Newton's Laws Legacy Problem #18 Guided Solution

In this unit, if you're practicing the habits of an effective problem solver, then what you're doing is you're reading each problem carefully and you're drawing a free body diagram. You're thinking real hard about what forces act upon the object and in what direction and you're representing it by these free body diagrams. You'll see some of these free body diagrams drawn for you in a few problems on this set of 30 problems and you'll also see them in the physics classroom tutorial. Here we read about Kelly and Jarvis who are pushing a baby grand piano onto stage. We're told they're pushing forward with a force of 524 newtons. We call that an applied force, an F-app. And on our free body diagram, we'd simply draw a box and draw an arrow off to the right and we label it F-app and we might even say it's equal to 524 newtons and put that right there on the diagram. We're told that they're budging it from rest and getting it up to speed and as they do, it's experiencing 418 newtons of friction. When you push something to the right, friction opposes that motion and pushes to the left. So we have a leftward friction force. So we put an arrow on our diagram again, we label it F-frict and we say it's equal to 418 newtons. Now those are not the only two forces upon our object. There's gravity pulling down and then the floor is pushing up with a supporting force known as F-normal. So we could draw those two forces if we wish, an arrow called F-grab down. Its value can be calculated from the mass, simply m times g and then F-norm arrow up. And the importance of that is that the F-norm is balancing gravity such that our piano does not accelerate up and down. So the value of the F-normal equals F-grab and the two forces add to zero. Now in this unit, the reason we center everything around a free body diagram is because by knowing the forces, we can determine the net force and knowing the net force, we can determine the acceleration. And that's one of our two unknowns in this question. What's the acceleration? And the way I'm going to determine it is know the equation that A equals F-net over m. I'm going to calculate F-net and divide the value by mass. So we'll do that right now. We'll talk it through. We have 524 newtons to the right, 418 newtons to the left, some up and downs which don't matter. We have to add up the right and the left. We call the left negative, add it to the positive right. We end up with a net force of 106 newtons for this piano. Now we know A equals 106 newtons divided by the mass. Given here is 158 kilograms. I get my acceleration. I know that mass, that number 158, to be the mass because I notice it's in kilograms and mass is in units of kilograms. So now I've calculated the acceleration. The second part of the question is if this situation of a forward force of 524 newtons is maintained for 1.44 seconds, then what's the speed that the piano will have at the end of that time? The way we get that answer is we would take a kinematic equation and solve for a final speed. But to think about what I know. I know that the acceleration value is whatever I calculated from part A. I know that the V original, V0, is 0 meters per second since it's starting from rest. And I know that the T is 1.44 seconds. There's three known pieces of information about the kinematics of this piano. Now I should be able to find an equation that relates those three variables to Vf. The equation is Vf equals the original plus At. The V0 is 0 so that term cancels out on the right side. The equation becomes Vf equals At. The A you calculated. The T you've been given. Now you can calculate the speed.