In the previous labs, you have examined position–time, velocity–time, and acceleration–time graphs of different motions of the IOLab using the Wheel displays. You were not concerned about how you got the IOLab to move, i.e., what forces (pushes or pulls) acted on it. (You pushed it with your hand, allowed the Earth’s gravitational force to pull on it , and also used a hanging mass attached to a string to pull it.) From your previous experiences, you know that force and motion are related in some way. To start your bicycle moving, you must apply a force to the pedal. To start up your car, you must step on the accelerator to get the engine to apply a force to the road through the tires.
But exactly how is force related to the quantities you used in Labs 2 and 3 to describe motion—position, velocity, and acceleration? In this lab you will pay attention to forces and how they affect motion. You will learn how to measure forces. By applying forces to the IOLab and observing the nature of its resulting motion graphically, you will begin to understand the effects of forces on motion as described by Newton’s Laws.
In this investigation you will explore the concept of a constant force and the combination of forces in one dimension. You can use these concepts to learn how to set up a force scale and measure forces with a force sensor. You will need the following materials:
If you pull on a rubber band attached at one end, you know it will stretch. The more you pull, the more it stretches. Try it.
Standard stretched length of rubber band:
Question 1-1: How does the combined force of two rubber bands compare to what you felt when only one rubber band was used?
Repeat this comparison of how strong the forces feel with three, four, and five rubber bands stretched together to the same standard stretched length.
Question 1-2: Suppose you stretched a rubber band to your standard stretched length by pulling on it. Now you want to create a force six times as large. How could you create such a force?
Question 1-3: Suppose you applied a force with a stretched rubber band one day, and several days later you wanted to feel the same force or apply it to something. How could you assure that the forces were the same? Explain.
Question 1-4: Do side-by-side rubber bands provide a convenient way of accurately reproducing forces of many different sizes that you can apply to objects? Explain.
Comment: Pulling more and more rubber bands to the same length requires a larger pull. To be more precise about the pulls and pushes you are applying, you need a device to measure forces accurately. The electronic force sensor that is part of the IOLab is designed to do this.
In this activity you will explore the capability of the IOLab’s electronic force sensor as a force-measuring device.
Note: Since forces are detected by the computer system as changes in an electronic signal, it is important to first have the computer “read” the signal when the force sensor has no force pushing or pulling on it. This process is called “zeroing” the force sensor. This is also necessary because the electronic signal from the force sensor can change slightly as the temperature changes or when the IOLab collides with something. It is a good idea to click on Rezero sensor (below the axes) with nothing pulling or pushing on the force sensor, before you collect data.
Average reading:
Average reading with two rubber bands:
Average reading with one rubber band:
14. Use Excel or another graphing program to plot a graph of F vs. N, the number of rubber bands.
Question 1-5: How are force sensor readings related to the size of the pull exerted on the force sensor hook by the rubber bands? Describe the mathematical relationship in words.
Question 1-6: Based on your analysis (and/or graph), what force sensor reading would correspond to the pull of five rubber bands when stretched to your standard length? How did you determine this?
Now you can use the IOLab to explore the effects of forces applied to it by using the measurements of the Wheel and Force Sensor together. You will be able to explore the relationship between motion and force. You will need the following materials:
In this activity you will move the low friction IOLab by pushing and pulling it with your hand. You will measure the force, velocity, and acceleration vs. time. Then you will be able to look for mathematical relationships between the force applied to the IOLab and the velocity and/or acceleration, to see whether either velocity or acceleration (or neither) is related to the force.
Set up the IOLab and force sensor hook on a smooth level surface as shown below.
Prediction 2-1: Suppose you grasp the force sensor hook and move the IOLab forward and backward. Do you think that either the velocity graph, the acceleration graph or neither will look like the force graph?
Prediction 2-2: Explain the basis for your Prediction 2-1.
Test your prediction.
Note: Try to get sudden starts and stops, and to pull and push the force sensor hook along a straight line without lifting the IOLab off the tabletop.
Read the times off the graphs when each of these occurred:
A: You first began pulling the IOLab towards you the first time
B: You stopped the IOLab as it was moving towards you the first time.
C: You began to push the IOLab away from you the first time
D: You stopped the IOLab as it was moving away from you the first time.
Question 2-1: Explain how you identified each of the points A, B, C and D.
Question 2-2A: Does either graph—velocity or acceleration—resemble the force graph?
Question 2-2B: Explain how you reached this conclusion.
