Equilibrium. Observations
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1 Equilibrium Observations When you look closely at a rope you will see that it consists of several strands of twine. If you tried to hang a heavy (or massive) object on a single strand of twine it would probably break, but if you hung it from a rope it would hold. This happens because the weight of the object (force from gravity) is distributed among the strands of twine. What you may not realize is this situation is a result of Newton s First Law of Motion, Every object continues in its current state of motion unless acted upon by a nonzero net force. When all the forces on an object cancel out (add up to zero), then the object will not change its movement. It will remain at rest (or at a constant velocity). This situation is called mechanical equilibrium. On earth s surface all objects are subject to the force of gravity. If an object at rest is hanging from a rope then the force of gravity is balanced by the force of all the strands of twine making up that rope. If one strand breaks the weight is redistributed to all the remaining strands. This concept is true for ropes, table legs, columns holding up buildings, and many other mechanical situations. In this lab, you will explore equilibrium with a simple hands-on experiment. Procedure Equipment Diagram Meter stick 2 table clamps 2 support rods 4 perpendicular clamps 2 crossbars 2 spring 2 mass hangers Set of slotted masses
2 Setup 1. Attach table clamps to the table about 80 cm apart. 2. Attach the support rods to the table clamps. 3. Attach perpendicular clamps to the support rods. 4. Attach crossbars to the perpendicular clamps. 5. Attach another set of perpendicular clamps to the ends of the support rods 6. Hang the spring on the perpendicular clamps 7. Adjust the scale readings so they are at Hang the meter stick on the bottom of the spring. 9. Adjust the crossbars and connected equipment until the meter stick is supported at 10 cm and 90 cm. 10. Record the readings on the spring. Part 1 Step 1. Place one of the mass hangers at 50 cm on the meter stick. Note that the mass hanger has a mass of 50 g just by itself as marked on the hanger. Step 2. Add a 100 g slotted mass to the mass holder. Step 3. Record the readings on BOTH spring. Step 4. Repeat Steps 2 & 3 until the spring are maxed out. Part 2 Step 1. Place one of the mass hangers at the 20 cm mark on the meter stick. Step 2. Add 500 g of mass to the hanger. Step 3. Record the readings on both spring. Step 4. Move the hanger by 10 cm. Step 5. Record the readings on both spring. Step 6. Repeat Steps 4 & 5 until the hanger is at the 80 cm mark on the meter stick. Part 3 Step 1. Place two mass hangers on the meter stick, one at 30 cm and one at 60 cm. Step 2. Add 100 g to both mass hangers. Step 3. Record the readings on both spring. Step 4. Add 100 g to the hanger at 30 cm. Step 5. Record the readings on both spring. Step 6. Repeat Steps 4 5 until there is 1 kg on one of the hangers. Step 7. Repeat Part 3 but add mass to the hanger at 60 cm this time.
3 Analysis Part 1. Add the readings of the two together. Divide the mass on the hanger by 1000 g/kg to convert it to kg and multiple it by 10.0 m/s 2 to get the force of the hanger. (Force will be in units of Newtons, N). Create a scatter graph of your measurements for part 1 with the force on the hanger as the horizontal axis. The scale readings will be on the vertical axis. Plot two sets of data on the graph. One data set will be just one of the scale readings. The other data set will be the sum of both scale readings. Draw two lines, one through each data set, and measure the slope of each line. Part 2. Calculate the force of the hanger by dividing by 1000 g/kg and multiplying by 10.0 m/s 2. Graph the data for your measurements from part 2 with position of the hanger as the horizontal axis. Scale readings will be on the vertical axis. Plot three sets of data, one for each of the and the sum of the two readings. Draw three lines, one through each data set, and measure the slope of each line. Part 3. Calculate the force of the hanger by dividing by 1000 g/kg and multiplying by 10.0 m/s 2. Make two scatter graphs for part 3. One graph will be for adding mass to the hanger at 30 cm and the other for adding mass to the hanger at 60 cm. For both graphs the horizontal axis will be the combined force on both hangers. The vertical axis will be scale readings. Graph both the readings from each individual scale and the sum of the readings. Draw lines for each data set and measure the slope of each line.
4 Data Sheet Name: For part 1, how will the sum of the compare to the force of the hanger? Why? For part 2, will the sum of the change as the position of the hanger changes? Why? For part 3, will there be a difference in the slope of the sum of the depending on where you add the mass (at 30 cm or 60 cm)? Why? Part 1: Mass of hanger: units: Total Mass on hanger Force of the hanger Slope of single reading: units: Slope of sum: units:
5 Part 2: Mass on the hanger: units: Force on the hanger: units: Position of hanger Slope of scale 1: units: Slope of scale 2: units: Slope of sum: units: Part 3: Mass on hanger at 60 cm: units: Mass on hanger at 30 cm Force on both hangers Slope of scale 1: units: Slope of scale 2: units: Slope of sum: units:
6 Mass on hanger at 30 cm: units: Mass on hanger at 60 cm Force on both hangers Slope of scale 1: units: Slope of scale 2: units: Slope of sum: units: Questions 1. What do you observe (physically see) about all the systems you measured that tells you they are in a state of equilibrium? 2. In part 1, what would your results look like if your hanger were place somewhere besides 50 cm? 3. In part 1, what would be the slope of the line for an individual scale reading if there were three holding up the ruler instead of two? 4. In part 2, what would happen to your data and graph if you were using 1 kg instead of 500 g? 5. In part 2, how do the slopes from the individual scale readings compare to each other? Why is this a result of equilibrium? 6. In part 3, how are the results different between adding mass to the hanger at 30 cm and adding it to the hanger at 60 cm? What is similar about these results? 7. Compare the slopes of the sum of the two scale readings for parts 1 and 3? Why is this a results of equilibrium? 8. A hanging bird feeder is supported by three chains connected at three equally spaced points around the circumference of the bowl. How does the mass of the feed (and the bowl) compare to the tension in each chain? Does it matter where the feed is in the bowl? Bonus: Create a discussion question of your own.
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