Experiment 1: Stability

In this experiment you will test the stability of a stack of blocks as the angle of the surface the stack rests on gradually increases. Using a fishing sinker tied to the center of mass, you will be able to see the position of the center of mass relative to the base of the object as it begins to tip over.

Materials

1 Fishing Sinker

Protractor

30 cm. String

Masking Tape

Ramp Runway

Ruler

4 Wooden Blocks

*1 Empty Water Bottle with Lid

*Water

*You Must Provide

Procedure

Part 1

1. Mark the location of the center of gravity on one side of a wooden block with a piece of masking tape (the middle).

2. Using masking tape, attach one block above and below your original so that your center of gravity mark is visible, making a 3-block-high tower.

3. Use a ruler to measure and cut 30 cm. of string. Tape the string to the mark on the middle block with 20 cm hanging downward.

4. Attach a sinker to the end of the string. Set the block stack on top of the ramp, and line the edge of the ramp runway up with the edge of a table so that the string can dangle.

5. Increase the incline of the ramp runway, and notice the relationship between when the block stack starts to tip over and the location of the string. Record your observations in Table 1.

6. Try this out with four blocks stacked. Make sure to move your center of mass to the middle of the tower (between the second and third blocks). Record your observations in Table 1.

Table 1: Block Observations

Block Arrangement Observations

Three Stacked Blocks

Four Stacked Blocks

Part 2

1. Fill one of the water bottle one fourth full of water.

2. Stand the bottle upright on a table. Slowly tilt the bottle by pushing the top of one side with one hand while supporting the opposite side of the bottle with a finger form your other hand.

3. Push the top of the bottle further and further checking every once in a while to see if the bottle will fall back upright if you were to stop pushing.

4. Continue pushing the top of the bottle up until an angle where the bottle will not tip back upright and support that angle with the finger form your other hand.

5. Use the protractor to measure the angle between the side of the bottle your finger is supporting and the table. Record the angle in Table 2.

6. Repeat Steps 2 - 5 with the bottle half full, three fourths full and completely full. Record your angles in Table 2.

Table 2: Angle Just Before Bottle Tips Over

Amount of Water in Bottle Angle ()

Full

Full

Full

Full

Post-Lab Questions

1. When did the blocks typically fall over?

2. Which stack of blocks (3 or 4) had a lower center of mass? Which set tipped over at the largest angle? How do you know?

3. If you were building a skyscraper in a windy city, where would you want most of the building's weight to be located?

4. Draw a rough diagram for each case showing the placement of the center of mass (point CM) and the maximum angle of the bottle reached.

5. Explain why you were able to tilt the bottle more in some cases more than others.

6. How soon do you think the bottle would tip over if you could fill only the top half?

Experiment 2: Irregular Shapes

In this experiment, you will determine the center of mass for objects that have an irregular shape.

Materials

Hole Punch

Kit Box

30 cm. String

Permanent Marker

Printer Paper

1 Push Pin

Ruler

Scissors

2 Washers

*You Must Provide

Procedure

1. Use the scissors to cut an irregular shape out of a piece of paper. Any shape will work!

Figure 6: Step 3 reference.

2. Cut a 30 cm length of string and tie one metal washer to each end. This will function as a "plumb-bob" that hangs down as a vertical line.

3. Set one side of the physics kit box flush with the edge of a table and stick a push pin in the cardboard near the top (Figure 6).

4. Punch a hole in three different spots around the edge of the shape, but not too close together.

5. Hang the shape through one of the three holes on the push pin making sure the shape can move freely

6. Hook the plumb-bob to the push pin with the washer.

7. Note how the string hangs across the shape. Make a mark on the side of the shape opposite the hole in line with the plumb-bob string. Use this mark to draw a straight line through the shape, from the hole to your mark.

8. Take the shape and plumb-bob off the pin, and switch to a new hole on the shape. Repeat Steps 5 - 7 until you have three lines drawn on the shape.

Post-Lab Questions

1. What do you notice about the lines you drew?

2. What does the point where the three lines intersect represent?

3. When you hang the shape from the pin, it balances around that point. What does this tell you about the distribution of mass about this line?

4. Is the third line necessary to find the center of mass?

Experiment 3: Center of Mass of a Hanging Mass System

In this experiment you will determine the center of mass of a hanging mass system.

