Two shuffleboard disks of equal mass, one orange and the other yellow are involved in a
perfectly elastic glancing collision. The yellow disk is initially at rest and is struck by the
orange disk moving initially to the right at 7.00 ms"1. After the collision, the orange disk
moves in a direction that makes an angle of 39°.with its initial direction. Meanwhile, the
velocity vector of the yellow disk is perpendicular to the post collision velocity vector of the
orange disk.
a) Sketch a diagram showing the motion of both disks before and after collision.
(4 marks)
b) Determine the speed of each disk after the collision.
a) To sketch the diagram showing the motion of both disks before and after the collision, we can use arrows to represent the direction and magnitude of the velocities.
Before the collision:
- The yellow disk is at rest, so its velocity is 0 m/s.
- The orange disk is moving initially to the right at 7.00 m/s.
After the collision:
- The orange disk moves in a direction that makes an angle of 39° with its initial direction.
- The velocity vector of the yellow disk is perpendicular to the post-collision velocity vector of the orange disk.
Here is a sketch of the diagram:
(Yellow disk) ---(0 m/s)---
|
(Orange disk) |---(7.00 m/s)---->
(Collision)
|
(Yellow disk) |---(v1 m/s)----|
| (39°)
(Orange disk) |---(v2 m/s)----|
b) To determine the speed of each disk after the collision, we can use the law of conservation of momentum and the law of conservation of kinetic energy.
First, let's define the variables:
- Let m1 be the mass of the orange disk.
- Let m2 be the mass of the yellow disk.
- Let v1 be the velocity of the orange disk after the collision.
- Let v2 be the velocity of the yellow disk after the collision.
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision:
m1 * 7.00 m/s = m1 * v1 + m2 * v2
Since we are given that the collision is perfectly elastic, the law of conservation of kinetic energy can also be used. The total kinetic energy before the collision is equal to the total kinetic energy after the collision:
(1/2) * m1 * (7.00 m/s)^2 = (1/2) * m1 * v1^2 + (1/2) * m2 * v2^2
Using these two equations, we can solve for v1 and v2.
Note: We do not have enough information to determine the masses of the disks, so we cannot solve for the actual values of v1 and v2. However, we can determine the ratios of the velocities.
Hope this helps! Let me know if you have any further questions.
a) To sketch the motion of both disks before and after the collision, we can follow these steps:
1. Draw a horizontal line to represent the initial direction of motion.
2. Place the yellow disk on this line, indicating that it is initially at rest.
3. Place the orange disk to the right of the yellow disk, moving initially in the same direction (to the right) at a speed of 7.00 m/s.
4. After the collision, draw the post-collision direction of the orange disk. It should make an angle of 39° with its initial direction.
5. Draw a perpendicular line to represent the velocity vector of the yellow disk after the collision. This line should intersect the post-collision direction of the orange disk.
b) To determine the speed of each disk after the collision, we can use the principles of conservation of momentum and conservation of kinetic energy.
1. Conservation of momentum: The total momentum before the collision is equal to the total momentum after the collision. Since the yellow disk is at rest initially, its momentum is zero. Therefore, the momentum before the collision is equal to the momentum of the orange disk, which can be calculated as mass x velocity.
2. Conservation of kinetic energy: In an elastic collision, the total kinetic energy before the collision is equal to the total kinetic energy after the collision. The kinetic energy of a moving object can be calculated as (1/2) x mass x (velocity)^2.
Using these principles, we can set up equations to solve for the speed of each disk after the collision. Let's denote the mass of each disk as m and the speed of the orange disk after the collision as Vo, and the speed of the yellow disk after the collision as Vy.
Conservation of momentum: m x 7.00 m/s = m x Vo cos(39°)
Conservation of kinetic energy: (1/2) x m x (7.00 m/s)^2 = (1/2) x m x Vo^2 + (1/2) x m x Vy^2
Simplifying these equations will allow you to solve for the values of Vo and Vy, which represent the speeds of the orange and yellow disks after the collision.