How Do You Calculate the Final Velocities in a 2D Coin Collision Problem?

[alphadog0309]

Homework Statement

Two coins, one at rest (c1), the other flicked towards the other (c2). Initial positions are marked, as are final positions and angles. Coordinate system's origin is placed at center of C1 with +x in direction of C2's motion.
knowns:
$$\mu$$ = .36
V₁ = 0
C1 final position- 10.25 cm @ 16 degrees
C2 final position- 5.6 cm @ 302 degrees (-58 degrees)
m1 = m2

UNKNOWNS-
V2
V1F
V2F

Homework Equations

(x):
m₂v₂ = m_1fv_1fcos(16) + m_2fv_2fcos(302)

(y)
0 = m_1fv_1fsin(16) + m_2fv_2fsin(302)

(cons. of KE)

1/2m₁v₁² + 1/2m₂v₂² = 1/2m_1fv_1f² + m_2fv_2f²

(acceleration? idk if this is necessary...)

a = $$\mu$$g
-- derived from $$\Sigma$$F = ma = $$\mu$$mg... not sure if there should be any other forces in this...

The Attempt at a Solution

i keep getting .36587v_f² = 2.0767v_f²

i have a feeling i need to find v2 right before collision using v² = v_o² + 2a(x-x_o)

 

[Nate810]

with a = \mug but i have no idea how to use that equation to solve for v2 after the collision (v2f)any help is appreciated :)

 

[kerimek]

and then use that in the equations above, but i'm not sure...I would approach this problem by first identifying the key concepts and equations that are relevant to solving it. From the given information, we know that there are two coins with equal mass (m1 = m2) and a coefficient of friction (\mu = 0.36). We also know the initial position and velocity of one coin (c1) and the final position and angle of both coins (c1 and c2).

To solve for the unknowns (V2, V1F, V2F), we can use the equations of motion for linear and angular motion, as well as the conservation of kinetic energy. We can also use the equation for acceleration (a = \mu g) to calculate the acceleration of the coins.

First, we can use the equations of motion to find the velocity of c2 right before the collision (vo2) by using the given information on its initial and final positions. Then, we can use the conservation of kinetic energy to find the final velocities (V1F and V2F) of both coins after the collision.

Next, we can use the equations for linear and angular motion to find the final velocity of c2 (V2F) in terms of V1F. We can then substitute this expression into the conservation of kinetic energy equation and solve for V1F.

Finally, we can use the equation for acceleration to find the acceleration of the coins, and then use this value to calculate the final velocity of c2 (V2F).

In summary, the solution to this problem involves using the equations of motion, the conservation of kinetic energy, and the equation for acceleration. It is also important to clearly define the coordinate system and use the correct signs for velocities and forces.