How Is Momentum Conserved in Collisions at Angles?

[benji]

So I have ball 'A' with mass 0.10 kg and velocity 1.4 m/s is traveling towards stationary ball 'C' with mass 0.10 kg. Ball 'C' is struck by ball 'A' and shoots off at an angle of 30 degrees to the x-axis, landing on the floor 1.20 meters below.

I figured the time it takes the ball to hit the ground (0.5 seconds), and the velocity of ball 'C' after it is struck and travels at an angle of 30 degrees to the x-axis (0.36 m/s).

Now I am asked to figure the y-axis value of momentum for ball 'A'. Momentum is conserved so p=mv => .1*1.4 => .14 (the total momentum before the collision). So I figure the y-axis value of the momentum for ball 'C' using p=mv and trig. and I come up with .018.

So I have Pi=Pa+Pc (intial momentum equals the momentum of ball 'A' plus the momentum of ball 'C').

I can figure the momentum of ball 'A' after the collision, but I don't know at what angle the ball is travelling... So I'm stuck.

How do I figure the y-axis value for the momentum of ball 'A'?

 

[OlderDan]

So I have ball 'A' with mass 0.10 kg and velocity 1.4 m/s is traveling towards stationary ball 'C' with mass 0.10 kg. Ball 'C' is struck by ball 'A' and shoots off at an angle of 30 degrees to the x-axis, landing on the floor 1.20 meters below.

I figured the time it takes the ball to hit the ground (0.5 seconds), and the velocity of ball 'C' after it is struck and travels at an angle of 30 degrees to the x-axis (0.36 m/s).

Now I am asked to figure the y-axis value of momentum for ball 'A'. Momentum is conserved so p=mv => .1*1.4 => .14 (the total momentum before the collision). So I figure the y-axis value of the momentum for ball 'C' using p=mv and trig. and I come up with .018.

So I have Pi=Pa+Pc (intial momentum equals the momentum of ball 'A' plus the momentum of ball 'C').

I can figure the momentum of ball 'A' after the collision, but I don't know at what angle the ball is travelling... So I'm stuck.

How do I figure the y-axis value for the momentum of ball 'A'?

Is energy conserved in this collision? If so, what does that tell you about the final velocities?

 

[thepatientmental]

To figure out the y-axis value for the momentum of ball 'A', we can use the conservation of momentum principle. This states that the total momentum before and after a collision remains the same. In this case, the initial momentum (Pi) is equal to the sum of the final momentums of both balls (Pa + Pc).

Since we know the final momentum of ball 'C' in the y-axis direction (0.018 kg*m/s), we can use this value to solve for the final momentum of ball 'A' in the y-axis direction. Rearranging the equation, we get Pa = Pi - Pc. Plugging in the values, we get Pa = 0.14 kg*m/s - 0.018 kg*m/s = 0.122 kg*m/s.

Now, to find the angle at which ball 'A' is traveling, we can use the fact that momentum is a vector quantity and can be represented by its x and y components. Since we know the final momentum in the y-axis direction (0.122 kg*m/s), we can use this value along with the final velocity of ball 'A' (which we can calculate using the given mass and initial velocity) to find the angle at which it is traveling. This can be done using trigonometric functions such as tangent or sine.

In summary, to figure out the y-axis value for the momentum of ball 'A', we can use the conservation of momentum principle and solve for it using the final momentum of ball 'C' in the y-axis direction. Then, we can use the final momentum and velocity of ball 'A' to find the angle at which it is traveling.