Inelastic collision between two perpendicular particles

In summary, the problem involves a collision between two particles with masses of 3kg and 2kg and initial velocities of 2m/s and 3m/s respectively. The coefficient of restitution is given as e=0.4. Using the conservation of momentum and the coefficient of restitution equation, the final velocities and angles at which the particles leave the collision site were attempted to be calculated. However, due to the inelastic nature of the collision and not knowing the normal direction, the question is not well-defined and multiple solutions are possible.
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Homework Statement


A particle of mass m1 collides with a particle of mass m2 initially moving at right angles to it(see Figure 1 below). Calculate the final velocities of each particle, and the angles at which the particles leave the collision site( as measured with respect to the original direction of m1) assuming that the coefficient of restitution is e=0.4, m1=3kg, m2=2kg, and the initial speeds of the particles are v1=2m/s, and v2=3m/s respectively.

Homework Equations


conservation of momentum
coefficient of restitution, e = |Vsep|/|Vapp|

The Attempt at a Solution


I attempted to solve this question using the conservation of momentum, as well as the coefficient of restitution equation. My work is shown in the figure below. Where I get confused now, is that I think I have 3 unknowns (v1', theta1 and theta2) in 2 equations. I thought about using energy conservation to obtain more equations, but then since this collision is inelastic, wouldn't I have to know the Q term(the energy lost) in order to use them? Any help would be greatly appreciated.

 

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  • #2
I don't think this question is well-defined if the usual definition of coefficient of restitution is applied.

See http://www.brown.edu/Departments/Engineering/Courses/En4/notes_old/oblique/oblique.html

Note how the coefficient of restitution is defined in terms of the normal components of the velocities. But, you don't know the normal direction for this problem.

For example, the answer would be different for the two cases shown below:

upload_2017-2-5_23-24-6.png


These are only two possibilities out of an infinite number. For the possibility shown on the left, the normal direction is the horizontal direction. For the figure on the right, the normal direction is the vertical direction.
 
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Related to Inelastic collision between two perpendicular particles

1. What is an inelastic collision between two perpendicular particles?

An inelastic collision is a type of collision between two particles in which the total kinetic energy is not conserved. This means that some of the kinetic energy is lost during the collision, usually in the form of heat or sound.

2. How is an inelastic collision different from an elastic collision?

An elastic collision is a type of collision between two particles in which the total kinetic energy is conserved. This means that there is no loss of kinetic energy during the collision. In contrast, an inelastic collision involves a loss of kinetic energy.

3. What factors affect the amount of kinetic energy lost in an inelastic collision?

The amount of kinetic energy lost in an inelastic collision depends on the materials and properties of the particles involved, as well as the angle and speed at which they collide. Generally, particles with greater mass and lower elasticity will experience a greater loss of kinetic energy in an inelastic collision.

4. What happens to the kinetic energy that is lost during an inelastic collision?

The kinetic energy that is lost during an inelastic collision is typically converted into other forms of energy, such as heat or sound. Some of it may also be used to deform the particles involved in the collision.

5. Are there any real-life examples of inelastic collisions between two perpendicular particles?

Yes, there are many real-life examples of inelastic collisions between two perpendicular particles. Some common examples include collisions between vehicles in a car accident, collisions between billiard balls, and collisions between atoms in a gas. In all of these cases, some kinetic energy is lost during the collision due to the inelastic nature of the interaction between the particles involved.

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