complete all of the following based on the data: Newton’s Second Law Lab   

Half Atwood Machine 

 

Objective: To show that unbalanced forces acting on a mass lead to a proportional amount of acceleration.   

 

 

 

Procedure:  Set up your Half-Atwood Machine as shown.  Test your setup!  Make a note of where the cart is still accelerating due to the tension in the string.  

In the following lab, the applied force on the car is equal to the WEIGHT of m2.  We will choose m2 = 100 g.  The mass of the car by itself is 500 g. 

  

 

 

Procedure:  Run this lab by increasing the mass of m1 by adding mass to the car but keeping the weight of the hanging mass (m2) the same. Each time this happens the acceleration of the car will change.  You will measure the time it takes the car to go the same distance for every trial. 

 

Record the distance the car travels for each trial here:   67 cm  

 

 

 

 

 

 

 

 

Now, complete the following data table.  

Data Table 1 (20 points) 

 

m1 

m2 

t average  

a 

Net Force 

500g  

100g 

0.87s 

1.77m/s2 

8.33 N 

550g 

100g 

0.87s 

1.77m/s2 

8.46 N 

600g 

100g 

0.92s 

1.58m/s2 

8.57 N 

650g 

100g 

0.95s 

1.48 m/s2 

8.67 N 

750g 

100g 

1.05s 

1.22 m/s2 

9.38 N 

850g  

100g 

1.11s 

1.09m/s2 

8.95 N 

950g 

100g 

1.28s 

0.82m/s2 

9.05 N 

1000g 

100g 

1.29s 

0.81m/s2 

9.19 N 

 

(5 points) You will need to calculate the acceleration of each trial by using kinematics.  Please show the work for one trial only, in the space below.  Show ALL work! 

a = 2x/t2 

Trial 1  

A=2x/t2 

A = 2(0.67m)/ (0.87s)2 

A=1.34m /0.7569s 

A = 1.77 m/s2 

 

Trial 2 

A=2x/t2 

A=2(0.67m)/0.87s2 

A = 1.34/0.7569s 

A= 1.77m/s2 

 

Trial 3 

A=2x/t2 

A = 2(0.67m)/(0.92s)2 

A = 1.34m/0.8464s 

A = 1.58m/s2 

 

Trial 5 

A=2x/t2 

A = 2(0.67m)/(1.05s)2 

A = 1.34m/1.1025s 

A = 1.22 m/ s2 

Trial 6 

A = 2x/t2  

A = 2(0.67m)/(1.11s)2 

A = 1.34m/1.2321s 

A= 1.09m/s2 

Trial 7 

A = 2x/t2 

A = 2(0.67m)/(1.28s)2 

A = 1.34m/1.6384s 

A = 0.82m/s2 

 

Trial 8 

A = 2x/t2 

A = 2(0.67m)/(1.29s)2 

A= 1.34m/1.6641s 

A = 0.81m/s2 

   

(5 points) Calculate the Net Force on the system and insert into the last column of the data table. Please show the work for one trial only, in the space below.  Show ALL work! 

 

Trial 1  

F = m1g/m1 + m2   

F = 500g(10m/s2) / 500g + 100g 

F = 5000g/600g 

F = 8.33 N  

Trial 2 

F = m1g/m1 + m2 

F = 550g(10m/s2)/ 550g + 100g 

F = 5500g/ 650g 

F = 8.46 N 

Trial 3  

F = m1g/m1 + m2 

F = 600g(10m/s2)/ 600g + 100g  

F = 6000g / 700g 

F = 8.57 N 

Trial 4  

F = m1g/m1 + m2 

F = 650g(10m/s2)/ 650g + 100g 

F = 6500g/750g 

F = 8.67 N 

Trial 5 

F = m1g/m1 + m2 

F = 750g(10m/s2)/ 750g + 100g  

F = 7500g/ 850g 

F = 9.38 N 

Trial 6 

F = m1g/m1 + m2 

F = 850g(10m/s2)/ 850g + 100g  

F = 8500g/950g  

F = 8.95 N 

Trial 7  

F = m1g/m1 + m2 

F = 950g(10m/s2)/ 950g + 100g 

F = 9500g/1050g 

F = 9.05 N 

Trial 8  

F = m1g/m1 + m2 

F = 1000g(10m/s2)/ 1000g + 100g  

F = 10000g/1100g 

F = 9.19 N 

  

 

 

 

(20 points) Using excel, sheets or graph paper, make a graph of the data that you gathered that represents the relationship between net force, mass and acceleration.  The slope of the graph should represent the mass of the system. Insert your graph below.  If you made a paper graph, insert a picture here….it MUST be neat! 

 

 

 

(5 points) Using the appropriate physics terms, does the slope of the graph make sense with what you know about N2L? Should it be the shape that it is?  Is this surprising?  Why or why not? Use evidence to support your claim.   

 

 

 

 

 

(5 points) Using N2L and the “problem solving process”, derive an expression for the acceleration of the system in terms of m1, m2 and g. Show work and appropriate diagrams below. (You may insert a picture of your work from a notebook if you like).  

 

 

 

 

 

New data table! Using the data from the first table, complete the following: 

Data Table 2 (20 points)  

 

m1 

m2 

a 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(5 points) Look at the expression that you derived for the acceleration of the system.  You are going to make a graph based on this data whose slope is the acceleration due to gravity g.  What data needs to be entered into the last column to achieve this goal? Fill this in now.  

 

(10 points) Using excel, sheets or graph paper, make a graph of the data.  The slope of the graph should represent the acceleration due to gravity and it should be a line. Insert your graph below.  If you made a paper graph, insert a picture here….it MUST be neat! 

 

 

 

(5 points) Calculate the % error between this slope and the given value of g. Show work below.