We first had to find the coefficient of friction between the different tires of the vehicles and the road. This was done by taking the information it took 100N to drag a 130N car tire. This was plugged into the friction force equation Ff= coefficient of friction * Fn. Fn=130 because that is the weight of the tire in newtons and Ff is 100 because that is force to pull. This give a car coefficient of friction of 0.769. We are told the trucks coefficient is 70% so we multiplied to 0.769 by .7 and got a coefficient of friction of 0.538 for the truck.
We were the able to determine the speed of each vehicle directly after the crash. After the crash the net force on the car is just the friction force. This can be calculated by multiplying the coefficient of friction by the normal force which was given. We then can plug the values into the equation Acceleration = net force/mass. This will allow us to find the negative acceleration of the vehicles after the crash. We can then put what we know in the equation Velocity final ^2= Velocity initial ^2 +2a* change in X. The change in X is given, we just calculated acceleration, and velocity final is 0 because the car is at rest. We can then solve for the initial velocity which is the speed just after the crash and can be seen above.
The final piece of this needed is the speed before the collision which we can calculate. This requires us to use momentum as it is a conserved vector value in the direction of motion. Because of how the vehicles approached the crash we know that the car had only vertical (in the top down view) momentum while the truck started with all horizontal momentum. Because momentum is conserved we then know that Pcar initial= Pcar vertical final + Ptruck vertical final and Ptruck initial= Pcar horizontal final + Ptruck horizontal final. We can find the horizontal and vertical momentum by taking cosine and sine respectively of the angles the vehicles traveled at after the collision and multiplying that by the velocitys of the vehicles right after the collision in the momentum equation P=mass * velocity. This can then be solved like done above to find the velocities of the vehicles right before the crash.
Conclusion
The car driver Mike Rokar was at fault for this collision. Through the calculation above it can be found that right before the collision Mike was traveling at 11.43m/s. Ford motor company states that Mikes Ford Escort can only accelerate at 3m/s/s. Because Mike had a flashing red light he should have stopped before entering the intersection but in order to reach the speed he was at he would have to have been accelerating for over 4 seconds. This clearly did not happen in an intersection meaning that Mike did not reach a full stop like he said breaking the law and putting him at fault. But the Truck driver did lie in his statement as it was found his speed was 12.67m/s not the 6.7m/s he claimed.
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If any clarification is needed on the physics concepts outlined in this report please visit our content pages on the confusing piece of information.