PHYSICAL QUANTITIES BASIC VS DERIVED QUANTITIES BASIC DISTANCE

PHYSICAL QUANTITIES BASIC VS. DERIVED QUANTITIES BASIC • • • DISTANCE (also LENGTH or DISPLACEMENT) MASS TIME DERIVED QUANTITIES ARE ARRIVED AT BY COMBINING BASIC QUANTITIES IN VARIOUS WAYS. e. g. , Velocity = Change in Position/Time VELOCITY AND ACCELERATION 1. VELOCITY: v = Δx/t, where: v = velocity (more precisely, average velocity) Δx = change in position (Δ means “change in”) t = time over which the position change occurred

Examples: 60 mph: 60 miles (the distance) divided by 1 hour (the time) 800 meters per sec: 800 meters (the distance) divided by 1 sec (the time) 2. ACCELERATION CHANGE IN VELOCITY OVER TIME (e. g. , "0 to 60 in 6 seconds") a = Δv/t a = acceleration (more precisely, average acceleration) Δv = change in velocity t = time over which velocity change occurred English translation: Change in velocity divided by the time over which the velocity change occurred. Basic idea: Speeding up or slowing down. Note that slowing down is also acceleration – called deceleration or negative acceleration. Negative acceleration is every bit as important as positive acceleration: When a car strikes a tree, for example, the force that occurs is related to the rapid deceleration of the car.

3. FORCE Amount of "push" or "pull" on an object F=Ma F = force M= mass a = acceleration So, force will be high when massive objects are highly accelerated; e. g. , a Buick hitting a tree at 100 mph will generate more force than a Miyata hitting the same tree at 10 mph.

4. PRESSURE Force per unit area E = F/A ('E' is used because P will be needed later for power) E = pressure F = force A = area over which force is delivered Pressure is high when the force is large and/or when that force is focused on a small area. Pressure can be increased either by increasing force, or by decreasing the area over which the force is delivered. (The middle ear uses this trick to amplify pressure. )

Suppose these two objects – identical except for orientation – were dropped from exactly the same height on a napkin below. Which would be more likely to rip the napkin? Obviously, it’s the on the right, but why? Greater force? No. F = Ma. The masses are equal and, if dropped from the same height, the acceleration would have to be the same. So, they hit the napkin with the same force. So, what’s the difference? The pressure is greater for the object on the right since the force is being delivered over a smaller area. On this subject: (a) Why do sharp knives cut better than dull ones? (b) Why are thumb tacks pushed in pointy end 1 st rather than the other way around?

5. WORK Work is related to the ability to move things. When large forces are used move objects great distances, a lot of work has been done. When small forces are used to move objects small distances, a small amount of work has been done. W = Fx W = work F = force x = distance Laborer 1: Applies a given force to move a pile of bricks a distance of 30 meters. Laborer 2: Applies the same size force to move the same pile of bricks a distance of 60 meters. Conclusion: Laborer 2 has done twice the work of Laborer 1.

6. POWER Power = work per unit time, or the rate at which work is done. P = W/t P = power W = work t = time taken to complete the work Laborer 1: Applies a given force to move a pile of bricks a distance of 30 meters and completes the job in 30 minutes. Laborer 2: Applies the same size force to move the same pile of bricks the same distance of 30 meters, but completes the job in 15 minutes. Conclusions: • Work performed is identical (since the force and distance are the same) • Twice as much power is generated by Laborer 2 than Laborer 1 because the work was accomplished in a shorter period of time.

7. INTENSITY Intensity = power per unit area, i. e. , the amount of power that is "focused“ on a given area. I = P/A I = intensity P = power A = area over which power is measured Note: relationship between power and intensity is analogous to the one we saw earlier between force and pressure: pressure = force per unit area intensity = power per unit area There is a close relationship between pressure and intensity. We will see how this works when we talk about the decibel scale.

_________________________________________________________________ Summary of Physical Quantities Quantity Formula Units Concept _________________________________ force F = Ma Newton dyne amount of "push" or "pull" on an object Newton/sq meter dynes/sq centimeter Pascal pressure is high when a large force is delivered over a small area meters per sec miles per hour high velocity means covering a large distance in a short period of time meters per second miles per hour per second speeding up or slowing down; i. e. , a change in velocity over time M = mass a = acceleration pressure E = F/A F = force A = area velocity v = x/t x = distance t = time acceleration a = (v 2 -v 1)/t v 1 = starting vel v 2 = ending vel v 1 = starting vel t = time ___________________________________________________________________

___________________________________________________________________ Summary of Physical Quantities Quantity Formula Units Concept __________________________________ work W = Fx joule erg a large amount of work is done when a large force moves an object a great distance watt horsepower the rate at which work is done watts/square meter watts/square centimeter intensity is high when a large amount of power is focused on a small area F = force x = distance power P = W/t W = work t = time intensity I = P/A P = power A = area ___________________________________________________________________