FORMULA SHELF
28 of 370
The arithmetic behind the work: what to measure, what to type in, and what the answer comes out as. Every formula says what the symbols mean and gives a worked example, so you can check it against a job you have already done.
SHELVES
Physics
28 formulas
Count the rope, not the pulleys. A block and tackle with the load on a four-part reeve has an advantage of about 4, less the friction in every sheave.
A four-part tackle lifts 400 kg with a 110 kg pull.
For a gearbox, a quad final drive, a mower gearbox or a winch. A 3:1 reduction triples the torque and drops the speed to a third. The power stays the same, less the losses.
A 12-tooth pinion driving a 36-tooth gear is 3:1.
For a shed, a polytunnel, a cold room or a house. Insulation works by lowering U, and a door left open works by raising it again every time.
A 30 m2 shed wall with U = 2.5 and 10 K of difference loses 750 W.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Why a fence rail sags, why a steel beam needs to be deep rather than wide, and why a long trailer bed needs cross members. Depth beats width every time.
Doubling the depth of a beam reduces its sag by 16 times.
Convenience only. Double-check the result against the worked example or a second method before you use it.
For a drive belt on a tractor, a mower, a compressor or a bandsaw. Measure the old belt and copy it, or use the formula for a different pulley set.
A 300 mm and a 100 mm pulley at 500 mm centres needs about 2,110 mm of belt.
Why a boat floats, why a tractor wheel floats in mud, and why you cannot lift a submerged post out of a hole by pulling on it.
A 1 m3 of wood in water gets 9,810 N of lift, which is 1,000 kg of weight.
Loading a trailer, tipping a wheelbarrow, setting a ladder, and why a tall stack of bales topples. Keep the load low and forward.
Half the load over the axle and half behind it puts the balance point over the axle.
Converts a volume of something into a weight. Water is 1 kg per litre. Milk is about 1.03, oil 0.92, honey 1.42, fertiliser 1.1, wheat 0.75, chopped straw 0.25.
A 200 litre drum of fertiliser at 1.1 kg/litre holds 220 kg.
Convenience only. Double-check the result against the worked example or a second method before you use it.
How much more than the job the part can take. Check it when you weld something load bearing - a gate bracket or a trailer chassis - and never design a lifting point yourself.
A bracket with a 20 kN failure load used for 5 kN has a factor of safety of 4.
Why a ramp needs enough grip, why oil makes a bolt easier to undo, and why a ladder needs its feet on level ground.
A 500 N ladder on a wet floor with mu = 0.3 slips at 150 N of sideways push.
The energy stored by lifting something. It is why a raised bale or a full water tank is dangerous, and why a ramp gains you the power to lift a load higher.
A 100 kg load lifted 3 m stores 2,943 J.
Convenience only. Double-check the result against the worked example or a second method before you use it.
The energy of something that is moving. Double the speed and you have four times the energy, which is why a braking problem gets serious very quickly above a certain speed.
A 1,200 kg car at 10 m/s carries 60,000 J.
Convenience only. Double-check the result against the worked example or a second method before you use it.
A lever, a block and tackle, a ramp, a screw jack. You trade distance for force, and no machine beats 100% efficiency. A ramp 4 m long and 1 m high has a theoretical advantage of 4.
A block and tackle with 4 supporting parts needs a quarter of the force.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Why a soft bag of sand and a hard block hit differently at the same speed, and why you roll with a fall. Doubling the speed doubles the momentum and quadruples the stopping force.
A 2 kg tool at 5 m/s has 10 kg m/s of momentum.
Convenience only. Double-check the result against the worked example or a second method before you use it.
The force needed to move a mass. The tractor pulling a trailer, the ramp lifting a load, a horse pulling a plough. Double the mass and you double the force, for the same acceleration.
A 1,500 kg trailer accelerating at 1 m/s2 needs 1,500 N.
Convenience only. Double-check the result against the worked example or a second method before you use it.
The jack, the brake press, the loader bucket and the post hole rammers. A 10 cm piston moved with 100 N will lift 1,000 kg on a 1 m piston.
A 100 N push on a 10 cm2 piston lifts 1,000 kg on a 1,000 cm2 piston.
How fast work gets done. 1 hp = 746 W, so a 50 hp engine is 37 kW. A machine doing the same work in half the time has twice the power.
37 kW (50 hp) = 74,000 W.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Why a spade is sharp and a boot is not, and why a dam holds back a growing force. A 1 m column of water pushes 9,810 Pa on every square metre at the bottom.
A 500 N boot on 0.02 m2 of sole = 25,000 Pa.
Convenience only. Double-check the result against the worked example or a second method before you use it.
To work out a pulley size for a different speed, and to check whether a driven machine is running at the speed it was designed for.
A 200 mm pulley at 1,400 rpm gives a belt speed of 14.7 m/s.
Why a stick looks bent in a pond, why a greenhouse bends the light, and how a lens focuses.
Light going from air into water bends towards the normal because water has the higher index.
How much fuel or electricity a heater needs. Water needs far more energy per kilo than steel, which is why a hot water cylinder takes so long.
Heating 200 L of water by 60 degrees takes 50,160 kJ, which is about 3.8 kWh.
Convenience only. Double-check the result against the worked example or a second method before you use it.
The stiffness of a material. Steel is nearly twenty times stiffer than oak, which is why a steel frame sags less and lasts longer than a timber one of the same size.
A 10 mm steel bar pulled by 5 kN across 78.5 mm2 = 64 MPa.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Ramps, loading ramps, the screw jack, the post hole auger and the cider press. Work in always equals work out, so a gentle ramp just means more walking.
A 2 m ramp at 500 mm high gives an advantage of 4.
Why a long fence rail buckles in a heatwave, why a steel tank needs a sliding bearing, and why a concrete slab needs expansion joints.
A 10 m steel rail expands 1.2 mm for every 10 degrees C.
Convenience only. Double-check the result against the worked example or a second method before you use it.
The whole of the spanner, the jack, the pump handle and the gate hinge. Torque depends on where you put your hand, not on how hard you pull. A 100 N push at 0.3 m gives 30 N m.
A 300 N pull on a 0.4 m spanner gives 120 N m.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Sound, water, light and radio. Also the drum length of a pipe organ and the spacing of ripples on a pond.
Sound at 340 m/s at 170 Hz has a wavelength of 2 m.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Mass is how much there is, weight is how hard it presses. A sack of fertiliser has the same mass everywhere and a different weight on the moon. Lifting power is usually quoted in kilograms, which is really a mass in disguise.
A 200 kg sack weighs about 1,962 N.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Work only happens when the force is in the direction of the movement. Lifting a load 2 m and pushing a barrow 100 m are different amounts of work.
Pushing with 100 N over 50 m = 5,000 J.
Convenience only. Double-check the result against the worked example or a second method before you use it.
SOURCES & PROVENANCE
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This page is an AI-organised index. The label means the grouping and cross-links were compiled with AI; the information itself comes from the public-domain books, reports and manuals listed below. Open any source to read the local copy or follow the link to the original publication.