Particle A of mass 'm' has initial velocity v.After colliding with a particle B of mass'2m' the particles have the following paths B makes an angle 45 degree
while A makes an angle X.first,A was moving straight.Find X.
To find the angle X, we need to use the concept of conservation of momentum and conservation of kinetic energy.
Let's assume that particle A is moving in the positive x-direction and has a velocity of v. After the collision, particle B makes an angle of 45 degrees (with respect to the positive x-axis), and particle A makes an angle X.
Conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision.
Before the collision:
Momentum of particle A = m * v
Momentum of particle B = 2m * 0 (assuming particle B is initially at rest)
Total momentum before the collision = m * v
After the collision, the momentum can be broken down into x and y-components. Let's consider the x-component:
x-component of momentum before the collision = x-component of momentum after the collision
m * v = m * v_Ax + 2m * v_Bx (since v_Bx = 0, as stated earlier)
Simplifying the equation, we get:
v = v_Ax
This means that both particles move in the same x-direction after the collision with equal x-components of velocity.
Now, let's consider the y-component:
Before the collision, particle A is moving straight, which means the y-component of its initial velocity is 0.
After the collision, the y-component of particle A's velocity will be non-zero, leading it to make an angle X.
Therefore, to find the angle X, we need to find the y-component of particle A's velocity.
Since both particles move in the same x-direction after the collision, the magnitude of particle A's velocity remains the same. Therefore, the magnitude of the y-component of particle A's velocity will be the same as its initial velocity.
Using basic trigonometry, we can determine the y-component of particle A's velocity as:
v_Ay = v * sin(X)
Since we know that v_A = v, we can rewrite the equation as:
v * sin(X) = v
Simplifying the equation, we get:
sin(X) = 1
The angle whose sine value is 1 is 90 degrees (or π/2 radians). Therefore, angle X is 90 degrees.