Materials

50 g Mass

100 g Mass

250 g Mass

Masking Tape

Mirror Support

3 Paper Clips

Ruler

(1) 8 oz. Styrofoam Cup

Procedure

1. Find a flat stable surface such as a table or floor.

2. Place the cup upside down on the surface.

Figure 7: System set up.

3. Place the mirror support on top of cup and secure each side of the base with one piece of masking tape

4. Take the ruler and balance it on the mirror support (Figure 7). As soon as you get the ruler to balance, record the location in Table 2 as the origin.

5. Use three paper clips to fabricate mass hangers that will hold the masses. The easiest way to is to bend the outer wire through the inner loop of the paper clip and then pull them down together (Figure 8).

Figure 8: Paper clips molded into mass hangers.

6. Holding the ruler above the table, slide on the three mass hangers.

7. Still holding the ruler with one hand, place the masses onto the mass hangers.

8. Once the masses are hanging, slide the 250 g mass to 6.5 cm left of the origin and the 100 g mass 9 cm to the right of the origin. Record the location of the masses on the ruler in Table 3. For example, if the origin is located at 16 cm, the 250 g mass is located at 9.5 cm.

9. Place the 50 g mass at the location you calculated in Pre Lab Question 3.

10. Now set the origin of the ruler on the mirror support and slowly let go of the ruler to see if your system of hanging masses balances.

11. If it does not balance perfectly, adjust the position of the 50 g mass to get the system to balance.

12. Once the system is balanced, record the location of the 50 g mass on the ruler in Table 3.

Table 3: Location of Masses on Balanced Ruler

Origin

(cm) m1 (g) x1 (cm) m2 (g) x2 (cm) m3 (g) x3 (cm)

Table 4: Location of Masses Balanced as Calculated from the Origin

Mass (g)

Distance from

Origin (cm)

