Question

Your team at the lab has developed a new and hopefully non-toxic liquid, named gloop by marketing, to be used in swimming pools. Gloop is denser than water, so it provides more buoyancy for swimming. 1. The equation sheet lists P = P?+?gd . Briefly describe what this equation is about, and what each of these symbols (except g) represents in this equation. 2. Diving in deep water can cause pressure-induced pain in the eardrums. How deep would you have to dive into gloop (density 2000-4000 kg/m³) to experience the same total pressure felt at a depth of 3-8 m in real water? 3. Suppose you accidentally dropped a phone or a tablet into a big tank of gloop. Making reasonable (but randomized) assumptions about the length and width of the device's screen, calculate the amount of force the gloop exerts on the device's screen at the depth calculated in Q1. Hint: always best to do conversions first. 4. Next you'll be dropping a ball into the gloop tank. Let the ball's mass be 0.3-0.5 kg, and its radius 5-10 cm. Prove that the ball will float when dropped in. Show work and briefly explain. Again, conversions first. 5. Calculate the percentage of the ball's volume below the surface when floating in gloop. Briefly explain your work, since it won't involve any equations from the equation sheet (or any other special equations). 6. Now you push downward on on the ball, making it sink lower into the gloop, but not fully beneath the surface. Draw a complete FBD for the ball as you hold it steady in this partly-submerged state. 7. Calculate the amount of force you have to exert to keep the ball submerged with 60-80% of its volume below the surface. This is not equal to the buoyant force, so if your FBD suggests otherwise, the FBD is incomplete. 8. Now you push the ball down so it first sinks completely beneath the surface and then all the way to the bottom of the gloop tank. Sketch a graph of the magnitude FB of the buoyant force acting on the ball vs. t (time) for this entire process. Mark the start time, the time when the ball is first fully submerged, and the time when it reaches the bottom. Then explain the physics: why does FB behave as shown in the graph? No further calculations are needed to answer this question, and no numerical values should appear in your graph – this is a qualitative question, not a quantitative one. FB goes on the vertical axis, time on the horizontal axis.

Your team at the lab has developed a new and hopefully non-toxic liquid, named gloop by marketing, to be used in swimming pools. Gloop is denser than water, so it provides more buoyancy for swimming.

1. The equation sheet lists P = P?+?gd . Briefly describe what this equation is about, and what each of these symbols (except g) represents in this equation.

2. Diving in deep water can cause pressure-induced pain in the eardrums. How deep would you have to dive into gloop (density 2000-4000 kg/m³) to experience the same total pressure felt at a depth of 3-8 m in real water?

3. Suppose you accidentally dropped a phone or a tablet into a big tank of gloop. Making reasonable (but randomized) assumptions about the length and width of the device's screen, calculate the amount of force the gloop exerts on the device's screen at the depth calculated in Q1. Hint: always best to do conversions first.

4. Next you'll be dropping a ball into the gloop tank. Let the ball's mass be 0.3-0.5 kg, and its radius 5-10 cm. Prove that the ball will float when dropped in. Show work and briefly explain. Again, conversions first.

5. Calculate the percentage of the ball's volume below the surface when floating in gloop. Briefly explain your work, since it won't involve any equations from the equation sheet (or any other special equations).

6. Now you push downward on on the ball, making it sink lower into the gloop, but not fully beneath the surface. Draw a complete FBD for the ball as you hold it steady in this partly-submerged state.

7. Calculate the amount of force you have to exert to keep the ball submerged with 60-80% of its volume below the surface. This is not equal to the buoyant force, so if your FBD suggests otherwise, the FBD is incomplete.

8. Now you push the ball down so it first sinks completely beneath the surface and then all the way to the bottom of the gloop tank. Sketch a graph of the magnitude FB of the buoyant force acting on the ball vs. t (time) for this entire process. Mark the start time, the time when the ball is first fully submerged, and the time when it reaches the bottom. Then explain the physics: why does FB behave as shown in the graph? No further calculations are needed to answer this question, and no numerical values should appear in your graph – this is a qualitative question, not a quantitative one. FB goes on the vertical axis, time on the horizontal axis.

Your team at the lab has developed a new and hopefully non-toxic liquid, named gloop by marketing, to be used in swimming pools. Gloop is denser than water, so it provides more buoyancy for swimming.

1. The equation sheet lists P = P?+?gd . Briefly describe what this equation is about, and what each of these symbols (except g) represents in this equation.

2. Diving in deep water can cause pressure-induced pain in the eardrums. How deep would you have to dive into gloop (density 2000-4000 kg/m³) to experience the same total pressure felt at a depth of 3-8 m in real water?

3. Suppose you accidentally dropped a phone or a tablet into a big tank of gloop. Making reasonable (but randomized) assumptions about the length and width of the device's screen, calculate the amount of force the gloop exerts on the device's screen at the depth calculated in Q1. Hint: always best to do conversions first.

4. Next you'll be dropping a ball into the gloop tank. Let the ball's mass be 0.3-0.5 kg, and its radius 5-10 cm. Prove that the ball will float when dropped in. Show work and briefly explain. Again, conversions first.

5. Calculate the percentage of the ball's volume below the surface when floating in gloop. Briefly explain your work, since it won't involve any equations from the equation sheet (or any other special equations).

6. Now you push downward on on the ball, making it sink lower into the gloop, but not fully beneath the surface. Draw a complete FBD for the ball as you hold it steady in this partly-submerged state.

