Do notice that there is a forward force on the lower carton in addition to the frictional force acting backwards on it, and so you do need to justify to yourself that it doesn’t affect that answer.
Regardless, this problem is provided as a sample because it illustrates how you would apply Newton’s 2nd and 3rd Law in a wide variety of problems that you might be asked to solve on your homework, and so it is worth looking at the mathematical analysis. At the start of the problem, the truck and both cartons are traveling forward.
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A delivery truck with two stacked cartons in the back brakes quickly.
If there was no kinetic friction, any object that you nudge (for example, a toy car) would never stop moving, as, according to Newton's first law, no force would act on it, so it would keep on going with a constant velocity.
Even though the formula is the same for static and kinetic friction, you need to remember that the coefficients of friction are different.It is true that the bottom carton feels the weight of the top carton.However, that information is transmitted through the force of contact, n.You can use this tool as a coefficient of friction calculator, too.Static friction acts when the object remains stationary. If we don't take friction into account, even the smallest force should cause some acceleration of the box according to Newton's second law.The coefficient of kinetic friction is usually lower than the one of static friction.Friction Calculator can be embedded on your website to enrich the content you wrote and make it easier for your visitors to understand your message.The carton on the bottom just barely stays put on the floor of the truck. The top carton has a mass of 27 kg and the mass of the bottom carton is 22 kg.The coefficient of static friction between the bottom carton and the truck is 0.42, and the coefficient of kinetic friction for that surface is 0.35.As the truck slows down, the bottom carton wants to slide forward (continue at a constant velocity) so the friction that the truck puts on the bottom carton (fr) opposes a motion in which the top carton slides forward relative to the bottom (friction on the top carton is directed backwards) and the bottom carton slides backward with respect to the top (friction on the bottom carton is directed forward.) A good analogy for friction is Velcro—if the bottom tape pulls backward on the top tape, the top tape pulls forward on the bottom one.I used the same symbol for this force (fr) on both free body diagrams, because both cartons feel the strength of the interaction equally (Newton’s Third Law.) The gravitational force on the bottom carton is due to its mass only.