In Investigation Five, students studied the importance of balanced and unbalanced forces. They learned that if all forces acting on a stationary object are equal and balanced, the object will remain stationary. However, as soon as the forces become unbalanced (an object is dropped, pushed, or kicked), the object will begin to accelerate and move. 

On the other hand, if the forces acting on an object moving at a constant speed are balanced, the object will continue moving in the same direction and at the same speed. However, as soon as the forces acting on the moving object become unbalanced (for example, stepping on the brakes of a bicycle, peddling harder, or turning the handlebars), the object will accelerate (its speed or direction will change).

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A. Begin the analysis of the trials by collating data from the first six trials into a table.

1. Direct students to assemble into the same collaborative groups as in the Lab. Students will begin to complete the Table in Problem 11 of the Student Data Record. Use this slide as a guide for students to reference.

a. Allow students to work together to review the problems completed in the lab in order to transfer the data into the first two empty columns of the Table. Each row of the Table corresponds to a Trial.

b. If necessary, remind students of the steps in the Procedural Tool, Completion of a Data Table.

c. After a sufficient period, Ask students: What was the weight of the bucket and the 100 g mass weight in Newtons? Approximately 1.5 N.

d. Ask students: For which type of motion does the pull force on the spring scale equal the weight of the white bucket and the 100 g mass weight combined? Students should indicate that the pull force is equal to the weight when the object is not accelerating (stationary or constant speed).

e. Ask students to subtract the difference between the weight and the pull force, for each Trial. Students should record this number for each trial in the third empty column of the Table. 

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2. After students have established the weight and pull forces present in each Trial, direct students’ attention to establishing in which Trials balanced forces were present and in which trials unbalanced forces were present.

a. Encourage students to review the table for evidence of balanced forces. Ask students: In which conditions were the forces balanced? How do you know? Students should indicate that balanced forces existed where the difference between the pull force and the weight was zero. This was the case in the following conditions:

• When the bucket was stationary.

• When the bucket was moving upwards at a constant speed.

• When the bucket was moving downwards at a constant speed.

b. Direct students to write “balanced” in the appropriate rows in the fourth empty column of the Table.

c. Ask students: What do you notice about the acceleration of the bucket when the forces were balanced? Students should indicate that the bucket was not accelerating when the forces were balanced. That is, the bucket either remained stationary or remained in motion at a constant speed. 

d. Encourage students to review the Table for evidence of unbalanced forces. Ask students: In which conditions were the forces unbalanced? How do you know? Students should indicate that unbalanced forces existed where the difference between the pull force and the weight was not zero. This was the case in the following conditions:

• When the bucket was speeding up, upwards.

• When the bucket was speeding up, downwards. 

• When the bucket was slowing down, upwards.

• When the bucket was slowing down, downwards.

e. Ask students: What do you notice about the acceleration of the bucket when the forces were unbalanced? Students should indicate that the bucket was accelerating when the forces were unbalanced. That is, the bucket either slowed down or speeded up. 

f. Direct students to write “unbalanced” in the appropriate rows in the fourth empty column of the Table.

g. Direct students’ attention to the Trials in which the forces were unbalanced. Ask students: If the forces are unbalanced, in which direction is the larger of the two forces? How do you know? Students should indicate that:

• In the Trial where the bucket was speeding up, upwards, the pull force was larger than the weight. The direction of the resulting force was upwards.
• In the Trial where the bucket was speeding up downwards, the pull force was less than the weight. The direction of the resulting force was downwards.
• In the Trial where the bucket was slowing down, upwards, the pull force was less than the weight. The direction of the resulting force was downwards.
• In the Trial where the bucket was slowing down, downwards, the pull force was greater than the weight. The direction of the resulting force was upwards.

h. Direct students to draw the arrow in the fifth empty column to reflect the resulting direction of the force. For balanced forces, the cells should contain a dash.

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3. Begin analysis of the result of the balanced and unbalanced forces in terms of acceleration. During this portion of the PostLab analysis, the instructor will guide students to calculate acceleration.

a. Direct students to transfer the mass of the bucket in kilograms, to the appropriate column of the Table. 

b. Direct students to look at the first Trial in which the forces are unbalanced. In this Trial, the bucket was speeding up, upwards. Ask students: Was the bucket accelerating? Students should indicate that the bucket was accelerating.

c. Ask students: How fast was the bucket accelerating? Student answers may vary.

d. Assist students in calculating the rate of acceleration. Remind students that acceleration is measured in meters per second, squared (m/s²). 

e. Point to the equation on this slide that students can use to calculate acceleration:

f. Calculate the first example of acceleration as a class. The acceleration of the bucket when it was speeding upwards is equal to 1/0.15 = 6.7 m/s².

g. Ask students: In what direction is the acceleration? Students should indicate that the direction of acceleration is upwards. 