Question 2-3A: Based on your observations, does it appear that there is a direct mathematical relationship between either
Question 2-3B: Explain based on your graphs.
You have seen in the previous activity that force and acceleration seem to be related. But just what is the mathematical relationship between force and acceleration?
Predictions: Suppose that you have a cart (e.g., the IOLab) with very little friction and you pull it with a constant force as shown on the force–time graph below.
Prediction 2-3: Which of the following graphs would represent velocity vs. time as the cart with very little friction is pulled by the force above.
Prediction 2-4: Describe in words the predicted shape of the velocity vs. time graph that you selected.
Prediction 2-5: Which of the following graphs would represent acceleration vs. time as the cart with very little friction is pulled by the force above.
Prediction 2-6: Describe in words the predicted shape of the acceleration vs. time graph that you selected.
To test your predictions, you will need the following:
Record the times for the following:
Question 2-4A: the time interval before the mass is released
Question 2-4B: the exact moment it is released
Question 2-4C: the moment you stop the IOLab at the edge of the table.
Question 2-5A: Measure the average force only including the time interval during which the IOLab was being pulled by the falling mass across the table (not including the time interval before you released it, or the time interval after you first touched it to stop it).
Question 2-5B: Measure the average acceleration during the same time interval as the average force.
Question 2-6A: After the cart is moving, is the force that is applied to the IOLab by the fishing line constant, increasing, or decreasing?
Question 2-6B: Explain based on your graph.
Question 2-7: How does the acceleration vary in time? Does this agree with your prediction? Does a constant force applied to the IOLab produce a constant acceleration?
Question 2-8: How does the velocity vary in time? Does this agree with your prediction? What kind of change in velocity corresponds to a constant force applied to the IOLab?
In the previous activity you examined the motion of the IOLab with a constant force applied to it. But what is the relationship between acceleration and force? If you apply a larger force to the same IOLab (with the same mass) how will the acceleration change? In this activity you will try to answer these questions by applying different forces to the IOLab, and measuring the corresponding accelerations.
If you accelerate the same IOLab with two other different forces, you will then have enough data to plot a graph of acceleration vs. force. You can then find the mathematical relationship between acceleration and force (with the mass of the IOLab kept constant).
Prediction 2-7A: Suppose you pull the IOLab with a force about twice as large as before. What would happen to the acceleration of the IOLab?
Prediction 2-7B: Explain your Prediction.
To test your prediction, accelerate the IOLab with a larger force than before. To produce a larger force, hang a mass from the fishing line two times as large as in the previous activity. Don’t forget to follow the same steps as before:
Record the times for the following:
Question 2-9A: the time interval before the mass is released
Question 2-9B: the exact moment it is released
Question 2-9C: the moment you stop the IOLab at the edge of the table.
Question 2-10A: Measure the average force only including the time interval during which the IOLab was being pulled by the falling mass across the table (not including the time interval before you released it, or the time interval after you first touched it to stop it).
Question 2-10B: Measure the average acceleration during the same time interval as the average force.
Question 2-11: How did the force applied to the cart compare to that with the smaller mass in Activity 2-2?
Question 2-12: How did the acceleration of the cart compare to that caused by the smaller force in Activity 2-2? Did this agree with your prediction? Explain.
Repeat using larger (60g) mass:
15. Use Excel or another graphing program to plot a graph of average Force vs. average Acceleration.
Question 2-13: Does there appear to be a simple mathematical relationship between the acceleration of the IOLab (with fixed mass and small friction) and the force applied to the IOLab (measured by the force sensor)? Write down the equation you found and describe the mathematical relationship in words.(You may want to refer to the Comment about mathematical relationships on slide 8)
Question 2-14: If you increased the force applied to the IOLab by a factor of 10, how would you expect the acceleration to change? How would you expect the acceleration–time graph of the IOLab’s motion to change? Explain based on your graphs.
Question 2-15: If you increased the force applied to the IOLab by a factor of 10, how would you expect the velocity–time graph of the IOLab’s motion to change? Explain based on your graphs.
Comment: The mathematical relationship that you have been examining between the acceleration of the cart and the force applied to it is known as Newton’s second law. In words, when there is only one force acting on an object, the force is equal to the mass of the object times its acceleration. (Note: You will see in the next lab that when more than one force is acting on an object, it is the vector sum of the forces--or "net force"--that is equal to mass times acceleration.)
Please remember to edit the report (insert your name - and if necessary your partners), export the report and submit it on D2L.
Now do the homework associated with this lab.