- #1
Samuelriesterer
- 110
- 0
Problem statement:
Two pucks of radius 0.05 meters collide as shown in attached picture.
The mass of puck 1 is 0.1 kg and that of puck 2 is 0.15 kg. The initial velocities are v1i = 1 m/s and v2i= 0.6 m/s. (1) Assuming no friction between the pucks, only normal forces during collision, in what direction is the acceleration for each puck during collision?
Relative equations:
m1v1i_x + m2v2i_x = m1v1f_x + m2v2f_x
m1v1i_y + m2v2i_y = m1v1f_y + m2v2f_y
½ m1v1i + ½ m2v2i = ½ m1v1f + ½ m2v2f
Work done so far:
1) In what direction is the acceleration for each puck during collision
Both are accelerating toward the center of the pucks during the collision phase
2) Choose your coordinate axes to be in the direction of the acceleration and perpendicular to it. Determine the components of the original velocities along these axes.
We will choose a coordinate system that places the x-axis along the pucks’ centers of mass and the y-axis perpendicular to the x-axis and through the center of collision.
V1i_x = V1i cos (θ) v1i_y = v1i sin (θ)
v2i_x = -v2i v2i_y = 0
(3) What happens to the velocity components perpendicular to the line between centers?
The components perpendicular to the line between the centers (i.e. the y axis) remain the same while the x components change signs.
(4) For the components in the direction of the acceleration, use momentum and kinetic energy conservation to determine the final values for these components. {You could use the center of mass frame here.}
I will use a constant of q = 3/2 to change the equations of momentum conservation and KE conservation:
m1v1i_x + m2v2i_x = m1v1f_x + m2v2f_x →
(m1)(v1i_x) + q(m1)(v2i_x) = (m1)(v1f_x) + q(m1)(v2f_x) →
(v1i_x) + q(v2i_x) = (v1f_x) + q(v2f_x) →
(v1i_x) + q(v2i_x) = (v1f_x) + q(v2f_x) →
V1i cos (θ) + q(-v2i) = (v1f_x) + q(v2f_x)
½ (m1)(v1i^2) + ½ q(m1)(v2i^2) = ½ (m1)(v1f^2) + ½ q(m1)(v2f^2) →
(v1i^2) + q(v2i^2) = (v1f^2) + q(v2f^2)
Not sure at this point on how to solve this system.
(5) Combine the results from (3) and (4) to find the final velocities for both pucks.
Two pucks of radius 0.05 meters collide as shown in attached picture.
The mass of puck 1 is 0.1 kg and that of puck 2 is 0.15 kg. The initial velocities are v1i = 1 m/s and v2i= 0.6 m/s. (1) Assuming no friction between the pucks, only normal forces during collision, in what direction is the acceleration for each puck during collision?
Relative equations:
m1v1i_x + m2v2i_x = m1v1f_x + m2v2f_x
m1v1i_y + m2v2i_y = m1v1f_y + m2v2f_y
½ m1v1i + ½ m2v2i = ½ m1v1f + ½ m2v2f
Work done so far:
1) In what direction is the acceleration for each puck during collision
Both are accelerating toward the center of the pucks during the collision phase
2) Choose your coordinate axes to be in the direction of the acceleration and perpendicular to it. Determine the components of the original velocities along these axes.
We will choose a coordinate system that places the x-axis along the pucks’ centers of mass and the y-axis perpendicular to the x-axis and through the center of collision.
V1i_x = V1i cos (θ) v1i_y = v1i sin (θ)
v2i_x = -v2i v2i_y = 0
(3) What happens to the velocity components perpendicular to the line between centers?
The components perpendicular to the line between the centers (i.e. the y axis) remain the same while the x components change signs.
(4) For the components in the direction of the acceleration, use momentum and kinetic energy conservation to determine the final values for these components. {You could use the center of mass frame here.}
I will use a constant of q = 3/2 to change the equations of momentum conservation and KE conservation:
m1v1i_x + m2v2i_x = m1v1f_x + m2v2f_x →
(m1)(v1i_x) + q(m1)(v2i_x) = (m1)(v1f_x) + q(m1)(v2f_x) →
(v1i_x) + q(v2i_x) = (v1f_x) + q(v2f_x) →
(v1i_x) + q(v2i_x) = (v1f_x) + q(v2f_x) →
V1i cos (θ) + q(-v2i) = (v1f_x) + q(v2f_x)
½ (m1)(v1i^2) + ½ q(m1)(v2i^2) = ½ (m1)(v1f^2) + ½ q(m1)(v2f^2) →
(v1i^2) + q(v2i^2) = (v1f^2) + q(v2f^2)
Not sure at this point on how to solve this system.
(5) Combine the results from (3) and (4) to find the final velocities for both pucks.