Force, Work and Energy
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- Last Updated: Friday, 27 June 2025 23:48
- Published: Monday, 14 August 2023 22:58
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Force:
There are 4 fundamental forces or interactions in nature. All the motion that you see around as are due to forces. These forces may be friction, gravitation, push, etc. They ultimately belong to one of these 4 forces. It's easier to visualize these forces by considering a field, and then this field exerting forces. Force is always a vector as the effective force due to multiple forces is a vector sum of these forces. We are omitting the arrow sign on top of force for simplicity, but it should always be there to indicate it's a vector. The 4 fundamental forces or fields are:
- Gravitational force: This is attraction force due to mass of an object, and it's range is infinite. Newton's formula for gravitational force (published in 1686) gives us the formula for this:
- Newton's Gravitational Law: Force between 2 bodies of mass m1 and m2 as F = G*m1*m2/R^2, where G=Gravitational Constant of 6.674*10^-11 m^3/(kg*s^2). Here both F and R are vectors.
- Gravitation Field is defined as field due to presence of mass M and is given as g = F/m = G*M/R^2. The other mass is removed in eqn here, as F =m*g where g is the Gravitation Field due to mass M,
- The value of G wasn't determined at Newton's time. It was used to calculate forces relative to one another. It was in 1798 (>100 years later) that value of G was found out experimentally. It can be seen that this gravitational force is very weak (as G is a very small number), and is only relevant when at least one of the bodies is very large as moons, planets, stars, etc. What in the mass causes gravity or gravitational field is unknown. Even Newton hypothesized that cause of this power is unknown and contrary to sound science.
- Electromagnetic Force: This is the attractive or repulsive force due to charge. Look under "ElectroMagnetism" section.
Newtonian Laws:
Ex of force/work => To get an idea of how much 1N of force is, consider a 100g weight that you carry on your hand. That is 1N of force that you are applying to counteract earth's gravitational force. Now if ou lift it up by 1m, that's 1J of work that you did. So, 1N of force and 1J of force look like very small amounts, as your body doesn't feel any tiredness doing this.
Pressure: Pressure is Force per unit area. i.e P = F/A. SI unit of P is Pascal (Pa) which is 1N/m^2. 1 N is the force equiv to holding 100g of weight. This doesn't sound like too much weight. Now if we spread this weight over 1m^2, that's almost negligible Pressure. 100g of weight over 100cm*100cm = 0.01g/cm^2 of weight is 1 Pa. It's more convenient to use 1kPa (1 kilo pascal) or 1 bar (=100 kPa). 1kPa is 10g/cm^2, while 1 bar is 1kg/cm^2. Atmospheric pressure due to air is measured in atm (atmospheric pressure), where pressure at sea level is defined as 1 atm=101,325 Pa, which is ~1 bar (To be precise, 1 atm is slightly greater than 1 bar). Pressure is also measured in inches/mm of Mercury (Hg) where pressure at sea level = 760mm = 29.9 inches (approximated to 30 inches) = 1 atm pressure.
In USA, pressure is measured in pounds of force per square inch (psi)—for example, in car tires. 1 lb=453.6g => 1 lb force = 453.6g*9.8N/kg = 4.445N. So 1 psi = 4.45N/(0.0254)^2=6897.5N/m^2 = 6.9kPa. => 1 bar = 100/6.9=14.5 psi. So, 1 atm=14.7 psi. Pressure readings in excess of atmospheric pressure are usually more relevant in measurements, so we use psig (pounds per square inch gauge) in such cases. PSIG is measured relative to atm pressure, i.e 1 PSIG = 1 PSI - 14.7, so at sea level PSIG =0. PSI measures pressure relative to vacuum.
Barometer: Barometers are used to measure pressure. We take a tube closed at end end, and fill it with liquid as Mercury or water. Now, if we invert and immerse it in container of same liquid, then liquid inside the tube will rise until the point where pressure due to weight of liquid (+ any air/vapor pressure inside the tube in the empty space above the liquid) inside is same as pressure due to air outside. Mercury rises to 760 mm (or 2.5 ft), while water rises to 34 ft (since Hg is ~13,6 times denser than water). P = h*ρ*g.
In pressure gauges (usually in HVAC applications), pressure is usually shown as PSIG. In a barometer, if the air inside the tube is at atm pressure, then the mercury level will be at 0 inside the tube. But if the air inside the tube is in perfect vacuum, then the mercury will rise to 30 inches. We take these readings inverted to indicate relative pressure and indicate it as inch Hg Pressure, So a pressure reading of "0 in Hg" means the pressure is same as atmospheric pressure, while a "-30 in Hg" pressure means absolute 0 pressure. These can also be shown in bar as "0 bar" for 1 atm pressure and "-1 bar" for absolute 0 pressure. However, showing these on linear scale is hard, because we can never go to 0 vacuum. We keep on going down by a factor of 10 or something infinitely. So, a log scale is preferred in many gauges, where very precise measurement is required.
Micron unit: Since pressure becomes very low close to vacuum, we use another unit called micron in pressure gauges to indicate very low level of pressures. 1 mm Hg of pressure is divided into 1000 parts called microns. So, 1 micron pressure = 0.001 mm of Hg pressure. At 1kPa (or 0.01 bar), water boils at 10C. We usually try to get to this vacuum level, when we want to get rid of moisture in any system (as at this pressure, liquid water will get converted to steam, and get sucked out via vacuum pump). 100 kPa = 760 mm of Hg, so 1kPa=7.6mm Hg or 7600 micron. As a thumb rule, going to 1% of atm pressure starts the process of water to boil at room temp. People in HVAC industry accept a pressure of 1000 micron or lower in order to guarantee that no water is present in the evacuated system. Usually 500 micros or lower is what people shoot for when vacuuming an HVAC system. These kind of low pressures can only be read by "micron gauge", which are very expensive ($200 for branded ones)
1 Pascal = 7 micron of Hg (implying 1 micron is extremely low pressure, since 1 Pascal is already too low of pressure)
1000 micron = 1 mm of Hg pressure = 0.02 psi
100K micron = 100 mm of Hg pressure = 2 psi or 0.1 atm (this is the highest pressure that a micron gauge will read, since it's designed to read vacuum pressure and NOT high pressure)
Manometer: These are similar to Barometer, and are used to measure pressure of gases. Manometers are used in measuring blood pressure using device called a sphygmomanometer (Greek sphygmos = “pulse”).