Two disks are on a frictionless plane as shown. The first disk, with mass M is initially at rest. The second disk with mass 2M has an initial velocity of 6 m/s in the y direction before colliding with the first disk. After the collision, the disk with mass 2M is deflected 15° (deflected to the left) and has speed 3 m/s. (Ignore the effects of gravity, all the pieces are moving in a horizontal plane, and you may neglect friction). What is the x component of the velocity of disk 1(deflected to the right) (mass M) after the collision?
IT is much to complicated to work out here.
worke it this way:
conservation of momentum in x direction
conservation of momentum in y direction
conservation of energy.
That should give you all you need.
To find the x component of the velocity of disk 1 after the collision, we can use the conservation of momentum principle. According to this principle, the total momentum of the system before the collision is equal to the total momentum after the collision.
First, let's calculate the initial momentum of the system. The first disk is initially at rest, so its momentum is zero. The second disk with mass 2M has an initial velocity of 6 m/s in the y direction, which means its initial momentum is 2M * 6 m/s = 12M m/s in the y direction.
Now, let's consider the final momentum of the system after the collision. The second disk with mass 2M is deflected 15° to the left and has a speed of 3 m/s. To find its final momentum, we need to calculate its x and y components separately.
The x component of the final momentum (p2x) can be found using the formula: p2x = mv * cos(θ), where m = mass of the second disk = 2M, v = final velocity of the second disk = 3 m/s, and θ = deflection angle = 15°. So, p2x = 2M * 3 m/s * cos(15°).
The y component of the final momentum (p2y) can be found using the formula: p2y = mv * sin(θ), where m, v, and θ are the same as above. So, p2y = 2M * 3 m/s * sin(15°).
Since the initial momentum of the system is zero, the sum of the x components of the final momenta should also be zero. So, we have:
p2x + p1x = 0.
Now, we can solve for p1x, which is the x component of the final momentum of disk 1 (mass M):
p1x = -p2x = -2M * 3 m/s * cos(15°).
Therefore, the x component of the velocity of disk 1 after the collision is -2M * 3 m/s * cos(15°).