Collision of Clay Balls: Solving for Velocity and Direction

In summary, the 50g ball of clay is traveling east and north at 2.0m/s. The north/south velocity is 1.2 and the east/west velocity is 1.697.
  • #1
aligass2004
236
0

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.
 
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  • #2
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...
 
  • #3
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.
 
  • #4
aligass2004 said:
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.
 
  • #5
Momentum = mv. So (mi)(vi) = (mf)(vf)?
 
  • #6
aligass2004 said:
Momentum = mv. So (mi)(vi) = (mf)(vf)?

Yes exactly... what do you get for vx?
 
  • #7
Ok, so Vx = (.02)(3)/(.05) = 1.2
 
  • #8
aligass2004 said:
Ok, so Vx = (.02)(3)/(.05) = 1.2

exactly. do the same type of thing to get Vy.
 
  • #9
Vy = (.03)(2)/(.05) = 1.2 also.
 
  • #10
aligass2004 said:
Vy = (.03)(2)/(.05) = 1.2 also.

cool. so now you have vx, vy... you can get the speed and direction...
 
  • #11
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.
 
  • #12
aligass2004 said:
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.
 
  • #13
Right. I got 1.697 as the velocity.
 
  • #14
aligass2004 said:
Right. I got 1.697 as the velocity.

yup. that's it.
 

1. What is a vector in physics?

A vector in physics is a quantity that has both magnitude and direction. It is represented by an arrow pointing in the direction of the vector and its length represents the magnitude. Vectors are commonly used in physics to describe motion, forces, and other physical quantities.

2. How does a ball of clay represent a vector in physics?

A ball of clay can represent a vector in physics when it is thrown or rolled, as it has both magnitude (speed) and direction (the direction it is thrown or rolled). The clay's trajectory can be represented by a vector, with its initial position and final position being the starting and ending points of the arrow, respectively.

3. What is the difference between a vector and a scalar quantity?

A vector has both magnitude and direction, while a scalar quantity only has magnitude. For example, velocity is a vector quantity as it has both speed (magnitude) and direction, while speed is a scalar quantity as it only has magnitude.

4. How are vectors used in the study of motion?

Vectors are used in the study of motion to describe the displacement, velocity, and acceleration of an object. They can also be used to analyze forces acting on an object and determine its resultant force, which is also a vector quantity.

5. Can a vector be negative in physics?

Yes, a vector can be negative in physics. This indicates the direction of the vector is in the opposite direction of the positive value. For example, a negative velocity vector indicates the object is moving in the negative direction (opposite to the positive direction).

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