• Direct students to draw an arrow in the final column to reflect the direction of acceleration.

h. Allow students to collaborate and use calculators to calculate the remaining rates of acceleration for the remaining Trials in which there were unbalanced forces. Students should record their answers in the appropriate column in the Table. 

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4. Direct students to consider the results of the completed Table.

a. Ask students: What do you notice about the arrows that represent the direction of the difference between forces and the direction of acceleration? Students should indicate that the direction of the difference between forces and the direction of the acceleration is the same. That is, if the direction of the difference between forces is upwards, the direction of acceleration is also upwards.

b. Remind students that the mass of the bucket was the same in each case. Ask students: What number changes in order to cause the change in acceleration?  Student answers may vary. The difference in the direction of forces is the number that changes. 

c. Explain to students that these three factors, 1) the difference in forces, 2) the mass of the object, and 3) the acceleration that results, are all related in an equation. Point to the acceleration equation. 

“This means that if you know any two of these variables, you can calculate the third”.

Note to Teacher: This is an extremely important mathematics correlation! 

d. Explain to students that another way to think about the equation is to put it into words. Ask a volunteer to put the equation into words. Student answers may include the following: acceleration is equal to the difference between the forces divided by the mass of the object; if you divide the difference between the forces by the mass of the object, you can calculate the rate of acceleration.

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B. Continue the analysis by reviewing Trials Seven through Ten. Through the questions that follow, students will depict the horizontal and vertical forces acting on the woodblock as it experienced several forms of motion.

1. Refer students to Trial 7. 

a. Ask students: In what direction was the woodblock moving? Were the forces balanced or unbalanced?  Students should indicate that the forces were balanced. The woodblock did not move. 

b. Refer to the drawing of the teacher and the box, and guide students to complete the diagram in the first square in Problem 12 of the Student Data Record. Assist students in depicting both the vertical forces and the horizontal forces using the appropriate length and direction of vector arrows.  

c. Ask students: What would have happened if the pull force had been greater than the frictional force? Students should indicate that the wood box would start to move. It would accelerate.

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2. Refer students to Trial 8. 

a. Ask students: In what direction was the woodblock moving? Were the forces balanced or unbalanced?  Students should indicate that the forces were unbalanced. The woodblock began to move. 

b. Ask students: Was one force greater than another force? Students should indicate that the pull force was greater than the frictional force.

c. Guide students to complete the diagram in the second square in Problem 12 of the Student Data Record. Assist students in depicting both the vertical forces and the horizontal forces using the appropriate length and direction of vector arrows.

3. Refer students to Trial 9. 

a. Ask students: In what direction was the woodblock moving? Were the forces balanced or unbalanced? 

Students should indicate that the forces were balanced. The woodblock moved at a constant speed across the table.

b. Guide students to complete the diagram in the third square in Problem 12 of the Student Data Record. Assist students in depicting both the vertical forces and the horizontal forces using the appropriate length and direction of vector arrows.

4. Refer students to Trial 10. 

a. Ask students: In what direction was the woodblock moving? Were the forces balanced or unbalanced? Students should indicate that the forces were unbalanced. The woodblock slowed down due to a decrease in pull force and the maintenance of frictional force.

b. Guide students to complete the diagram in the fourth square in Problem 12 of the Student Data Record. Assist students in depicting both the vertical forces and the horizontal forces using the appropriate length and direction of vector arrows.

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Tell students that they should begin to think about the Conclusions that can be drawn from their data. The following questions are designed to prompt students to draw appropriate conclusions from their experiments. 

1. Direct students to review the Table in Problem 11. Ask students: What can you conclude about the effect of balanced forces on an object that is stationary?  Students should indicate that when a stationary object experiences balanced forces, the object will remain stationary.   

2. Ask students: What can you conclude about the effect of unbalanced forces on an object that is stationary?  Students should indicate that a stationary object that experiences unbalanced forces will begin to accelerate. 

3. Ask students: What can you conclude about the effect of balanced forces on an object that is moving?  Students should indicate that when a moving object experiences balanced forces, the object will continue to move in the same direction and at the same speed.

4. Ask students: What can you conclude about the effect of unbalanced forces on an object that is moving? 

Students should indicate that when a moving object experiences unbalanced forces, the object will accelerate. That is, it will speed up, slow down, or change direction.

5. Direct students to review Trials Seven through Ten. Ask students: Did you observe the same principles when experimenting with the woodblock? Give an example. Students should indicate that the same principles were observed. When the forces were balanced, in this case when the pull force and frictional force were discrepant, a stationary block began to accelerate and a moving block accelerated. When the pull force and frictional force were equal and opposite, the stationary woodblock remained stationary and the woodblock moving at a constant speed remained in motion at a constant speed.