LAB 5: MORE ABOUT NEWTON'S LAWS

Please list the members of your group:

OBJECTIVES

OVERVIEW

In previous labs you have examined the one-dimensional motions of an object caused by a force applied to the object. You have seen that when friction is small enough that it can be ignored compared to the force applied to the object, a single constant force will cause an object to have a constant acceleration. (The object will speed up at a steady rate.)

Under these conditions, you have seen that the acceleration is proportional to the force applied to the object, if the mass of the object is not changed. If the force is made larger, then the acceleration is proportionally larger. This allows you to define force more precisely not just in terms of the stretches of rubber bands and springs, but as the “thing” that causes acceleration.

The major goal of this lab is to continue to develop the relationships between force and acceleration: Newton’s famous laws of motion.

OUTLINE

Investigation 1: You will explore under what conditions a force applied to an object will make the object slow down instead of speed up.

Investigation 2: You will examine what happens when there is more than one force acting on an object at the same time. You will develop the idea of the net or combined force. In particular, you will explore the motion of objects when the net force is zero (Newton’s first law).

Investigation 3: You will again look at Newton’s second law. Previously, you examined what happened when you changed the force applied to an object, while keeping the mass of the object constant. Now you will see what happens with the same force applied to objects of different mass.


Copyright © 2018 John Wiley & Sons, Inc.

INVESTIGATION 1: SLOWING DOWN

In the previous lab you looked at cases where the velocity, force, and acceleration all have the same sign. That is, the vectors representing each of these three quantities all point in the same direction. For example, if the cart is moving toward the right and a force is exerted toward the right, then the cart will speed up. The acceleration is also toward the right. The three vectors can be represented as:


If the positive direction is toward the right, then you could also say that the velocity, acceleration, and force are all positive. In this investigation, you will examine the vectors representing velocity, force, and acceleration for a different motion of the cart. This will be an extension of your observations in Lab 3, Changing Motion.

You will need the following:

Activity 1-1: Slowing Down

  1. Calibrate the force sensor on the IOLab with nothing pulling on it by selecting Calibrate from the menu, and following the directions.
  2. Set up the IOLab on the smooth surface, with the fishing line and hanging mass as shown in the diagram below. The fishing line should be tied to the screw eye which is screwed into the force sensor.

Now when you give the IOLab a push to the left (the negative y direction), it will slow down after it is released. You will examine the acceleration and the force in this situation.

Activity 1-1: Slowing Down

Suppose that you give the IOLab a push toward the left and release it. The diagram below shows the positions of the IOLab at four times. Assume that the IOLab is moving toward the left at all four times.



a) What are the signs of the velocity, force, and acceleration when the IOLab is at ? ( + ) Velocity ( + ) Force ( + ) Acceleration ( - ) Velocity ( - ) Force ( - ) Acceleration b) What are the signs of the velocity, force, and acceleration when the IOLab is at ? ( + ) Velocity ( + ) Force ( + ) Acceleration ( - ) Velocity ( - ) Force ( - ) Acceleration c) Compare the magnitude of the velocity at to the velocity at .

Activity 1-1: Slowing Down



d) Compare the magnitude of the force at to the force at . e) Compare the magnitude of the acceleration at to the acceleration at .

Activity 1-1: Slowing Down

  1. With the fishing line loose, zero the force sensor by clicking Rezero sensor.
  2. Click Record, give the IOLab a quick, very short push toward the left.
  3. When the IOLab has come to rest, stop it with your hand to prevent it from returning to the right, and click Stop.
  4. Adjust the vertical axes to best display Force, Velocity and Acceleration, as clearly as possible.

Question 1-1: Did the signs of the velocity, force, and acceleration agree with your predictions? If not, can you now explain the signs? Explain. Question 1-2: Did the velocity and acceleration have the same or different signs? Explain these signs based on the relationship between acceleration and velocity.

