Inelastic collision at an angle

In summary, the question is asking for the angle theta with respect to north made by the velocity vector of two cars after a collision, expressed in terms of phi. The equation tan(theta) = v_final in the x direction / v_final in the y direction should be used, taking into account the negative y-component of momentum for the angled car. The attempt at a solution involves finding v_finalx and v_finaly, and using the equation tan(theta) = cos(phi)/sin(phi). The final equation for v_final is sqrt((v_final * cos(phi))^2 + (2v_final - v_final * sin(phi))^2).
  • #1
powerofsamson
6
0

Homework Statement


What is the angle theta with respect to north made by the velocity vector of the two cars after the collision?
Express your answer in terms of phi. Your answer should contain an inverse trigonometric function.
6318.jpg


the cars are both of mass m.

Homework Equations


I already found v_final for the first part of the question. The hint says that tan theta = v_final in the x direction / v_final in the y direction.

The Attempt at a Solution



This equation is wrong: (m(2v)+m(v)sin(phi))/(2mv_final cos(theta)) = tan(theta)
 
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  • #2
Write the momentum equations in x and y.

Note that the y-component of momentum of the car at an angle is negative (opposite) that of the car traveling north at 2v.
 
  • #3
For x I have v_finalx = (2m)v_final * cos (phi). For y i have v_finaly = (2m)v_final * sin (phi). This would mean that tan (theta) = cos (phi)/sin(phi). I've already tried atan (cos(phi)/sin(phi).
 
  • #4
how do i do the first part?
my question is asking me the speed of v_final

i think its sqrt ( (v_final * cos (phi))^2 + (2v_final - v_final * sin (phi) ) ^2 )
 

1. What is an inelastic collision at an angle?

An inelastic collision at an angle is a type of collision between two objects where there is a loss of kinetic energy and the objects stick together after the collision. This type of collision occurs when the objects have different masses and collide at an angle.

2. How is momentum conserved in an inelastic collision at an angle?

In an inelastic collision at an angle, momentum is conserved in the same way as in any other type of collision. The total momentum of the system before the collision is equal to the total momentum after the collision. However, in this type of collision, the direction of momentum may change due to the objects colliding at an angle.

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

The amount of energy lost in an inelastic collision at an angle depends on the masses of the objects involved, the angle at which they collide, and the coefficient of restitution (a measure of the elasticity of the objects). Objects with higher mass and lower coefficient of restitution will result in a greater loss of energy.

4. Can an inelastic collision at an angle be elastic?

No, an inelastic collision at an angle is, by definition, not elastic. In an elastic collision, there is no loss of kinetic energy and the objects bounce off each other after the collision. In an inelastic collision at an angle, the objects stick together, resulting in a loss of kinetic energy.

5. How is an inelastic collision at an angle different from a head-on inelastic collision?

An inelastic collision at an angle differs from a head-on inelastic collision in terms of the direction of momentum. In a head-on collision, the objects collide directly with each other, resulting in a change in direction of their momentum. In an inelastic collision at an angle, the objects collide at an angle, causing a change in both the magnitude and direction of momentum.

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