Fluids and Solids Introduction

From MyMCAT

Contents 1 Introduction 2 Density 2.1 Specific Gravity 3 Pressure

[edit] Introduction

Since grade school everyone has learned that matter comes in three states. These states are distinguished by the strength of the bonds holding the molecules of the matter together. The three states of matter are:

• Solids: The strong bonds between molecules make solids rigid and very difficult to deform.
• Liquids: The relatively weak bonds between molecules allow liquids to be deformed without effort. Liquids have a fixed volume, but their shape is determined by the shape of the container holding them.
• Gases: Virtually no bonds exist between gas molecule so a gas will spread into any available space. The volume of a gas is determined by the size of the container holding it.

The most important distinction is that while solids are rigid and can withstand shearing, fluids (both liquid and gas) can flow and conform easily to the containers they are in. Fluids are also capable of exerting forces perpendicular to their surfaces.

[edit] Density

For all the states of matter density is defined as the mass per unit volume:

where, in SI Units:

ρ (rho) is the density of the substance, measured in kg·m^–3

m is the mass of the substance, measured in kilograms (kg)

V is the volume of the substance, measured in cubic meters (m³)

Note that the density of water is 1g/mL = 1g/cm³ = 1000kg/m³ (You need to know this value for the MCAT!)

1. What is the mass of 25mL's of a liquid who's density is 3.2g/mL?

	40 g
	80 g
→	Using the formula density = mass / volume, we can rearrange and solve for mass. Because all the density is given in terms of g/mL and we are asked about a volume in mL, there is no need to convert units to cm or m, but keep in mind that in most problems meters cubed are used for volume. (Remember: 1cm cubed is equivalent to 1 mL.)
→	mass = density * volume = 3.2 * 25 = 80.
	160 g
	320 g

2. An 32kg object with an irregular shape displaces 2.5 L of water when it is placed in a large overflow container. What is the density of the object?

	6.4 kg/L
	7.2 kg/L
	9.6 kg/L
	12.8 kg/L
→	While the dimensions of the object are unknown if we know how much liquid it displaces we know exactly what its volume is as these two are equivalent. (The volume of fluid displaced as the object is submerged in water is equal to the volume of the object). Thus, the density is mass/volume = 32kg/2.5L. (If we assume its close to 30/2 or 15 and then note that division by 2.5 is going to be more than 2 then it must be slightly less that 15, or 12.8)

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[edit] Specific Gravity

Often, density is given in terms of Specific Gravity. Specific gravity (SG) is a special case of relative density defined as the ratio of the density of a given substance, usually water. Substances with a specific gravity greater than 1 are more dense than water, and those with a specific gravity of less than 1 are less dense than water. Thus an object with a specific gravity > 1 will sink, while those with a specific gravity < 1 will float.

SG is by definition dimensionless and therefore not dependent on the system of units used Based on the SG-value of a given substance, the density of that substance can be calculated easily by rearranging and knowing the density of water.

[edit] Pressure

It is often ideal to talk about forces being applied to a whole surface, or as an example, when gas is expanding, the force along the container walls. When we speak of these situations, we in fact are discussing pressure. Pressure is a measure of force based on the area it is applied, or force/area. Thus, by using pressure, we can explain why an individual nail can easily tear through skin, but a bed of nails will do relatively nothing to the individual lying across it.

Mathematically, we define pressure as,

where is the pressure, is the normal force, and is the area. Pressure is always perpendicular to the surface that is exhibiting the force, thus pressure is regarded as a scalar quantity. The SI units of pressure are the pascal, Pa, where 1 Pa = 1 N/m².

1. The head of a nail experiences 0.00026 Pa of pressure when a hammer slams it. Assuming the force of the hammer was 0.3N, what must the radius of the nail head be?

	2mm
	4mm
	5mm
	10mm
→	To solve this problem we must first determine what the total area of the nail head is. Using we can solve for this easily. The area must be F/P = (0.00026)(0.3) = 0.000078m2. Now, assuming that we know the nail head is a perfect circle, we can determine the radius from area = pi*r2. Or r = √(area/pi) = √(0.000078/3.14159) ~= √(0.000025) = 0.005, or 5mm.

2. A 50kg student and a 40 kg student both attempt to walk on the surface of a snowbank. The 50kg student contacts the snow with a total area 100cm² while the 40kg student contacts the snow with a total area of 60cm². Which student is most likely to sink?

	The 50kg student
	The 40kg student
	They both have the same pressure so either both or neither will sink
	not enough information, it depends on the coefficient of static friction
→	Trying to walk on the surface of snow without sinking is an effect of pressure. If one can increase the total area that they make in contact with the snow, then their total weight will be evenly distributed and the snow can hold. Thus, the student must likely to sink is the one who experiences the greater pressure. Student one's pressure is (50kg)(g)/(100cm) while student two's pressure is (40kg)(g)/(60cm). Although these are not "true" pressure's because they are using cm, we can still compare them without the extra work of converting them to N/m2.

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