Unit II Graphing and Gravity

Gravity Gravity is defined as a force exerted on all objects within an objects atmosphere. All objects have mass, this doesn’t EVER change. The force of gravity causes an object to have weight. The weight of an object depends on the force of gravity being exerted. This weight is also known as inertia. This means that an objects weight and its inertia are equal.

Calculating Gravity On the surface of the earth, the acceleration due to gravity equals 9.81m/s2. As you move closer to the center of the earth, this number would increase, farther away and it would decrease

Calculating Gravity When you leave the earth’s atmosphere, gravity no longer has an effect, therefore the object is “weightless”. It still has mass, but it has no inertia. The acceleration due to gravity is different on different planets. It can be calculated using this formula: Fg=mg Fg= force of gravity m= mass of object g= acceleration due to gravity

Sample Problem An object weighs 15N on Planet X and has a mass of 3kg. What is the acceleration due to gravity on Planet X? Fg= mg 15N=3kg(g) g=5mls2 *note: N= newtons, a unit of force/ weight

“g” Force Different types of motion can affect “g” in various ways. Roller Coasters Rapid ascents and descents on rides can add or subtract “g”s Moving quickly uphill increases the force of gravity by increasing the acceleration This increased “g” will cause you to be pressed into your seat This also happens to astronauts as they “blast off” Too many “g”s and the force will cause the body to cave in A rapid descent downhill causes negative “g”s this will cause the body to feel weightless (airtime)

2. Elevators The same positive and negative “g”s can be felt on a moving elevator. Rising rapidly will cause an increase in “g”s. Falling rapidly will cause a state of weightlessness.

Using “g” in equations When solving problems involving gravity, the value of g may be substituted for a in any equation. Examples: a = v/t becomes g= v/t d= 1/2 at2 becomes d= ½ gt2 v2 = 2ad becomes v2= 2gd

Sample problems g=v/t 9.81mls2 = v/4s An object falls from a cliff a distance of 30m before it hits the ground. How long did it fall for? d=30m g=9.81mls2 d=1/2gt2 30m=1/2(9.81mls2)(t2) t=2.5s An object is in free-fall for 4 seconds. What speed does it reach? t= 4 seconds g= 9.81 mls2 g=v/t 9.81mls2 = v/4s V=39.2 mls

II: Graphing Motion: Slope Slope is defined in many ways. It can be the change in (y) divided by the change in (x) It is also known as “rise over run” It is not difficult to calculate: use the formula Slope =(y2-y1)/(x2-x1) Choose any two points on your graph to make your calculation. It is often helpful to use the origin (0,0) as one of the points.

Applying the slope concept to graphs of motion In physics, a slope calculation doesn’t just yield a number, it actually is a measurable quantity We will concentrate on calculating slopes for distance/time and velocity/time graphs

Slope of a distance/time graph To show the meaning of the slope in this graph, we will include the units in our calculation. We will choose the origin (0,0) and (5,10) for our calculation. Slope=y/x 10m-0m/5s-0s 10m/5s 2 m/s Please note that by calculating the slope, you have calculated the velocity of the object for that interval of the graph. Please memorize: The slope of a distance/time graph is a measure of the object’s velocity.

Slope of a velocity/time graph We will repeat the slope calculation with the new graph Slope=y/x 30m/s-0m/s -------------- 20s - 0s (30m/s) / 20s 1.5 m/s2 In this example we have calculated the acceleration of the object for that interval of the graph Please memorize: The slope of a velocity/time graph is a measure of the object’s acceleration

Interpreting the data presented in graphs Distance/time graphs Most times, you will see graphs in two forms, either a simple single line graph, or a complete trip sketched out Each graph can be interpreted either by looking at the trends in the data, or by looking at the slope.

Simple distance/time graphs Conclusion: object is at rest (slope=0) Conclusion: object is moving with constant velocity (slope is constant)

More simple graphs Object is accelerating (slope is changing)-note the line is curved

Looking at a complete trip What is happening at each interval? A-B - Moving with constant speed B-C - Decelerating, object going back towards the start C-D - Object at rest D-E - Object again moves away with constant velocity

Simple velocity/time graphs Conclusion: object is moving at constant speed (slope=0) This distance/time graph matches the velocity/time graph on the left

Here’s another one Conclusion: object has a constant acceleration (slope is steady) This graph matches the one on the left

One more Velocity is changing, acceleration is changing (slope is changing)

Looking at a complete trip What is happening at each interval? A-B - constant acceleration, increasing velocity B-C - constant acceleration, decreasing velocity C-D - constant acceleration, increasing velocity D-E - constant acceleration, decreasing velocity E-F - constant velocity, no acceleration

Making simple graphs of physics equations It is important to be able to determine what various equations look like when they are graphed The relationships may be direct, direct squared, inverse, or inverse squared, depending on the equations

What is the relationship between v and d in v=d/t As v increases, d has to get bigger-direct

How does v affect KE in KE=1/2mv2 Note that v is squared. The line will be curved-direct squared

Try these Sketch the relationship between PE and m in PE=mgh Sketch the relationship between V and R in V=I/R Sketch the relationship between F and r2 in F= G(m1 * m2) ---------------- r2