TBR: Momentum Question

[justadream]

---

Members do not see this ad.

TBR Physics I page 194 #15

You have two clay balls that will stick together after colliding. Mass of ball I = .100kg. Mass of ball III = .200 kg.

They are fired with the same amount of energy (via a spring) from a common distance. Since ball I is smaller in mass, it attains a faster velocity (and vice versa for Ball III). Thus, the balls miss each other.

But I'm wondering: what would happen if it were set up so that they would collide? What would the resultant path be?

The angle that Ball I's path makes with the horizontal is 30 degrees.

My hypothesis:
If I remember a TBR question correctly, given the same amount of initial energy, the heaver object has greater momentum than the lighter object.

I'm a bit unclear what to do from here. I know I need to take into account the angle of the velocities (to figure out the x-component).

Secondary question: What would happen to the resultant path if the masses of the balls were switched?


@Cawolf

 

[Cawolf]

To answer that question we need to quantify the energy transferred from the spring.

So we use our kinetic energy formula to determine the velocity of the balls and then we can determine the momentum's given the mass.

Then it is a simple matter of vector addition using the conservation of momentum formula.

I solved it with a random spring PE of 10 J just to have numbers.

Pretty lengthy to work out by hand though!

 

[Cawolf]

If the masses were swapped then the ball traveling to the left would have the lesser momentum - so the path of travel would be more impacted by the rightward traveling ball.

We would see a final path that was in the (edit FIRST) quadrant (positive velocity by my sketch).

 

[justadream]

@Cawolf

Wow! Impressive work.

Regarding the second scenario (if the masses were swapped), can you conclude "for sure" that the ball will be in the second quadrant?

Although the momentum of the ball traveling rightward would be greater, it would come at an angle. Thus, you will need to find the x-component of its momentum. This x-component may or may not be greater than the x-component of of the ball traveling leftwards. I guess this would depend on the relative velocities, masses, angle.

 

[Cawolf]

You could follow my steps and rework the problem with the position of the balls swapped.

The x component is mvcos30 = (.2)(10)(.866) = 1.73

This is greater than the x component of the lighter ball = mv = (.1)(14.1) = 1.41

So yes, you can conclude that the stuck together objects will travel right and up. It has to be upwards since the only contribution to the y momentum is positive from the left ball.

 

[justadream]

You could follow my steps and rework the problem with the position of the balls swapped.

The x component is mvcos30 = (.2)(10)(.866) = 1.73

This is greater than the x component of the lighter ball = mv = (.1)(14.1) = 1.41

So yes, you can conclude that the stuck together objects will travel right and up. It has to be upwards since the only contribution to the y momentum is positive from the left ball.

@Cawolf
Do you mean the first quadrant (north east direction)?

 

[Cawolf]

Yes sorry.