Newton's Laws Legacy Problem #26 Guided Solution

A good problem solver is going to approach this problem by carefully reading the problem, getting a mental picture of what's going on, representing the physical situation with a free body diagram. Then they are going to identify the known information and the unknown quantity trying to be calculated. They are going to proceed from there by plotting out a strategy to get from the known information to the unknown information. That process applied to this problem of Mr. Schneider being pulled across the floors by Mr. London would involve drawing a free body diagram representing the forces of Mr. Schneider. First of all, Mr. Schneider weighs something as does everybody and so there is a down force on Mr. Schneider's body. You can represent Mr. Schneider by a square, no offense to him, and you can draw a force or arrow down and label it F-grab. We know the mass of Mr. Schneider so we could calculate that and eventually we will get around to calculating that F-grab value as m times g, 84 kilograms times 9.8. Additionally, there is a support force from the floor pushing up on Mr. Schneider, so draw an arrow upwards and label it F-norm, that's the force of the floor pushing up on Mr. Schneider. Mr. Schneider is accelerating but not vertically, thus the two vertical forces are going to balance each other. That's a concept I draw in this problem. Now we begin to look at the horizontal forces and it begins with an applied force. Mr. London is applying a force to Mr. Schneider to pull him across the floor. So we draw an arrow to the right and we label it F-app or F-applied. We don't know this value. This is the unknown value, the big question mark, the thing we are trying to determine. Finally, there is a friction force upon Mr. Schneider's body so we draw an arrow to the left and friction force pushes left on Mr. Schneider. Friction as it usually does opposes the motion of an object or at least the would-be motion of an object. So we draw this sliding friction force arrow to the left. We label it F-friction. Now what we wish to do is to take the known information and solve for the F-applied. We know M equals 84. We know mu or the coefficient of friction equals 0.35. That's the mu from the equation F-frict equals mu F-norm. We know A equals 1.2 meters per second per second. Now plot your strategy. Think relationships. How are things related to one another? How can you relate the mu and the A and the M? Well first thing, when I think about mu, the only place that ever shows up is in the equation F-frict equals mu F-norm. Now F-norm I don't know but I can calculate because as mentioned it balances F-graph and we can calculate F-graph as mg and F-norm is the same value. So go ahead and calculate that now and use what you have for the value of F-norm to calculate F-friction as this 0.35 times the normal force you just calculated. Now know the friction force. We know M and we know A. You've got to think relationships again. What can you calculate if you know M and A? Well you can calculate the F-net. It's always equal to MA. So you can take your 84 times the 1.2 and you can determine the net force upon Mr. Schneider. Now when I do that calculation I get about 100.8 newtons and that's to the right since the acceleration is to the right. So what this F-net of 100.8 newtons tells me is that when you add up all the forces they have to add up to that value 100.8 which means that the rightward force has got to be bigger than the leftward force by that amount, by 100.8. And so if I know the leftward force I must figure that the rightward force is bigger by 100.8. Just add that to the value you got for F-friction and that gives you the applied force. It's always reasonable at this time to just kind of do a check. Does that look right? Is that applied force minus the friction force going to add up to 100.8 and if it does you've got your answer correct.