Newton's Laws Legacy Problem #16 Guided Solution

Good problem solvers seldom rush to their calculator before they first get a good conceptual and visual understanding of the physical situation described in the problem. That comes from a careful reading of the problem and a representation of the physical situation using a diagram. Here we read about Myra and Tariq who are doing a lab which involves pulleys and bricks and evidently there's a brick up on a table. We read that it's accelerating across the table top, table tops run horizontally so you know it's accelerating to the right or to the left, it doesn't really matter, just so it's horizontal. And you read about two forces acting upon the brick, ultimately you're asked to determine the net force and acceleration of this brick accelerating across the table top. So now represent this brick by a diagram in which you show the forces acting upon the brick. Now you have to think about the physical situation in order to determine what those forces are and you have to look in the problem for cues. The biggest cue in the problem is that this brick is accelerating horizontally under the influence of two horizontal forces. One of them being the forward force and you can just simply draw an arrow to the right and label it F tension or F tense or tension and say it's equal to 9.54. So we have a rightward force, I just draw a box and put a force starting from the center of the box off to the right, put an arrow on it and label it F tense and I put equal 9.4 newtons. We also read of a friction force on our box, 8.69 newtons. We reason friction opposes the motion of sliding objects and so that's going to the left. I just draw an arrow off to the left, I label it F frict or friction or something of that nature and I say it's equal to 8.69 newtons. Now those aren't the only two forces but those are the two of greatest importance. There is on every object an F grab force straight down. So you can go ahead and draw an arrow down and label it F grab and say it's equal to mg, whatever mg is. Now if you look at your diagram at the moment, there's three forces and the down force isn't being balanced by any other force and that's just not consistent with objects accelerating only horizontally. So there must be a support force and the support force is the normal force and the F norm value is going to be equal to the F grab value, whatever that ends up being. mg, 2.15 times 9.8 would be the F grab. The normal force value is the same amount. Now those two forces up and down are going to balance each other such that the only forces that are left as you add your forces are the forward and the reverse force. And you can add up the forward and the reverse force if you call the reverse friction force negative. And you add the negative 8.69 to the positive 9.54 newtons and you end up with 0.85 newtons in the forward direction right according to your diagram. Now the other quantity we have to calculate in this problem is the acceleration. So you have to think how do you calculate the acceleration. And that's either going to be through kinematics like A equals delta B over T or something like that. Or it's going to be through Newton's laws like A equals F net over M. And here we have just calculated the net force and they even kind of ask us to calculate the net force and then the acceleration. So we take the net force we just calculated and we divide it by the mass. Now you need to be able to look at a problem and know what the 2.15 kilograms is. The fact that it's listed in kilograms means that that's the mass. So plug that into the denominator of your equation and calculate your acceleration.