Materials Included In Kit

Additional Materials Required

Prelab Preparation

1. Obtain three 3-mL, one 1-mL and two 20-mL syringes, three syringe-tip connectors and a 250-mL beaker. Fill the beaker three-quarters full with water.
2. Remove the plunger from one of the 3-mL syringes. (Call this Syringe A.)
3. Connect the Luer Lock syringe-tip connector to another 3-mL syringe. (Call this Syringe B.)
4. Place the open end of the syringe-tip connector on Syringe B into the 250-mL beaker of water. Pull back on Syringe B’s plunger to draw water into the syringe until it is approximately three-quarters full.
5. Invert the syringe so that the tip is up and the plunger end is down—any air bubbles trapped in the syringe will rise to the tip end. Carefully flick the syringe body with a finger to release any air bubbles clinging to the sides of the syringe.
6. Connect Syringe A to the open end of the Luer Lock syringe-tip connector on Syringe B.
7. Hold the coupled syringes vertically so that Syringe A is above Syringe B. Then slowly push on Syringe B’s plunger to fill Syringe A (see Figure 6a).
   {13953_Preparation_Figure_6}
8. If Syringe A does not become completely filled, use a 50-mL graduated cylinder to add enough water to Syringe A until it is just overflowing (see Figure 6b).
9. Once Syringe A is overflowing, replace the plunger into Syringe A making sure no air bubbles become trapped in the syringe body (see Figure 6c). Repeat steps 4–9 if air bubbles become trapped.
10. Repeat steps 2–9 for a 20-mL/3-mL system. Refer to the 3-mL syringe as “Syringe A” and the 20-mL syringe as “Syringe B” in the procedure.
11. Repeat steps 2–9 for a 20-mL/1-mL system. Refer to the 1-mL syringe as “Syringe A” and the 20-mL syringe as “Syringe B” in the procedure. Note: The 1-mL syringe does not have the Luer Lock tip. It will not lock into the syringe tip connector.

Safety Precautions

When pressing on the syringe systems, be sure to press only the input plunger with your thumb and hold the output syringe with your other hand to prevent the syringes from separating. Do not use the syringe as a “squirt gun.” Wear safety glasses. Please follow all laboratory safety guidelines.

Disposal

Empty the water in the syringes into a sink after completing the experiments. Consult your instructor for appropriate storage procedures. The materials should be saved for future use.

Teacher Tips

• Enough materials are provided in this kit for 8 groups of students. The entire activity can reasonably be completed in two 50-minute class periods.
• Save time by cutting enough 300-cm and 60-cm strings for each group before the lab.
• Notching the plunger ends with a triangular file will help prevent the string from slipping off the plunger end during the Mechanical Advantage Part 2 experiment (see Figure 7).
  {13953_Tips_Figure_7}
• If spring scales are not available, a setup such as that shown in Figure 8 can be used to obtain semi-quantitative data. Have students determine the maximum number of books they can push with each syringe system. However, depending on the strength of your student’s fingers, many (8 or more) books may be needed for the 3-mL/20-mL and 1-mL/20-mL systems.
  {13953_Tips_Figure_8}
• This activity is designed as a qualitative and semi-quantitative introduction to hydraulics. If improved quantitative measurements of Pascal’s law are desired, refer to the setup in the optional Quantitative Investigation section. See also the Flinn Scientific Principles of Hydraulics Kit, AP6494, for a complete quantitative hydraulic system.
• This activity provides a good understanding of the mechanical advantage gain from hydraulics, as well as the efficiency of simple machines. A tabletop pulley can be used at the end of the table to lower the frictional force, if desired.
• If hooked masses are not available for Mechanical Advantage Part 2, a plastic holding cup can be used and filled with sand or stones. Obtain a clear, 12-oz plastic cup and use a hot nail to poke two holes 180° apart near the top of the cup. Loop the string through the holes in the cup so that the cup is balanced (the support strings are on opposite sides of the cup). Tie the string ends together to form a loop. Then loop the end of the string around the output plunger on the tabletop (see Figure 9).
  {13953_Tips_Figure_9}
• This hydraulic system will not work with air; water must be used. Air will be compressed in the input syringe before it begins to move the output plunger. Most liquids are incompressible and therefore pressure is distributed equally to all surfaces inside the system.
• Additional syringe configurations can be used for Mechanical Advantage Part 2. However, stronger (2000-g or higher) spring scales will be needed for the 20-mL/3-mL, 20-mL/1-mL and 3-mL/3-mL input/output systems in order to overcome the frictional forces and the low mechanical advantage of these systems—even if less mass is lifted.

