LAB: NEWTON ’s SECOND LAW  (F = ma )

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CONSTANT FORCE AND CHANGING MASS

 

The amount of an object’s acceleration depends on the mass of the object and the size of the object acting on the object. In this lab, you will learn what happens to acceleration when mass is varied. (F = m a). You will show that the acceleration is inversely proportional to the mass (for a given force). The purpose of this lab is to investigate the effect of increasing mass in an accelerating system.

 

SKILLS: observing, measuring, graphing

 

MATERIALS: small cart      masses   meter sticks   time watch  pulley         C-clamps

                           masking tape         string               masses        graph paper.

                 

 

 

PROCEDURE

 

Step0: find the mass of the car using a spring scale. Mass car = ______________

 

Step1: Fasten a pulley over the edge of the table. The pulley will change the direction of the force from a downward pull on the pass into a sideways pull on the cart.

 

Step2: Mark off a distance on the table top slightly shorter than the distance the mass can fall from the table to the floor.

 

Step3: Add 5 masses of 100g to the cart. It may be necessary to secure the masses with masking tape. Tie one end of the string to the cart and thread it over the pulley. Add a 5g holder to the other end of the string so that when the cart is pushed slightly it moves at a constant speed.

 (GIVE ME A BREAK, STOP THE CART BEFORE IT CRASHES INTO THE PULLEY)

 

Step4: Practice accelerating the cart a few minutes to ensure proper alignment. Add a 20g mass to the mass holder. KEEP THIS FALLING WEIGHT THE SAME AT ALL TIME.

 

Step5. Time the motion. You can use stop watch. Repeat 4 times and record the data in table 1.

                                                                                

Step 6: Repeat step 5 4 times, removing 100g mass from the cart each time. Record the time in the table, along with the average time for each experiment.

 

Step 7: Use the average times for each mass from steps 5 and 6 to compute the acceleration of the system. TO do this, use one of the equations of motion: d = 0.5 a t². So a = 2d/t².

Since the cart always accelerates through the same distance d , the acceleration is proportional t 1/t². Simply calculate 1 /t² and make 1/(second)² your unit of acceleration. Record the data in the table.

 

Step 8: Using graph paper, make a graph of

 acceleration (vertical axis) vs. mass (horizontal axis). Trace the best fit curve.

You can use excel or just trace it. Don’t connect the dots. Go through the points.

 

ANALYIS

 

1. Describe your graph of acceleration vs mass. Is it a straight-line graph or a curve ?

What kind of relationship: linear y = kx ?  Inverse y = k / x ? Or quadratic y = k x² ?

(value of K does not matter. It is just a constant or proportionality. Could be 2, 3,10 ...

 

2. you know F = ma . In your experiment F (the pulling force ) is equals to :

F = Weight pulling the car = _______ N (use W = mg, g= 9.8m/s/s and convert g into kg)

Plug the value found for F into F = m a and solve for a:

a = __________ . Think for a while and find the equation of your line.

Remember: y = acceleration a  and x = total mass of the car in your lab.

 

 

3. Share results with other class members. For a constant applied force, how does increasing the mass of an object affect its acceleration ?

 

4. for Math lovers:

Plug the x values and y values in your TI and find the best fit curve y = k/x using the STAT key.

The TI will find the equation of the curve you plotted. Does it match what you found in 2 ?

 

4. A group of students collected the above data:

 

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?

 

 

 

GOING FURTHER: HOMEWORK