = initial velocity of the second object

`v_(1)` = final velocity of the first object

`v_(2)` = final velocity of the second object

In our case, let Object A be the first object and let Object B be the second object.

`m_(1)` = 3 kg

`m_(2)` = 2 kg

`u_(1)` = 4 m/s

`u_(2)` = 0 m/s

`v_(1)` = 1 m/s

`v_(2)` = ? m/s

Lets enter our values into the equation

`(3*4)+(2*0)=(3*1)+(2*v_(2) )`

`12+0=3+2v_(2)`

`12=2v_(2)+3`

`9=2v_(2)`

`v_(2)=4.5`

Now we have all the information we need to answer the questions.

Question A) What is the initial momentum of object A and object B?

The linear momentum formula is

`p=mv`

For Object A

`p=3*4`

`p=12` kg*m/s

For Object B

`p=2*0`

`p=0` kg*m/s

Question B)

12 kg*m/s + 0 kg*m/s

12 kg*m/s

Question C)

Part I.

For Object A

`p=3*1`

`p=3` kg*m/s

For Object B

`p=2*4.5`

`p=9` kg*m/s

Part II.

The velocity of Object B after the collision is 4.5 m/s.