### PHYS 103, Module 3 (Chapter 5) Textbook Problems

Chapter 5

48. Show that the water pressure at the bottom of the 50-m-high water tower in Figure 5.3 is 490,000 $N/m^2$, or is approximately 500 kPa.

The water pressure at depth H (in meters) below the surface is

$P = \rho*g*H = 1000*9.8*50 =490000 N/m^2$

Since $1 Pa = 1 N/m^2$ then $490000 N/m^2 = 490 kPa = approx. 500 kPa$

(above $\rho$ is the water densitry (in $kg/m^3$) and g the gravitational acceleration (in $m/s^2$))

74. Stand on a bathroom scale and read your weight. When you lift one foot up so you’re standing on one foot, does the reading change? Does a scale read force or pressure?

The reading on the scale will not change. The weight scale reads the total force applied. NOT THE PRESSURE. This is because the surface area of the scale is much larger than the contact area of one or both feet, and therefore it does not matter if you stand on a foot or on both feet.

78. Why is it inaccurate to say that heavy objects sink and light objects float? Give exaggerated examples to support your answer.

The property of sinking or floating on water depends on the relative density of the object with respect to the water density.

Suppose you have a ping pong ball filled with lead and a large basketball made of sheet of rubber inflated with air. The ping pong ball is lighter than the basketball (because it is much smaller), yet the ping pong ball will sink (because its total density is higher than the water density) and the basketball will float on the water (because its total density is smaller than the water density).

88. In a sporting goods store you see what appears to be two identical life preservers of the same size. One is filled with Styrofoam and the other one is filled with lead pellets. If you submerge these life preservers in the water, upon which is the buoyant force greater? Upon which is the buoyant force ineffective? Why are your answers different?

Buoyant force = weight of the liquid displaced by the object.

Since both live preservers are identical the buoyant force is equal on both.

However the buoyant force is ineffective on the lead filled item.

This happens because flotation on water depends on the relative density of the object with respect to the water density. Since the density of lead is greater than the water density and the Styrofoam density is lighter the water density, the lead filled item will sink and the Styrofoam filled item will float.

94. Your friend says that the buoyant force of the atmosphere on an elephant is significantly greater than the buoyant force of the atmosphere on a small helium-filled balloon. What do you say?

Buoyant force = weight of the displaced fluid by the object volume.

Since the elephant is bigger than the baloon (has a larger volume) the buoyant force on the elephant is bigger than the buoyant force on baloon. My friend is right.

96. When you replace helium in a balloon with hydrogen, which is less dense, does the buoyant force on the balloon change if the balloon remains the same size? Explain.

Buoyant force = weight of the displaced fluid by the object volume.

Since the balloon remains the same size, the buoyant force is the same regardless the gas that fills the balloon.

The total upward force (= buoyant force - weight) on the hydrogen balloon is greater than the total upward force on the helium balloon since hydrogen weight is less than helium weight for the same size balloon.

98. Two identical balloons of the same volume are pumped up with air to more than atmospheric

pressure and suspended on the ends of a stick that is horizontally balanced. One of the balloons is then punctured. Is there a change in the stick’s balance? If so, which way does it tip?

The answer is YES the balance of the stick will change. Initially both balloons exerts the same force on both ends of the stick (they are identical). Because the density of the air in the balloons is proportional to the pressure inside (greater than atmospheric pressure), it means both balloons are heavier than normal air. When a balloon is punctured the other balloon becomes heavier, and stick will tip toward the heavier balloon (the balloon not punctured).

108. The photo shows physics teacher Marshall Ellenstein walking barefoot on broken glass bottles

in his class. What physics concept is Marshall demonstrating, and why is he careful that the broken

pieces are small and numerous? (The Band-Aids on his feet are for humor!)

This demonstrates the concept of PRESSURE. Pressure is by definition the total force divided by the surface area on which the force is applied. If the glass pieces are numerous and small the total contact area between the foot and the glass is bigger. Since the force is the same (equal to the weight of the teacher), then the pressure on glass will be smaller and therefore the broken glass will not puncture the skin of the teacher.

114. If liquid pressure were the same at all depths, would there be a buoyant force on an object submerged in the liquid? Discuss your explanation of this with your friends.

Buoyant force = weight of the liquid displaced by the object.

The weight of the liquid does not depend on its pressure but on its density. The density of a liquid does not vary at all (in the first approximation) with the pressure. The buoyant force will still exist.

