Newton's Laws Legacy Problem #20 Guided Solution

Good problem solvers have good habits, and in this unit, those good habits involve reading the problem carefully and interpreting the physical situation in such a way that they construct a free body diagram representing the forces acting upon the object. Here we read about a rope that is used to pull a bucket out of a deep well. We're given that 2.89 kilograms has the mass of the bucket. What we wish to do is calculate the acceleration that the bucket will have if the tension in the rope is 30.2 newtons. So our unknown in the first part of this problem is the A. We want to know what A is. Now you begin by drawing a picture of the bucket or just representing the bucket by a box and then drawing the forces which act upon the bucket. Label them according to their type and give them a magnitude. So if you think about that bucket, there's a rope connected to it and the tension force is described. So I just draw an arrow up and label it F tension. I know it's up because it's pulling the bucket up out of the well. There's also an F grab on the bucket, the weight of the bucket. So I draw an arrow down and I label it F grab. Now the up arrow, F tension, is equal to 30.2 newtons. If I want to calculate the acceleration, I need to know the down arrow so I can find the net force. After all, A equal net force divided by mass. So I have to think, how do I get the down force value? It's F grab, which is always equal to mg. The m here is given as 2.89 newtons. Multiply it by the 9.8 and you get the down force. Now you know the only two forces acting on the bucket. The up force, whose value is given. The down force, whose value you just calculated, and add them as vectors. When you add the two forces up as vectors, you would get a small upward force. That upward force is going to cause an upward acceleration. And so what I will do is I will say A equal that F net divided by the mass of 2.89. That gives me the value for acceleration. In the second part of the problem, they're asking you a kinematic question. They're asking you to find the final speed of the bucket if it starts from rest and it accelerates in this manner for 2.16 seconds. So what you know about that motion is you know that V0 is zero. You know that A is whatever you calculated from part A. And you know that T is 2.16 seconds. And what you're looking to calculate is VF. The way you do this, you would look for a kinematic equation. The big four has as one of the equations one that goes VF equal VO plus AT. Where the VF is our unknown we're looking for. The VO is zero, the A you calculated, and the T is 2.16. So the VO term drops out of the right side of the equation. You have VF equal AT. Plug in the numbers for A and T and you have your answer for the final speed.