What is the tension of the string in FIGURE EX14.19?

Question

Accepted Answer

Welcome back, everyone. We are making observations about the following cylindrical copper object. Now we are told this object is occupying a volume of 68 centimeters cute and is suspended from a cord. Now, the object is submerged in petrol. Now the density for petrol is equal to 730 kg per meter cubed. And while we're at it, the density for copper is kg per meter cubed. Now we are tasked with finding what is the tension in our chord. Now, before we get started here, I do wish to acknowledge the multiple choice answers on the left hand side of the screen, those are gonna be the values that we strive for. So without further ado let us begin. Well, what are the forces that are at play here on our copper object? We're going to have two forces acting upward, the tension force of the cord, which is what we want to find as well as the buoyant force acting on the copper object and acting in the other direction, of course, is going to be the weight of copper. Now the copper object here it's not moving right. So what we have is when we use Newton's second law in the y direction, what we have is that tension plus the buoyant force minus the weight is equal to zero, actually going to subtract the buoyant force and add the weight to both sides of my equation. And what I get is that tension is equal to the weight minus the buoyant force. We have formulas for each of these forces. So let's go and plug them in. For the weight. Of course, we just have mass times the acceleration due to gravity minus for a buoyant force, we are going to have the density of the liquid that is in casing the object. So that's going to be the density of our petrol times the volume of the object that is actually submerged, right? So it's fully submerged. That's just going to be the volume of our copper object times our acceleration due to gravity. Now, we can actually, we don't have the mass, right. So we need to sub in for our mass, we know that mass is equal or mass divided by volume is equal to density. In this case, the density of the object multiplying both sides by v. What we get is that mass is equal to the density of copper times the volume of our object dubbing this into our equation here. And actually, I'm gonna go ahead and change colors. What we get for our tension is that tension is equal to density of copper times the volume of our object times the acceleration due to gravity minus the density of petrol times the volume of our copper object since it's fully submerged times our acceleration due to gravity. Now, before we can start plugging values, we need to make sure everything is in the correct units and it looks like everything is except our volume. We need this in meters, cubes. So let's go ahead and convert. We know that there are 100 centimeters in 1 m. And I'm gonna go ahead and cube both the top and the bottom centimeters. Cube cancel out on top and bottom, but we still need to cube that 100 value. So what we get multiplying straight across is that our volume of our copper object is 0.000068 m cubed. Now that we have that let's go ahead and find the tension in our court. Tension in our court is going to be equal to times 0. times 9.81 minus 730 times 0. times 9.81 which gives us that our tension is equal to 5.49 newtons corresponding to our final answer. Choice of D Thank you all so much for watching. I hope this video helped. We will see you all in the next one.

What is the tension of the string in FIGURE EX14.19?

Verified Solution

Key Concepts

Tension in a String

Equilibrium Conditions

Free Body Diagram (FBD)