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Classic Hit and Stick momentum?

  • #1

Homework Statement



Three balls of clay have masses m1 = 106 g, m2 = 148 g, m3 = 120 g, and speeds v1 = 1.48 m/s, v2 = 1.19 m/s, v3 = 1.85 m/s. They move in the directions: (1) at 45° from the horizontal, (2) horizontally left, and (3) vertically up. They collide simultaneously and stick together. Calculate the speed and the direction (angle) of the resulting blob of clay.

Homework Equations



p=mv

The Attempt at a Solution



Vx = 106 * 1.48 * cos(45) - 148 * 1.19 = -65.189882 m/s

Vy = 106*1.48sin(45) + 120*1.85 = 332.0309 m/s

V = sqrt(332.0309^2 + [-65.189882]^2) (answer?)

angle = arctan (Vy/Vx)


This isn't right is it,
 

Answers and Replies

  • #2
Andrew Mason
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Homework Statement



Three balls of clay have masses m1 = 106 g, m2 = 148 g, m3 = 120 g, and speeds v1 = 1.48 m/s, v2 = 1.19 m/s, v3 = 1.85 m/s. They move in the directions: (1) at 45° from the horizontal, (2) horizontally left, and (3) vertically up. They collide simultaneously and stick together. Calculate the speed and the direction (angle) of the resulting blob of clay.

Homework Equations



p=mv

The Attempt at a Solution



Vx = 106 * 1.48 * cos(45) - 148 * 1.19 = -65.189882 m/s

Vy = 106*1.48sin(45) + 120*1.85 = 332.0309 m/s

V = sqrt(332.0309^2 + [-65.189882]^2) (answer?)

angle = arctan (Vy/Vx)


This isn't right is it,
First of all we have to know the direction of the 45° ball. Is it 45° to the left or to the right?

It is not clear what you are doing in calculating vx and vy.

I suggest you write out the equations for momentum before and after the collision and then relate them. How are they related?

AM
 
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  • #3
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No that isn't right, remember that the conservation of momentum applies, use it. Calculate the total momentum in the x direction before the collision, then it them equal to the total momentum in the x direction after the collision, then do the same for the y direction. Then you will have two equations with two unknowns, use algebra to solve for both. What you did was incorrect, you cannot find the total momentum in the x direction and set it equal to the velocity in the x direction. If in doubt, check the units.
 
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  • #4
So

mv = m1 * v1 + m1*v2 + m2*v3? in the x and y directions then use trig to find speed and direction?
 
  • #5
haruspex
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So

mv = m1 * v1 + m1*v2 + m2*v3? in the x and y directions then use trig to find speed and direction?
Yes. What you calculated in the OP (assuming m1 was moving up and to the right, which is not clear) were the x and y momenta, not the x and y speeds. You just needed to divide by the combined mass.
 
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  • #6
Cool, I got it!
 

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