How Is Momentum Conserved in Collisions at Angles?

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In summary, the conversation discusses a collision between ball 'A' and stationary ball 'C'. The time it takes for ball 'C' to hit the ground and its velocity after being struck are calculated. The question of how to determine the y-axis value for the momentum of ball 'A' after the collision is raised. The concept of conservation of momentum and energy is also mentioned, implying that the final velocities must be related to the initial velocities in some way.
  • #1
benji
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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'?
 
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  • #2
benji said:
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?
 
  • #3


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.
 

Related to How Is Momentum Conserved in Collisions at Angles?

What is momentum?

Momentum is a measure of an object's tendency to keep moving in the same direction at the same speed. It is calculated as the product of an object's mass and velocity.

How is momentum conserved in a collision?

In a collision, the total momentum of the system remains constant. This means that the sum of the momentums of all objects involved before the collision is equal to the sum of the momentums after the collision.

What is the difference between elastic and inelastic collisions?

In an elastic collision, kinetic energy is conserved, meaning that the total energy of the system remains the same before and after the collision. In an inelastic collision, kinetic energy is not conserved and some energy is lost as heat or sound.

How do you calculate the angle of collision?

The angle of collision can be calculated using the law of cosines. This involves knowing the velocities and angles of the objects before and after the collision, as well as the masses of the objects.

Why do objects sometimes bounce off each other at an angle?

When objects collide at an angle, the force of the impact is not directly in line with the direction of motion. This causes the objects to bounce off each other at an angle, with the angle depending on the direction and magnitude of the forces involved.

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