2a: Motion and Force

The location of an object is called the position and is generally measured in meters (or centimeters or inches or feet, etc.) starting from an agreed upon starting point (called the origin). Sometimes it is convenient to set up a coordinate system with and x-axis, y-axis and z-axis in order to locate something precisely in three dimensional space. We may want to also know how far something is from where it started or from its normal, at rest position. This is the displacement from equilibrium and is also measured in meters. For example, when a violin string is plucked or bowed, different points on the string are displaced from their equilibrium positions by different amounts initially.

Speedv, is the rate of change of position and is measured in meters per second, m/s (or ft/sec or miles per hour, mph, etc.). If there is no acceleration, speed is related to distance traveled as rate multiplied by time equal distance; vt = dVelocity is speed with additional information about which direction something is moving. So if you are traveling at 50 mph (no direction given) you have a speed but if you are traveling 50 mph and headed north-east we call that a velocity.

Acceleration is a word that has a specific definition in science but gets confused with speed and velocity in everyday use. Acceleration is a change in velocity over a given time and is measured in meters per second squared, m/s2 (or ft/s2, etc.). A car going down the road in the same direction might have a constant speed of 50 mph. If neither the speed or direction changes then the acceleration is zero. If the car speeds up, slows down or changes direction then the velocity has changed and there is acceleration. The gas pedal in your car is both an acceleration pedal (if you push it to the floor or ease off the pedal you change your speed and get faster or slower) and also a speed pedal (if you hold it constant you keep a constant speed with no acceleration). Your brake pedal is also an acceleration pedal; it slows you down. Your steering wheel is also an accelerator control because it changes your direction.

For objects near the surface of the earth there is a special acceleration, called the acceleration of gravity. For something falling in the case where air resistance doesn’t slow it down too much, the speed changes by 9.8 m/s every second so we say it has an acceleration of 9.8 m/s per 1s or 9.8 m/s2 (or 32 ft/s2 in the English system). So if a pot gets pushed off an upper story window ledge it starts from rest (zero speed) and will be falling at a speed of 9.8 m/s after one second, 9.8 m/s + 9.8 m/s = 19.6 m/s after two seconds, 9.8 m/s + 9.8 m/s + 9.8 m/s = 29.4 m/s after three seconds, etc. This acceleration of gravity works the same for any object, regardless of size or weight, as long as air resistance is small and you are near the earth’s surface. This is what Galileo figured out by dropping different sized objects off the leaning tower of Pisa; objects accelerate (get faster) at the same rate no matter what their size (again, if you can ignore air resistance).

The amount of ‘stuff’ an object has regardless of where it is (in space, on earth, on the moon), its ‘heft’ you might say, is called mass and is measured in kilograms, kg (or sometimes grams where 1000 g = 1 kg). The English units of mass are the slug and the stone but we seldom use them.

force is a push or shove and is measured in Newtons , N, which is a kilogram-meter per second squared, kg m/s2. The tension in a guitar string is the force pulling at either end of the string (the force pulling each end is the same and balances out so the string doesn’t go anywhere). The English unit of force is the pound which is also the unit used to measure weight. This can lead to some confusion because the pound is also sometimes incorrectly used for mass.

Weight is the force that gravity causes an object to exert on the earth. Weight is measured in Newtons in the metric system or pounds in the English system. This is how mass and weight get confused; in everyday use we use weight and mass interchangeably which, strictly speaking is incorrect. For example in the grocery store you may see a bag of sugar that says 5 lbs or 2.3 kg which is really comparing different things; lbs measures weight but kg measures mass which is different. What the label should say is “this item weight 5 lbs or 22.3 Newtons” (because 2.3 kg times 9.8m/s2 is 22.3 Newtons which is a unit of weight). Or it could say “this item has a mass of 2.3 kg or 0.16 slug” (5 lbs divided by 32 ft/s2 is 0.16 slugs and slugs and kg measure mass). So if you see something that claims to have a weight of 2.3 kg (or 5 lbs) remember what that really means is its mass is 2.3 kg.

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