Table 5: 50 g Mass Data

x3, theoretical (cm) x3, experimental (cm) Percent error

Post-Lab Questions

1. Fill out the following Table 4 and 5 to calculate your percent error for the experiment

1. Percent Error = |(Experimental - Actual)| x 100%

a. Actual

2. How does your prediction compare to the actual center of mass? Explain.

Experiment 1: Stability In this experiment you will test the stability of a stack of blocks as the angle of the surface the stack rests on gradually increases. Using a fishing sinker tied to the center of mass, you will be able to see the position of the center of mass relative to the base of the object as it begins to tip over. Materials 1 Fishing Sinker Protractor 30 cm. String Masking Tape Ramp Runway Ruler 4 Wooden Blocks *1 Empty Water Bottle with Lid *Water *You Must Provide Procedure Part 1 1. Mark the location of the center of gravity on one side of a wooden block with a piece of masking tape (the middle). 2. Using masking tape, attach one block above and below your original so that your center of gravity mark is visible, making a 3-block-high tower. 3. Use a ruler to measure and cut 30 cm. of string. Tape the string to the mark on the middle block with 20 cm hanging downward. 4. Attach a sinker to the end of the string. Set the block stack on top of the ramp, and line the edge of the ramp runway up with the edge of a table so that the string can dangle. 5. Increase the incline of the ramp runway, and notice the relationship between when the block stack starts to tip over and the location of the string. Record your observations in Table 1. 6. Try this out with four blocks stacked. Make sure to move your center of mass to the middle of the tower (between the second and third blocks). Record your observations in Table 1. 2014 eScience Labs, LLC. All Rights Reserved Table 1: Block Observations Block Arrangement Observations Three Stacked Blocks Four Stacked Blocks Part 2 1. Fill one of the water bottle one fourth full of water. 2. Stand the bottle upright on a table. Slowly tilt the bottle by pushing the top of one side with one hand while supporting the opposite side of the bottle with a finger form your other hand. 3. Push the top of the bottle further and further checking every once in a while to see if the bottle will fall back upright if you were to stop pushing. 4. Continue pushing the top of the bottle up until an angle where the bottle will not tip back upright and support that angle with the finger form your other hand. 5. Use the protractor to measure the angle between the side of the bottle your finger is supporting and the table. Record the angle in Table 2. 6. Repeat Steps 2 - 5 with the bottle half full, three fourths full and completely full. Record your angles in Table 2. Table 2: Angle Just Before Bottle Tips Over Amount of Water in Bottle Angle () Full Full Full Full Post-Lab Questions 1. When did the blocks typically fall over? 2. Which stack of blocks (3 or 4) had a lower center of mass? Which set tipped over at the largest angle? How do you know? 2014 eScience Labs, LLC. All Rights Reserved 3. If you were building a skyscraper in a windy city, where would you want most of the building's weight to be located? 4. Draw a rough diagram for each case showing the placement of the center of mass (point CM) and the maximum angle of the bottle reached. 5. Explain why you were able to tilt the bottle more in some cases more than others. 6. How soon do you think the bottle would tip over if you could fill only the top half? Experiment 2: Irregular Shapes In this experiment, you will determine the center of mass for objects that have an irregular shape. Materials Hole Punch Kit Box 30 cm. String Permanent Marker Printer Paper 1 Push Pin Ruler Scissors 2 Washers *You Must Provide Procedure 1. Use the scissors to cut an irregular shape out of a piece of paper. Any shape will work! 2. Cut a 30 cm length of string and tie one metal washer to each end. This will function as a "plumb-bob\" that hangs down as a vertical line. Figure 6: Step 3 reference. 3. Set one side of the physics kit box flush with the edge of a table and stick a push pin in the cardboard near the top (Figure 6). 4. Punch a hole in three different spots around the edge of the shape, but not too close together. 5. Hang the shape through one of the three holes on the push pin making sure the shape can move freely 6. Hook the plumb-bob to the push pin with the washer. 2014 eScience Labs, LLC. All Rights Reserved 7. Note how the string hangs across the shape. Make a mark on the side of the shape opposite the hole in line with the plumb-bob string. Use this mark to draw a straight line through the shape, from the hole to your mark. 8. Take the shape and plumb-bob off the pin, and switch to a new hole on the shape. Repeat Steps 5 - 7 until you have three lines drawn on the shape. Post-Lab Questions 1. What do you notice about the lines you drew? 2. What does the point where the three lines intersect represent? 3. When you hang the shape from the pin, it balances around that point. What does this tell you about the distribution of mass about this line? 4. Is the third line necessary to find the center of mass? Experiment 3: Center of Mass of a Hanging Mass System In this experiment you will determine the center of mass of a hanging mass system. Materials 50 g Mass 100 g Mass 250 g Mass Masking Tape Mirror Support 3 Paper Clips Ruler (1) 8 oz. Styrofoam Cup Procedure 1. Find a flat stable surface such as a table or floor. 2. Place the cup upside down on the surface. 3. Place the mirror support on top of cup and secure each side of the base with one piece of masking tape 2014 eScience Labs, LLC. All Rights Reserved Figure 7: System set up. 4. Take the ruler and balance it on the mirror support (Figure 7). As soon as you get the ruler to balance, record the location in Table 2 as the origin. 5. Use three paper clips to fabricate mass hangers that will hold the masses. The easiest way to do this is to bend the outer wire through the inner loop of the paper clip and then pull them down together (Figure 8). Figure 8: Paper clips molded into mass hangers. 6. Holding the ruler above the table, slide on the three mass hangers. 7. Still holding the ruler with one hand, place the masses onto the mass hangers. 8. Once the masses are hanging, slide the 250 g mass to 6.5 cm left of the origin and the 100 g mass 9 cm to the right of the origin. Record the location of the masses on the ruler in Table 3. For example, if the origin is located at 16 cm, the 250 g mass is located at 9.5 cm. 9. Place the 50 g mass at the location you calculated in Pre Lab Question 3. 10. Now set the origin of the ruler on the mirror support and slowly let go of the ruler to see if your system of hanging masses balances. 11. If it does not balance perfectly, adjust the position of the 50 g mass to get the system to balance. 12. Once the system is balanced, record the location of the 50 g mass on the ruler in Table 3. Table 3: Location of Masses on Balanced Ruler Origin (cm) m1 (g) x1 (cm) m2 (g) x2 (cm) m3 (g) x3 (cm) Table 4: Location of Masses Balanced as Calculated from the Origin Mass (g) Distance from Origin (cm) 2014 eScience Labs, LLC. All Rights Reserved Table 5: 50 g Mass Data x3, theoretical (cm) x3, experimental (cm) Percent error Post-Lab Questions 1. Fill out the following Table 4 and 5 to calculate your percent error for the experiment 1. Percent Error = |(Experimental - Actual)| x 100% a. Actual 2. How does your prediction compare to the actual center of mass? Explain. 2014 eScience Labs, LLC. All Rights Reserved