If a car stops suddenly, you feel \"thrown forward\". We\'d like tounderstand wh

Question

If a car stops suddenly, you feel "thrown forward". We'd like tounderstand what happens to the passengers as a car stops. Imageyourself sitting on a very slippery bench inside a car.This bench has no friction, no seat back, and there's nothing foryou to hold on to.

a) Draw a picture and identify all of the forces acting on you asthe car travels at a perfectly steady speed on level ground.

b) Draw your free-body diagram. Is there a net force on you? If soin which direction?

c) Repeat parts a and b with the car slowing down.

d) Describe what happens to you as the car slows down.

e) Use Newton's laws to explain why you seem to be "thrown forward"as the car stops. Is there really a force pushing you forward?

f) Suppose now that the bench is not slippery. As the car slowsdown, you stay on the bench and don't slide off. What force isresponsible for your deceleration? In which direction does thisforce point? Include a free-body diagram as part of youranswer.

g) How would the force diagram change from that in (f)? Explain how you can slide forward (from rest), yet you are stillaccelerating backwards?! Hint: you’ve essentiallyanswered this in (e); explain how things look from the groundframe of reference as opposed to the car frame of reference. Whichone is an inertial frame of reference? Which onenon-inertial?

I answered all the parts but I am not sure if my answers arecorrect. In part a I thought there would be normal force up andgravity down, but nothing else meaning part a and part b would havea net force of zero. I thought part c would have a force going tothe right (forward, in the direction of travel) as the car slowsdown. Therefore the net force would be in the positive x directionin part d. However I was unsure how to describe the forces interms of Newton's laws in part e, and what would change in part fand g.

Any help would be appreciated.

Explanation / Answer

As for e): Newton's first law states that anything will continue in thedirection it was going if there is no force acting on it.Therefore, you will continue going as you did before the carstopped, but the car itself stopped moving. So, from theviewpoint of the car, the car has not moved at all (it isalways at the origin if we are looking from the car's point ofview), but you are suddenly moving forward. It is not that you havechanged velocity, but the car has and therefore you are slidingforward in relation to the car.See http://en.wikipedia.org/wiki/Non-inertial_frame for moreinformation.
f) The friction force between you and the bench is responsiblefor you not sliding off. It points in the positive x direction.Just draw you, the bench (a rectangle), the force of gravitypointing down, the normal force pointing up, and the friction forcepointing to the right.
g) "How would the force diagram change from that in (f)?"Didn't we just do (f)? It would change from (b) with the additionof the friction force. You are sliding forward from rest in relation to the car(remember, from the car's point of view it is always at theorigin). However, in relation to someone standing on the road, yourspeed is decreasing as you eventually come to a stop along with thecar. The car's frame of reference is non-inertial, while theoutside person's frame of reference is inertial. You can search forthese on wikipedia.

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