Collision of Clay Balls: Solving for Velocity and Direction

[aligass2004]

Homework Statement

A 20g ball of clay traveling east of 3.0m/s collides with a 30g ball of clay traveling north at 2.0m/s. What are the speed and the direction of the resulting 50g ball of clay?

Homework Equations

The Attempt at a Solution

For most of the other problems in this homework, I've been using m1v1 = m2v2 to find whatever the question asked. I tried using that equation to find v2, but it wasn't right.

 

[learningphysics]

You need to use vectors here...

split it up into 2 parts... the north/south directions... and east/west directions...

try to get the north/south velocity of the 50g clay... then the east/west...

so each part is treated just like the regular one dimensional collisions...

 

[aligass2004]

When you say "vectors" do you mean components? The y-component (north-south) would be vcos(theta)...I think. I can't remember if it's cos or sin.

 

[learningphysics]

When you say "vectors" do you mean components? The y-component (north-south) would be vcos(theta)...I think. I can't remember if it's cos or sin.

Just call the x-component of the 50g clay... vx. and vy for the north/south part...

so let's start with the east - west direction.

initial momentum in the east-west direction = final momentum in the east-west direction.

 

[aligass2004]

Momentum = mv. So (mi)(vi) = (mf)(vf)?

 

[learningphysics]

Momentum = mv. So (mi)(vi) = (mf)(vf)?

Yes exactly... what do you get for vx?

 

[aligass2004]

Ok, so Vx = (.02)(3)/(.05) = 1.2

 

[learningphysics]

Ok, so Vx = (.02)(3)/(.05) = 1.2

exactly. do the same type of thing to get Vy.

 

[aligass2004]

Vy = (.03)(2)/(.05) = 1.2 also.

 

[learningphysics]

Vy = (.03)(2)/(.05) = 1.2 also.

cool. so now you have vx, vy... you can get the speed and direction...

 

[aligass2004]

I know the direction is 45 degree NE. I tried finding the velocity by using Vx = vcos(theta) and by checking my answer with Vy = vsin(theta). I got .589, but it was wrong.

 

[learningphysics]

I know the direction is 45 degree NE. I tried finding the velocity by using Vx = vcos(theta) and by checking my answer with Vy = vsin(theta). I got .589, but it was wrong.

1.2 = v*sin(45)

solve for v.

you can also use pythogorean theorem with vx and vy.

 

[aligass2004]

Right. I got 1.697 as the velocity.

 

[learningphysics]

Right. I got 1.697 as the velocity.

yup. that's it.