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In my year 11 physics course, we only covered questions that gave you 3 of the 4 velocities, so I am interested as to how you are meant to figure this type of question out.

Thanks for any help.

- Thread starter Pharrahnox
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- #1

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In my year 11 physics course, we only covered questions that gave you 3 of the 4 velocities, so I am interested as to how you are meant to figure this type of question out.

Thanks for any help.

- #2

Nugatory

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In the easier one-dimension case conservation of kinetic energy and conservation of momentum give you two equations. You have two unknowns (the velocities after the collision) so with two equations for your two unknowns, you're just some algebra away from an answer.

The two-dimensional case needs more information. In general, there is a different solution for each possible angle of the cars coming out of the collision.

- #3

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More than one pair of final velocities could result from this collision and still conserve momentum.

Each possible pairing corresponds to a collision that conserves a varying amount of

0.5*mv^2 (before collision) = 10*[0.5*mv^2 (after collision)]

Without knowing how much kinetic energy is conserved, you cannot say for sure what the final velocities of the two cars will be.

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I.e. if a car crashed into a stationary wall, what is the force, just general F=ma, with some standard velocity equation.

In this case, car1 at 1000kg and car2 = 800kg, car1 now equals 1000+800kg. It's final velocity instead of 20m/s, can be 20+50m/s. Then the result would be the collision of car1 into a stationary object, however it is equivalent in force as the 2 opposing cars crashing to your question. Assuming speed is constant, v=u

I just realized I didn't answer your question, haha, I gave you the resultant force produced. Either way same concept applies as mentioned above, but deal with velocity instead of force. Just play around with the idea in your mind, until you arrive at a logical equivalent. I.e. both cars crashed into a wall, which produces largest force, that will be the car with a v>0 in your question, whereas the other will have v=0, but actually calculate v.

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In a collision such as this, the billiard balls should not deviate off their course as a result of the collision, should they, as it is directly in line?

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Nugatory

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You have two unknowns, namely the velocity of each of two balls after the collision. Write down the equation for conservation of momentum (sum of the momenta after the collision equals the sum of the momenta before) and conservation of energy (sum of the kinetic energies after the collision equals the sum of the kinetic energies before the collision) and you have two equations. Two equations is enough to solve for your two unknowns.

In a collision such as this, the billiard balls should not deviate off their course as a result of the collision, should they, as it is directly in line?

(BTW, you will actually find two solutions when you do the algebra. It's worth taking a moment to think about the physical significance of both solutions and why it makes sense that there are two solutions.... But don't do this until after you've found the solutions).

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Is there an easy way to do this, as it took several steps and different equations and formulae to work it out?

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jbriggs444

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One standard approach would be to start by changing to a coordinate system in which the center of gravity of the system is motionless at the origin. One ball approaches from the left with a rightward velocity and the other from the right with a rightward velocity.Is there an easy way to do this, as it took several steps and different equations and formulae to work it out?

Conservation of momentum implies that the velocities of the two balls (as judged against this coordinate system) are always directed oppositely to one another and that their speeds always have a fixed ratio. That ratio is the inverse of the ratio of the two masses.

This means that the total kinetic energy of the system is a simple function of the speed of one of the balls (either ball will work).

If the collision is dead-center on the x axis then the rebound direction is easy. All that's left is determining the rebound speed. In an elastic collision energy is conserved. Because energy is a function of the speed of the ball, its

Take the reversed velocities, transform back to the original coordinate system and read off the resulting velocity.

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arildno

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@jbriggs444 Would that be something like:

for 1000kg mass, final velocity = 1000/800 * -20?

for 800kg mass, final velocity = 800/1000 * -30?

For final velocity__relative__ to initial velocity.

@arildno So the equations would be different when having angled collisions?

I will do some research into this. Thanks for all your help.

for 1000kg mass, final velocity = 1000/800 * -20?

for 800kg mass, final velocity = 800/1000 * -30?

For final velocity

@arildno So the equations would be different when having angled collisions?

I will do some research into this. Thanks for all your help.

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