48. Show that the water pressure at the bottom of the 50-m-high water tower in Figure 5.3 is 490,000 $N/m^2$, or is approximately 500 kPa.

The water pressure at depth H (in meters) below the surface is

$P = \rho*g*H = 1000*9.8*50 =490000 N/m^2$

Since $1 Pa = 1 N/m^2$ then $490000 N/m^2 = 490 kPa = approx. 500 kPa$

(above $\rho$ is the water densitry (in $kg/m^3$) and g the gravitational acceleration (in $m/s^2$))

74. Stand on a bathroom scale and read your weight. When you lift one foot up so you’re standing on one foot, does the reading change? Does a scale read force or pressure?

The reading on the scale will not change. The weight scale reads the total force applied. NOT THE PRESSURE. This is because the surface area of the scale is much larger than the contact area of one or both feet, and therefore it does not matter if you stand on a foot or on both feet.

78. Why is it inaccurate to say that heavy objects sink and light objects float? Give exaggerated examples to support your answer.

The property of sinking or floating on water depends on the relative density of the object with respect to the water density.

Suppose you have a ping pong ball filled with lead and a large basketball made of sheet of rubber inflated with air. The ping pong ball is lighter than the basketball (because it is much smaller), yet the ping pong ball will sink (because its total density is higher than the water density) and the basketball will float on the water (because its total density is smaller than the water density).

88. In a sporting goods store you see what appears to be two identical life preservers of the same size. One is filled with Styrofoam and the other one is filled with lead pellets. If you submerge these life preservers in the water, upon which is the buoyant force greater? Upon which is the buoyant force ineffective? Why are your answers different?

Buoyant force = weight of the liquid displaced by the object.

Since both live preservers are identical the buoyant force is equal on both.

However the buoyant force is ineffective on the lead filled item.

This happens because flotation on water depends on the relative density of the object with respect to the water density. Since the density of lead is greater than the water density and the Styrofoam density is lighter the water density, the lead filled item will sink and the Styrofoam filled item will float.

94. Your friend says that the buoyant force of the atmosphere on an elephant is significantly greater than the buoyant force of the atmosphere on a small helium-filled balloon. What do you say?

Buoyant force = weight of the displaced fluid by the object volume.

Since the elephant is bigger than the baloon (has a larger volume) the buoyant force on the elephant is bigger than the buoyant force on baloon. My friend is right.

96. When you replace helium in a balloon with hydrogen, which is less dense, does the buoyant force on the balloon change if the balloon remains the same size? Explain.

Buoyant force = weight of the displaced fluid by the object volume.

Since the balloon remains the same size, the buoyant force is the same regardless the gas that fills the balloon.

The total upward force (= buoyant force - weight) on the hydrogen balloon is greater than the total upward force on the helium balloon since hydrogen weight is less than helium weight for the same size balloon.

98. Two identical balloons of the same volume are pumped up with air to more than atmospheric

pressure and suspended on the ends of a stick that is horizontally balanced. One of the balloons is then punctured. Is there a change in the stick’s balance? If so, which way does it tip?

The answer is YES the balance of the stick will change. Initially both balloons exerts the same force on both ends of the stick (they are identical). Because the density of the air in the balloons is proportional to the pressure inside (greater than atmospheric pressure), it means both balloons are heavier than normal air. When a balloon is punctured the other balloon becomes heavier, and stick will tip toward the heavier balloon (the balloon not punctured).

108. The photo shows physics teacher Marshall Ellenstein walking barefoot on broken glass bottles

in his class. What physics concept is Marshall demonstrating, and why is he careful that the broken

pieces are small and numerous? (The Band-Aids on his feet are for humor!)

This demonstrates the concept of PRESSURE. Pressure is by definition the total force divided by the surface area on which the force is applied. If the glass pieces are numerous and small the total contact area between the foot and the glass is bigger. Since the force is the same (equal to the weight of the teacher), then the pressure on glass will be smaller and therefore the broken glass will not puncture the skin of the teacher.

114. If liquid pressure were the same at all depths, would there be a buoyant force on an object submerged in the liquid? Discuss your explanation of this with your friends.

Buoyant force = weight of the liquid displaced by the object.

The weight of the liquid does not depend on its pressure but on its density. The density of a liquid does not vary at all (in the first approximation) with the pressure. The buoyant force will still exist.