Further Extensions

Alternative Quantitative Investigation Setup
Set up the equipment as shown in Figure 11 and follow the experiment procedure below to make quantitative measurements with the equipment provided in this kit. ⅛" ID Tygon (plastic) tubing is needed to connect the syringes.

To measure quantitatively, pull down on the spring scale to measure the force needed to lift the weights atop the large syringe. The frictional force can also be determined by measuring the force needed to raise the plunger with no mass on the plunger head. Reverse the equipment. Place weights atop the small plunger. How much force is needed to lift the weights atop the small syringe? Disassemble the equipment and pull out the plungers for both syringes. Measure the diameters of both plunger heads. Use the force and area determinations to calculate the pressure. The force from the weights is equal to mass times the acceleration due to gravity (mg), where g is equal to 9.81 m/s².

Sample Data

Data Table 1.

Data Table 2. Data Table 3.

Answers to Questions

1. Review the results of the experiments in Data Table 1. Was it easier to move the 20-mL plunger by pressing the 1-mL plunger, or to move the 1-mL plunger by pressing the 20-mL plunger? Which plunger has the larger surface area? Use Pascal’s law to explain the result.

   It was easy to press on the 1-mL plunger to move the 20-mL plunger. It was very difficult to move the 1-mL plunger by pressing on the 20-mL plunger.
   The 20-mL plunger has the larger surface area compared to the 1-mL plunger. In terms of Pascal’s law, the 20-mL plunger was harder to move compared to the 1-mL plunger because the surface area of the plunger is larger, meaning a larger force is needed to move it, since the pressure in the syringe system is constant.

2. Use the measurements from Data Table 2 and Equation 2 to determine the ideal mechanical advantage of the following syringe systems.

   Input: 1-mL, Output: 20-mL; Ideal Mechanical Advantage: 19
   Input: 3-mL, Output: 20-mL; Ideal Mechanical Advantage: 5.4
   Input: 3-mL, Output: 3-mL; Ideal Mechanical Advantage: 1
   Input: 20-mL, Output: 3-mL; Ideal Mechanical Advantage: 0.19
   Input: 20-mL, Output: 1-mL; Ideal Mechanical Advantage: 0.05

3. Compare the mechanical advantage calculations from Question 2 to how hard or easy it was to move the respective input plunger. Is it better to have a mechanical advantage greater than one or less than one?

   The easiest system to move has the highest mechanical advantage (19). A mechanical advantage less than one corresponded to a very difficult system to push.

4. Use the measurements from Data Table 3 and Equation 1 to determine the actual mechanical advantage of the following syringe systems.

   Input: 1-mL, Output: 20-mL; Actual Mechanical Advantage: 6.7
   Input: 3-mL, Output: 20-mL; Actual Mechanical Advantage: 1.3

5. Use Equation 3 to calculate the efficiency of the two systems described in Question 4.

   1-mL/20-mL Efficiency: 6.7/19 × 100% = 35%
   3-mL/20-mL Efficiency: 1.3/5.4 × 100% = 24%

6. List possible sources of error that may have led to the low efficiency. What improvements could be made to the systems to make them more efficient?

   Friction was a major source of error that led to low efficiency. Friction inside the syringe bodies, and friction of the string riding against the edge of the table were the two most influential friction sources.
   The friction may be reduced if the insides of the syringe tube were coated with a lubricant such as Vaseline^®. If a pulley was used at the edge of the table, that would significantly reduce the drag friction on the string.

7. Refer to Figure 11. Which would Pascal predict as the winner in a “thumb wars” match? Why?
   {13953_Answers_Figure_11}
   Pascal would predict that syringe A would win because the smaller syringe supplies more force on the large syringe. The mechanical advantage of the large syringe is very small, so even a large force supplied to the large plunger is still a very weak force on the small plunger.

Introduction

Pascal’s law applies to many aspects of our lives. An extremely important application of Pascal’s law occurs when a driver presses on a brake pedal to stop a car. Pascal’s law is also at work when a mechanic easily lifts a car using a hydraulic jack. In this activity, hydraulics will be studied to gain a better understanding of the principles of Pascal’s law.

Concepts

• Pascal’s law
• Pressure
• Mechanical advantage
• Hydraulics

Background

Blaise Pascal (1623–1662) is well known as a mathematician. Pascal also had a strong interest in physical events and spent much of his time trying to explain the phenomena he witnessed in his experiments. He performed many experiments involving pressure in fluids. One of the most important principles he discovered became known as Pascal’s law.

