Linear Momentum and Its Conservation

In summary: What you're looking for is the magnitude and direction of the momentum vector. To find the magnitude, you need to use the Pythagorean theorem. The magnitude is the square root of the sum of the squares of the x and y components. To find the direction, you need to use inverse tangent function. The direction is the angle between the momentum vector and the positive x-axis.In summary, the 3.00-kg particle has a velocity of (3.00i-4.00j)m/s. Its x and y components of momentum are (9.00i-12.00j)kg*m/s. To find the magnitude of the momentum, use the Pythagorean theorem by finding the square root of the sum
  • #1
Joyci116
45
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Homework Statement


A 3.00-kg particle has a velocity of (3.00i-4.00j)m/s. (a)Find its x and y components of momentum. (b) Find the magnitude and direction of its momentum.


Homework Equations


p=mv


The Attempt at a Solution


For part a, I found that the x and y components of momentum is (9.00i-12.00j)kg*m/s. But I am having trouble with the magnitude and direction. I was told to pythag it, but I am still not clear on what to do.

Thank you.
 
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  • #2
Joyci116 said:

Homework Statement


A 3.00-kg particle has a velocity of (3.00i-4.00j)m/s. (a)Find its x and y components of momentum. (b) Find the magnitude and direction of its momentum.


Homework Equations


p=mv


The Attempt at a Solution


For part a, I found that the x and y components of momentum is (9.00i-12.00j)kg*m/s. But I am having trouble with the magnitude and direction. I was told to pythag it, but I am still not clear on what to do.

Thank you.

Rather than say :"the x and y components of momentum is (9.00i-12.00j)kg*m/s."

Can you separately say

The x component is : ...
The Y component is : ...
 
  • #3
Okay.
 

FAQ: Linear Momentum and Its Conservation

What is linear momentum?

Linear momentum is a physical quantity that measures the motion of an object. It is defined as the product of an object's mass and its velocity. In other words, it is the amount of motion an object has in a particular direction. It is a vector quantity, meaning it has both magnitude and direction.

How is linear momentum conserved?

According to the law of conservation of linear momentum, the total linear momentum of a closed system remains constant over time, unless acted upon by an external force. This means that in any collision or interaction between objects, the total linear momentum before and after the event will be the same. This is due to the fact that forces occur in pairs and are equal and opposite, canceling out the changes in momentum.

What is an example of linear momentum in action?

A common example of linear momentum is a game of billiards. When the cue ball collides with the other balls, the total linear momentum of the system is conserved. The cue ball's momentum is transferred to the other balls, causing them to move in different directions and at different speeds.

How is linear momentum related to kinetic energy?

Linear momentum and kinetic energy are related through the equation: momentum = mass x velocity. Kinetic energy is also defined as 1/2 x mass x velocity^2, so by substituting this into the equation for momentum, we can see that they are directly proportional. This means that as the momentum of an object increases, so does its kinetic energy.

Can linear momentum be negative?

Yes, linear momentum can be negative. Since it is a vector quantity, the direction of the momentum can be positive or negative depending on the direction of the object's motion. A negative momentum simply means that the object is moving in the opposite direction of the chosen positive direction.

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