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# I am having a confusion in the following question-Q-To stimulate car accidents auto manufacturers study the collision of moving cars with mounted springs of different spring constants. consider a typical simulation with a car of mass 1000 kg moving with a speed 5m/s on a smooth road and colliding with a horizontally mounted spring of spring const-6.25*(10)^3 what is the maximum compression of the spring 1.when there is no friction and 2. when u=0.5 ?Now the first part is easy. we are able to find the kinetic energy which is converted to P.E. at max compression. so we get 12500 J =0.5*k*(x)^2 and then we get the compression x as 2.00 metres. But what about the second part? In this first and foremost lets consider the FBD which is my main problem in this question. why is the friction acting in the +ve x axis. if the wheels of the car are rolling the according to me the friction should be in the direction of the motion.

Shobhit Varshney IIT Roorkee
7 years ago
Hi,

The direction of friction is not always in the direction of motion in case of rolling. It depends on the net velocity of the lowermost point ,
ie, translational velocity of COM – rotational velocity (wR)
If v-wR > 0, then friction acts opposite to direction of motion
v – wR < 0, then it acts in the direction of motion.

In this question, you can assume either of the two directions of motion because we are applying conservation of energy and the work done by friction woud be same in both cases.

thanks