Pascal’s law states that pressure applied anywhere to a fluid causes a pressure to be transmitted equally in all directions. This is the result of fluids being incompressible. A force applied at one end is transmitted throughout the entire fluid system.

Pressure is equal to a force per unit area (P = F/A). Therefore, if the pressure in a fluid is constant, then the larger the surface area the pressure is in contact with, the larger the force. The smaller the surface area, the smaller the force. By arranging liquid columns of different sizes Pascal discovered that a relatively small force could lift a very heavy load. Pascal’s law serves as the basis for the development of much of what is now known as hydraulics.

Mechanical advantage is a ratio of the output force compared to the input force (Equation 1). where

F_o is the output force
F_i is the input force

The higher the mechanical advantage of a system, the higher the output force compared to the input force. The higher the mechanical advantage, the easier it is to do the work. However, mechanical advantage does not give something for nothing. With a large mechanical advantage, it is easy to move a heavy load with a relatively smaller force. The trade-off is that the smaller applied force must be carried over a longer distance compared to the distance the heavy load is moved. This is a result of the conservation of energy, in which the total energy in equals the total energy out. A small force will move a large distance while the large load moves a small distance. The mechanical advantage of a hydraulic system can also be determined by comparing the distance the input force moves compared to the output force (Equation 2). where

d_i is the input distance
d_o is the output distance

A hydraulic system is not perfectly efficient. Some energy will always be lost due to frictional forces. Equation 2 is considered the ideal mechanical advantage (MA_i) because it is based only on dimensions. Equation 1 provides the actual, real-world mechanical advantage (MA_a) because it is a ratio of the total force out (the lifted mass) to the total force in (the force necessary to raise the mass as well as the force necessary to overcome friction). The efficiency of the system can be calculated using Equation 3. Figure 2 shows a force of 20 Newtons pushing a fluid through a 1-cm² opening. Therefore, according to Pascal’s law, every square centimeter of the entire system is under a force of 20 N. The piston in the larger container has a surface area of 100 cm², making the amount of force lifting up the piston in the larger container equal to 2000‑N (20 N/cm² × 100 cm²). The total force increases as the surface area increases.

Materials

Safety Precautions

When pressing on the syringe systems, be sure to press only the input plunger with your thumb and hold the output syringe with your other hand to prevent the syringes from separating. Do not use the syringe as a “squirt gun.” Wear safety glasses. Please follow all laboratory safety guidelines.

Procedure

Observations

1. Working one at a time with the three syringe systems, press down first on one plunger and watch the movement of the second plunger. Then press on the second plunger and watch the movement of the first plunger. How do the opposing plungers in each system move? Is it easier to push on the smaller or larger plunger in each system? Record all observations in Data Table 1 on the Pascal’s Law Worksheet. Note: When pressing on the plunger of a syringe, be sure to hold the syringe body of the other syringe to prevent the syringes from coming apart. This is especially important for the 1-mL/20-mL system because the 1-mL syringe does not have a Luer Lock tip. Also, for the 20-mL syringe systems, do not push too hard on the 20-mL plunger since this may cause the 1-mL and 3-mL plungers to “pop out” of their respective syringes.

Mechanical Advantage—Part 1

2. Obtain the 3-mL/3-mL syringe system.
3. Press one plunger all the way down until it can no longer move, thereby moving all water into one of the syringe bodies. The empty syringe (with plunger pushed all the way in) will be the output syringe. The water-filled syringe will be the input syringe.
4. Measure the initial distance the input plunger is from the end of the syringe body (see Figure 3). Record this distance to the nearest 0.1 cm in Data Table 2 on the worksheet.
   {13953_Procedure_Figure_3}
5. Measure the initial distance the output plunger is from the end of the syringe body (see Figure 3). Record this distance to the nearest 0.1 cm in Data Table 2.
6. Press on the input plunger until the output plunger has moved to the end of the syringe body, or until the input syringe is completely empty and the plunger stops at the syringe body—whichever comes first. Caution: Do not push the output plunger out of the syringe body.
7. Measure the final distance the input plunger is from the syringe body. Record this distance to the nearest 0.1 cm in Data Table 2.
8. Measure the final distance of the output plunger from the syringe body. Record this distance to the nearest 0.1 cm in Data Table 2.
9. Repeat steps 2–8 with the 1-mL/20-mL and 3-mL/20-mL syringe systems. The 1-mL and 3-mL syringes should be used as the input syringes for each respective system. Record all measurements in Data Table 2.

