Momentum in two directions(q35)

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In summary: Since the particles have opposite directions for their y-components, the total y-component of momentum must be zero. This means that the particles cannot both move to the same side of the x-axis, as that would result in a non-zero total y-component of momentum. Therefore, the answer is b) that it is not possible for both particles to move to the same side of the x-axis. In summary, the conversation discusses a problem involving two particles with velocities at a 30 degree angle from the x-axis. The sum of their y-components of momentum must be zero, so it is not possible for both particles to move to the same side of the x-axis. This is determined through conservation of momentum.
  • #1
jack1234
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Hi, for this question
http://tinyurl.com/yvadld

This is what I have done:
in x direction
5*60=5*v1*cos30 + 2*v2*cos30 --(1)
In y direction
0=5*v1sin30 + 2*v2sin30 --(2)

From (2), v1=-(2/5)*v2 subs into (1)

And what I get is 300=-2*v2*cos30 + 2*v2*cos30

What is the problem?
 
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  • #2
jack1234 said:
Hi, for this question
http://tinyurl.com/yvadld

This is what I have done:
in x direction
5*60=5*v1*cos30 + 2*v2*cos30 --(1)
In y direction
0=5*v1sin30 + 2*v2sin30 --(2)

From (2), v1=-(2/5)*v2 subs into (1)

And what I get is 300=-2*v2*cos30 + 2*v2*cos30

What is the problem?

you should use:

0=5*v1sin30 - 2*v2sin30 --(2)

the two particles have opposite directions for y-components.
 
  • #3
Got it, answer is b:)

But does it mentioned in the question...or it just common sense?
 
  • #4
>>But does it mentioned in the question
What I mean is "the two particles have opposite directions for y-components."
 
  • #5
You are told that each particle has a velocity that is 30 degrees from the original direction (along the x-axis). Is it possible (considering conservation of momentum) that the two particles both move to the same side of the x-axis?

Hint: What's the y-component of total momentum?
 
  • #6
I see...so it is base on observation:)
 
  • #7
It is based on conservation of momentum.
 

1. What is momentum in two directions?

Momentum in two directions, also known as momentum in a two-dimensional system, is a measure of an object's motion in two perpendicular directions. It takes into account both the magnitude and direction of an object's velocity.

2. How is momentum in two directions calculated?

Momentum in two directions is calculated by multiplying an object's mass by its velocity in both the x and y directions. This can be represented by the equation p = mxv, where p is the momentum, m is the mass, and v is the velocity.

3. What are some real-life examples of momentum in two directions?

Some real-life examples of momentum in two directions include a car moving along a curved road, a ball rolling down a hill, and a satellite orbiting around a planet. In all of these scenarios, the objects have both a magnitude and direction of motion.

4. How does momentum in two directions relate to Newton's laws of motion?

Momentum in two directions is closely related to Newton's laws of motion, specifically the law of conservation of momentum. This law states that in a closed system, the total momentum of all objects involved will remain constant, regardless of any internal forces acting on the objects.

5. How is momentum in two directions different from momentum in one direction?

Momentum in two directions takes into account an object's motion in two perpendicular directions, while momentum in one direction only considers motion in one direction. Additionally, momentum in two directions is a vector quantity, meaning it has both magnitude and direction, while momentum in one direction is a scalar quantity, only having magnitude.

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