Determining position of an object after inelastic collision

In summary: You will get a quadratic equation in d, the distance the combined wreckage moved. That will give you two values of d, the "positive" one being the one you want. Then you can use the same angle to find the two components of d. You will find that the distance in each direction is negative, which is what you want because the wreckage moves in the negative direction (opposite to the direction of the collision).
  • #1
Synchron
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0

Homework Statement


A 39,000 lb truck A and a 3968 lb sports car B collide at an intersection. At the moment of the collision, the truck and the sports car are traveling with speeds vA = 70 mph and vB = 30 mph. Assume that the entire intersection forms a horizontal surface. Letting the line of impact be parallel to the ground and to the pre-impact velocity of the truck, determine the post impact velocities of A and B if A and B become entangled. Furthermore, assuming that the truck and the car slide after impact and that the coefficient of kinetic friction is 0.9, determine the position at which A and B come to a stop relative to the position they occupied at the instant of impact.

ple8030x_p05185.png


Homework Equations


What is required for the problem are the conservation of momentum and energy equations

The Attempt at a Solution


I've already determined the post impact velocities of A and B if they're entangled. The initial i component is the mass of car x vBand the final i component is the combined mass of car and truck x vi( i component of post impact velocity). Same is said for j component with initial as mass of truck x vA and the final j component is the combined mass of car and truck x vj. The result was v = 4.063i + 93.19j ft/s

What I'm having trouble with is determining the position. What I've tried to do is use conservation of energy in each direction 0.5v^2 = μgd, where v is each component and I solve for di and dj in two separate instances which did not work. I also tried to to use the magnitude of the velocity instead, solve for magnitude of d, then use the angle between the two velocity components to determine the components of distance. I can't seem to determine the method so any help is appreciated.
 

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  • #2
Synchron said:
where v is each component and I solve for di and dj in two separate instances
That is not going to work. That would produce the same answer whether the wreckage moved in a straight line to its destination or moved first in the x direction then in the y direction (which would clearly cost more frictional energy).
Synchron said:
use the magnitude of the velocity instead, solve for magnitude of d, then use the angle between the two velocity components to determine the components of distance.
That should do it.
 

Related to Determining position of an object after inelastic collision

1. How is the position of an object determined after an inelastic collision?

The position of an object after an inelastic collision is determined by considering the conservation of momentum and the kinetic energy of the system. The final position can be calculated using the equations of motion and the initial positions and velocities of the objects involved in the collision.

2. What is an inelastic collision?

An inelastic collision is a type of collision where kinetic energy is not conserved. This means that after the collision, the objects involved stick together and move with a common velocity. In this type of collision, some of the kinetic energy is lost in the form of heat or sound.

3. How is momentum conserved in an inelastic collision?

In an inelastic collision, the total momentum of the system is conserved. This means that the sum of the initial momentums of the objects involved in the collision is equal to the sum of the final momentums. This can be expressed mathematically as m1u1 + m2u2 = (m1 + m2)v, where m is the mass of the object and u and v are the initial and final velocities, respectively.

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

In an elastic collision, both momentum and kinetic energy are conserved. This means that the objects involved in the collision bounce off each other and continue to move with their original velocities. In an inelastic collision, only momentum is conserved and some of the kinetic energy is lost due to deformation or other factors.

5. Can the position of an object after an inelastic collision be predicted with 100% accuracy?

No, the position of an object after an inelastic collision cannot be predicted with 100% accuracy. This is because there are many factors that can affect the accuracy of the prediction, such as external forces, friction, and the elasticity of the objects involved. However, using the principles of conservation of momentum and energy, a close approximation of the final position can be calculated.

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