Elastic collision and angle of deflection problem

In summary, the conversation discusses the equations of conservation of momentum and energy in solving a problem involving an elastic collision. The person is having trouble with the algebra and asks for help, but is advised to solve it themselves in order to learn. Hints are given on how to approach the problem.
  • #1
Ahmed Farhan
1.
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2. The equations are the equations of conservation of momentum:
m1v = m1v1cosθ1 + m2v2cosθ2
0 = m1v1sinθ1 + m2v2sinθ2

3. I tried to solve it using the above equations and also tried using kinetic energy conservation since it's an elastic collision. But I can't work out the algebra. Is there something wrong with the logic? I'm completely lost on this one. Someone please solve this for me.
 
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  • #2
The relative sign in the "y" equation must be negative otherwise you cannot get the two to add to zero. The symbols v1 and v2 are speeds, therefore positive.
 
  • #3
kuruman said:
The relative sign in the "y" equation must be negative otherwise you cannot get the two to add to zero. The symbols v1 and v2 are speeds, therefore positive.
Should it matter? The sign can be determined by the value of the angles.
 
  • #4
Ahmed Farhan said:
I tried to solve it using the above equations and also tried using kinetic energy conservation since it's an elastic collision. But I can't work out the algebra. Is there something wrong with the logic? I'm completely lost on this one. Someone please solve this for me.
Hi Ahmed Farhan

It will be no good for you to get the solution by someone else. In order to learn Physics you have to solve it yourself. I'll give you some hints on this for (a):
take the conservation of momentum as you did and also the conservation of energy. Solve the system of these equations. Your aim is to get the ##cos\theta_{m}##. See how you can continue from there.
 

1. What is an elastic collision?

An elastic collision is a type of collision in which the total kinetic energy of the system is conserved. This means that the total energy before the collision is equal to the total energy after the collision.

2. How is the angle of deflection calculated in an elastic collision?

The angle of deflection is calculated using the law of conservation of momentum and the law of conservation of energy. The formula for calculating the angle of deflection is θ = sin⁻¹(m₁v₁sinα / m₂v₂), where m₁ and m₂ are the masses of the colliding objects, v₁ and v₂ are their velocities, and α is the angle of incidence.

3. Can the angle of deflection be negative in an elastic collision?

No, the angle of deflection cannot be negative in an elastic collision. It is always measured in a counterclockwise direction from the original path of the object before the collision.

4. What is the difference between an elastic collision and an inelastic collision?

In an elastic collision, the total kinetic energy of the system is conserved, while in an inelastic collision, some kinetic energy is lost to other forms of energy, such as heat or sound. Inelastic collisions also do not follow the law of conservation of momentum.

5. How does the mass and velocity of the objects affect the angle of deflection in an elastic collision?

The angle of deflection is directly proportional to the mass and velocity of the objects involved in the collision. This means that a larger mass or higher velocity will result in a larger angle of deflection.

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