Solving Momentum Questions: Two Rolling Golf Balls Collision

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In summary, the conversation is about a question that involves conserving momentum between two objects moving at different angles. The question specifically asks for the magnitude and direction of the unknown initial velocity after a collision between two rolling golf balls. The answer is given as 3m/s[W}. The suggested approach is to set up a coordinate system and break the momentum into components to solve for the unknown velocity.
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hulkster
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Ok. So I have spent about 40 mins on this question, and can't seem to get it. I know how to conserve momentum when an object hits another at rest, using the cosine and sine laws. but this question involves two objects both moving at different angles. We'll, here it is, if anyone can help:

Two rolling golf balls of the same mass collide. The velocity of one ball is initially 2.70m/s[E] . After the collision, the velocities of the balls are 2.49m/s [62.8 degrees N of W] and 2.37m/s[69.2 degrees S of E]. What is the magnitude and direction of the unkown initial velocity?

The answer is 3m/s[W}...Any help would be greatly appreciated...Thanks.
 
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  • #2
Have you drawn a diagram, show all the velocities?
 
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hulkster said:
Ok. So I have spent about 40 mins on this question, and can't seem to get it. I know how to conserve momentum when an object hits another at rest, using the cosine and sine laws. but this question involves two objects both moving at different angles. We'll, here it is, if anyone can help:

Two rolling golf balls of the same mass collide. The velocity of one ball is initially 2.70m/s[E] . After the collision, the velocities of the balls are 2.49m/s [62.8 degrees N of W] and 2.37m/s[69.2 degrees S of E]. What is the magnitude and direction of the unkown initial velocity?

The answer is 3m/s[W}...Any help would be greatly appreciated...Thanks.

Since momentum is a vector, if it is conserved, then it is conserved in all directions. So set up a coordinate system (E is +x and N is +y is fairly standard) and break everything up into components. So you have an initial momentum component for each golf ball in the x direction and the same for the y direction.
[tex]p_{01x}+p{02x}=p_{1x}+p_{2x}[/tex]
and a similar equation in the y direction. Plugging in your known values (and taking vector components) leaves you two equations in two unknowns.

-Dan
 

1. What is momentum in 2-D?

Momentum is a physical quantity that describes the motion of an object in two dimensions. It is a vector quantity that takes into account both the object's mass and its velocity.

2. How is momentum calculated in 2-D?

In 2-D, momentum is calculated by multiplying the object's mass by its velocity vector. This vector has both magnitude and direction, making momentum a vector quantity.

3. How is momentum conserved in 2-D?

Momentum is conserved in 2-D when there are no external forces acting on the system. This means that the total momentum of all objects in the system will remain constant, even if individual objects collide or change direction.

4. What are some real-life examples of 2-D momentum?

Some real-life examples of 2-D momentum include a ball being thrown in two dimensions, a car turning around a corner, or a satellite orbiting around a planet.

5. How does momentum relate to Newton's laws of motion in 2-D?

Momentum is closely related to Newton's laws of motion in 2-D. In fact, Newton's second law states that the net force acting on an object is equal to the rate of change of its momentum. This means that an object's momentum will change if there is a net force acting on it in 2-D.

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