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GRAPHING SKILLS

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In laboratory investigations, you generally control one variable and measure the effect it has on another variable while you hold all other factor constant. For example, you might vary the force on a cart and measure its acceleration while you keep the mass of the cart constant. After the data are collected, you then make a graph of acceleration (y)  versus force (x) using the techniques for good graphing. The graph gives you a better understanding of the relationship between the two variables.

In graph 1 we went over some direct relationship (y = mx), indirect (y = m/x), quadratic ( y = mx²) and inverse squared (y = m/x²).

Sometimes you can use your graph to get information about a value that you have not determined experimentally. This is called interpolation.

Exercises

1.

 

 

 

 

A. graph these data. Don’t forget to label the axes and title the graph.

B. Describe the relationship between force and acceleration as shown by the graph.

(linear (y=mx)? Inverse (y=m/x) ? Quadratic (y=mx²) ? )

 

C. What is the slope of the graph? Remember to include units with your slope.

 

D. What physical quantity the slope represent ? (look at the units)

 

E. Write an equation for the line. (y = m x  and m is the slope)

 

F. The graph shows that the force is ______________ to the acceleration

 

F. You just found Newton’s second law ______________

G. When the acceleration increases by 6 m/s/s, the force increases by __________N

 

H. What is the acceleration when the force is 50.0N ?

 

I. What is the value of the force for an acceleration of 15m/s²?

 

 

 

 

 

2.

A. Plot the graph. Connect the points.

B. Describe the relationship between x and y and write a general equation for the curve.

(if y = k x² and you need to find k, plug x=1 and y = 3,from the table, in y = kx² and solve for k.

C. Is the distance traveled greater between 0s and 1s or 3s and 4 s ?

D. Is the slope of the curve greater between 1s and 2s or 3s and 4s ?

E. As the time increases, the distance __________________________

F. The distance increases as the ______________ of the time.

 

3.    Graph each set match the description to one or more table (s):

· y is directly proportional to x (a line with a positive slope) ?

· y decreases as x increases ?

· Y is inversely proportional to x (y = m/x) ?

(see 5) from graph )

·  The graph has the general equation y = kx² ?

· Does not picture a simple relationship ?

 

 

4.

A. Graph the set of data.

 

B. What kind of relationship between the pressure and the volume?

 

C. So when the pressure increases the volume _______________

 

D. Can you find the equation of the graph ? (find k in y = k/x)

 

E. You found one law of Thermodynamic (Boyle’s law):

The Volume is inversely proportional to ___________________

5.

A. graph the data set.

 

B. Find the slope of the line. Make sure you have the right units.

 

C. Each time x increases by one unit (1), y increases by ______

 

D. Can you find the relationship between y and x ? y = ___ x

 

E. You just have found Hooke’s law that applies to a stretched spring The elongation of spring (stretch ) is proportional to ___________ exerted on the spring.

The spring.

 

6. The mass m is the quantity of matter an object has. Your mass will not change if you travel far from Earth. The weight w is the force of gravity a planet, like the Earth, exerts on object, at a distance. Your weight will not be the same if you are on the moon or on Earth or at the top of the Himalayas on Earth. The weight depends on the distance from the center of the planet. The relationship between weight and mass is linear: w = m g  . g is a constant. g is called the acceleration due to gravity or the gravitational acceleration. g = 9.8m/s/s on Earth.  is less on the moon (6 times less) and greater on Jupiter.

 

An astronaut on an distant planet conducted a experiment to determine the gravitational acceleration on that planet. The data table shows the results of the experiment.

 

A) plot weight (Y) vs mass (X)

Don’t forget to title the graph and to label the axes. !! Units .

B) plot the best fit line

C) use the graph to find the planet’s gravitational acceleration

(hint: find the slope, of course)

D) On the same grid sketch a line to represent Earth’s gravitational acceleration.