7. Calculate the amount of force you have to exert to keep the ball submerged with 60-80% of its volume below the surface. This is not equal to the buoyant force, so if your FBD suggests otherwise, the FBD is incomplete.

8. Now you push the ball down so it first sinks completely beneath the surface and then all the way to the bottom of the gloop tank. Sketch a graph of the magnitude FB of the buoyant force acting on the ball vs. t (time) for this entire process. Mark the start time, the time when the ball is first fully submerged, and the time when it reaches the bottom. Then explain the physics: why does FB behave as shown in the graph? No further calculations are needed to answer this question, and no numerical values should appear in your graph – this is a qualitative question, not a quantitative one. FB goes on the vertical axis, time on the horizontal axis.

Added by Maurice M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Rahul Kumar

04/16/2022

Step 1

- P is the total pressure at the depth d - Po is the atmospheric pressure - p is the density of the fluid - g is the acceleration due to gravity - d is the depth from the surface Show more…

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Your team at the lab has developed a new and hopefully non-toxic liquid, named gloop by marketing, to be used in swimming pools. Gloop is denser than water, so it provides more buoyancy for swimming. 1. The equation sheet lists P = P₀+̑gd . Briefly describe what this equation is about, and what each of these symbols (except g) represents in this equation. 2. Diving in deep water can cause pressure-induced pain in the eardrums. How deep would you have to dive into gloop (density 2000-4000 kg/m³) to experience the same total pressure felt at a depth of 3-8 m in real water? 3. Suppose you accidentally dropped a phone or a tablet into a big tank of gloop. Making reasonable (but randomized) assumptions about the length and width of the device's screen, calculate the amount of force the gloop exerts on the device's screen at the depth calculated in Q1. Hint: always best to do conversions first. 4. Next you'll be dropping a ball into the gloop tank. Let the ball's mass be 0.3-0.5 kg, and its radius 5-10 cm. Prove that the ball will float when dropped in. Show work and briefly explain. Again, conversions first. 5. Calculate the percentage of the ball's volume below the surface when floating in gloop. Briefly explain your work, since it won't involve any equations from the equation sheet (or any other special equations). 6. Now you push downward on on the ball, making it sink lower into the gloop, but not fully beneath the surface. Draw a complete FBD for the ball as you hold it steady in this partly-submerged state. 7. Calculate the amount of force you have to exert to keep the ball submerged with 60-80% of its volume below the surface. This is not equal to the buoyant force, so if your FBD suggests otherwise, the FBD is incomplete. 8. Now you push the ball down so it first sinks completely beneath the surface and then all the way to the bottom of the gloop tank. Sketch a graph of the magnitude FB of the buoyant force acting on the ball vs. t (time) for this entire process. Mark the start time, the time when the ball is first fully submerged, and the time when it reaches the bottom. Then explain the physics: why does FB behave as shown in the graph? No further calculations are needed to answer this question, and no numerical values should appear in your graph – this is a qualitative question, not a quantitative one. FB goes on the vertical axis, time on the horizontal axis.

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00:01 In the question it has been given that a team has developed a new non -toxic liquid named loop.

00:13 So in the question number one, there is the equation p equals to p -not plus row g d.

00:22 Basically p is here the pressure, that is absolute pressure.

00:28 For example, let's suppose this is the swimming pool and this is the liquid.

00:34 Then p -not is the pressure at the surface of the liquid and p is the pressure at the depth d that is d is here density sorry d is here the depth from the surface g is the acceleration due to gravity and row is the density so with depth p will be equals to p -0 plus density into acceleration due to gravity into depth.

01:24 Now in the second part of the question it has been asked.

01:28 To find the depth, one has to dive to experience the same total pressure felt at the depth of 3 to 8 meter in real water.

01:41 So let's say for 3 meter deep in water, pressure will be p equals to p p .0 plus row water that is density of water into g into depth that is equal to three meter.

02:07 Now similarly for gloop p will be equal to p .0 plus row that is the density of the gloop into g into h.

02:20 Now equating this p1 and p2 we will have p .0 plus row water into g into 3 equals to p .0 plus row gloop into g into h.

02:40 So p .0 p .0 will cancel out.

02:45 H will be equal to row water, that is let's say, row w into 3 divided by row g, that is row density of the gloop.

03:02 Now we know that density of water is 1000 into 3.

03:10 And let's suppose density of gloup is average 3 ,000 because it has been asked to choose from 2 ,000 to 4 ,000 so we have chosen here 3 ,000 so h will be here comes equal to 1 meter.

03:29 That means for water one has to go up to depth of 3 meter to fill the same pressure one has to go into gloop up to 1 meter only.

03:47 Now this is because the more density of the glupe fluid.

03:57 Now in the part 3 of the question it has asked if a mobile screen has been dropped into the big tank of gloop, then we have to find the amount of force the liquid will exert on the device screen.

04:17 We know that p is given as p0 plus r, rho d, so let's assume that p0 is here atmospheric pressure that is 101 .325 kilo pascal.

04:39 Now let's suppose depth is taken as 3 meter.

04:48 Density of the glup is taken as 3 ,000 kg per meter cube and g we all know that 9 .81.

04:59 So at the depth of 3 meter the ultimate pressure will be p equals to 101.

05:05 325 plus 3 ,000 into 3 into 9 .81.

05:15 That comes equals to 189 .1 kilo pascal...

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