Mechanical Advantage—Part 2

10. Obtain the 20-mL/3-mL syringe system, string, scissors, 1000-g spring scale, and a 1000-g mass.
11. Cut a length of string approximately 300 cm. Tie the ends together to form a loop.
12. Cut another length of string approximately 60 cm. Tie the ends together to form a second loop.
13. Using Figure 4a as a guide, loop the 300-cm string around the 20-mL syringe plunger and extend the loop to the left so that it hangs off the edge of the table. Loop the 60-cm string around the 3-mL syringe plunger and extend it to the right as shown in Figure 4b. Add a small piece of tape to the ends of the plungers to secure the string.
    {13953_Procedure_Figure_4a}
    {13953_Procedure_Figure_4b}
14. Follow steps 15–19 to determine how much force is needed to lift 1000 g.
15. Each lab partner must choose to be either a “holder” or a “measurer.”
    • The holder’s duties include:
      1. Checking that the strings are securely wrapped around both plunger ends.
      2. Making sure the input syringe is filled with water before each trial begins.
      3. To start the experiment, the holder must slide the entire syringe system a few centimeters to the left or right in order to raise the mass off the floor. The hanging mass will provide the output force on the output syringe.
      4. Once the mass is raised and the plungers are in position, the holder must firmly hold the input and output syringe bodies to the tabletop so that they will not slide when the measurer pulls on the spring scale (see Figure 4c).
         {13953_Procedure_Figure_4c}
    • The measurer’s duties include: 
      1. Adding the weight to the end of the string before the experiment.
      2. During the experiment, the measurer pulls on the spring scale evenly to move the mass at a constant speed (see Figure 4c).
      3. Measuring the constant force that registers on the spring scale.
      4. After the trial, the measurer must carefully lower the mass back down to the floor.
16. Measurer: Hang a 1000-g mass from the end of the 300-cm loop of string hanging over the edge of the tabletop.
17. Holder: Check that the strings on both plungers are securely supported. Make sure the 3-mL syringe is completely full.
18. Holder:
    1. Carefully slide the entire syringe system left or right (depending on the location of the hanging mass) a few centimeters in order to raise the mass off the floor slightly. It may be necessary to press on the input syringe plunger until the measurer is ready to pull because the force from the hanging mass may be enough to “pop” the input plunger out of the syringe body.
    2. Recheck the strings to make sure they are wrapped around the plunger ends.
    3. Hold the input and output syringe bodies firmly to the tabletop with a finger or two, making sure not to hold or interfere with the movement of the strings.
19. Measurer:
    1. Slowly pull on the spring scale until the plunger begins to move. Once the plunger begins to move, continue pulling evenly on the spring scale to move the plunger at a constant speed. Note: The plunger will be moving at a constant speed when the reading on the spring scale remains relatively constant. It will take more force to initially get the plunger moving than it will to keep it moving at a constant speed.
    2. When the plunger is moving with a constant speed, read the value that registers on the spring scale.
    3. Record this value in Data Table 3.
    4. After measuring the force from the spring scale, carefully lower the mass back down to the floor.

       Caution: Stop pulling on the spring scale before the output plunger is at the end of the syringe body—the plunger may “pop” out, along with the water.
       Note: Only record the value when the plunger moves with a constant speed. If necessary, repeat the trial until a constant lifting speed is achieved.

20. Repeat steps 13–19 for the 1-mL/20-mL syringe system. The 1-mL syringe will be the input syringe.
21. Answer the questions on the Pascal’s Law Worksheet.

Teacher Demonstration—Thumb Wars

1. Perform this demonstration before the experiment to show a simple hydraulic system and to show the benefit of mechanical advantage. It will also serve as a model that the students can see for the syringe system setup.
2. Follow the Preparation steps 1–9 to build a 1-mL/20-mL syringe system.
3. Before the lab, show students this simple hydraulic device.
4. Ask students to predict which syringe plunger will provide the most force on the other plunger when they are both pressed at the same time. Have students defend their answer with a hypothesis or past experience.
5. Ask for a student volunteer (possibly a strong, football player–type person).
6. Challenge them to a thumb “duel.”
7. Ask the student which plunger end they want to push. (Or, if you want to win, give the student the large, 20-mL plunger end.)
8. On the count of three, you and the student must press on the plungers at the same time and see who can push the plunger in first and win the thumb “duel” (see Figure 5).
   {13953_Procedure_Figure_5_Thumb “duel”}
9. Students will learn why the small syringe won while performing the lab.

Student Worksheet PDF

13953_Student1.pdf