Activity 1-1: Slowing Down

Question 1-3: Did the force and acceleration have the same sign? Were the force and acceleration in the same direction? Explain. Question 1-4: Based on your observations, describe the directions (right or left) of the Force, Velocity and Acceleration vectors during the observed motion. Do these agree with your predictions? If not, can you now explain the directions of the vectors? Question 1-5a: Based on your observations, which of the following statement(s) is (are) true? An object with negative acceleration always slows down. An object with negative acceleration always speeds up. An object with positive acceleration always speeds up. An object with positive acceleration always slows down. None of the above.

Question 1-5b: Explain your answer based on the observations you made.

INVESTIGATION 2: COMBINING APPLIED FORCES (NET FORCE) AND NEWTON’S FIRST LAW



As you know, vectors are mathematical entities that have both magnitude and direction. Thus, a one-dimensional vector can point either in the positive or negative direction. Vectors pointing in the same direction add together and vectors pointing in opposite directions subtract from each other. A quantity that has vector behavior is often denoted by a bold letter with a little arrow above it . The sum of several vectors is often denoted by placing a summation sign in front of a vector symbol

Objects are often acted on simultaneously by more than one force. The combination (sum) of all the forces acting on an object () is called the net or combined force.

As you have seen in the previous lab, forces applied to an object and the acceleration of the object are related by Newton’s second law. In this Investigation you will examine the concept of net force, and see what happens when the net force is zero.

Activity 2-1: Once a Pull, Always a Pull?



Prediction 2-1: Suppose that you grasp the screw eye, give the IOLab a short pull to the right (positive direction) and release it. Describe in words the force vs. time graph. Prediction 2-2: Describe the velocity and acceleration vs. time graphs.

To test your predictions you will need:

Activity 2-1: Once a Pull, Always a Pull?

  1. Be sure that the force sensor has been calibrated.
  2. As always, zero the force sensor with nothing pulling on it just before graphing by clicking Rezero sensor.
  3. Click Record, grasp the screw eye, give the IOLab a very brief pull to the right and release it. After the IOLab has stopped moving, click Stop.

Question 2-1: Does the force vs. time graph agree with your prediction? If not, how do they differ? What happened to the force of the pull after you released the screw eye? After you released the screw eye is there still a force applied to the force sensor? Explain based on your force vs. time graph. Question 2-2: Describe the motion of the IOLab after it is released. Is it speeding up, moving with a constant speed or slowing down?

Activity 2-1: Once a Pull, Always a Pull?


Question 2-3: Do the velocity and acceleration vs. time graphs agree with your predictions? If not, how do they differ? How do they represent the motion described in Question 2-2? Question 2-4: Measure the average value of the acceleration during the time interval when the IOLab is slowing down. What is the value: Question 2-5: You know from Activity 1-1 that an object will slow down if the force applied to the object (and the acceleration) are in the opposite direction to the velocity. Once you release the IOLab, no force is applied to the force sensor. What force is causing the IOLab to slow down? What is its direction?

Activity 2-2: Net Force and Newton’s First Law



Is it possible to have the IOLab move at a constant velocity (zero acceleration) after it is pushed and released as shown in the figure above?


Prediction 2-3: Describe the direction and magnitude of the force you would need to apply so that the IOLab will continue to move with a constant velocity (zero acceleration) after it is given a brief push toward the right and released.

To test your prediction, in addition to the equipment in Activity 2-1 you will need:

Activity 2-2: Net Force and Newton’s First Law



  1. Set up the IOLab as shown.
  2. Use the paper and tape to fabricate a small “envelope” to hold the coins (weights). Attach the fishing line to the eye bolt of the IOLab and to this coin holder.

In this activity, you will give the IOLab a brief push to the right (instead of a pull as in Activity 2-1) and release it. The IOLab force sensor will measure the force applied to the IOLab by the fishing line. Your objective is to find the combination of coins (hanging mass) so that the IOLab moves with a constant velocity after it is pushed and released.

Activity 2-2: Net Force and Newton’s First Law


  1. Be sure that the force sensor has been calibrated, and also be sure to click Rezero sensor with nothing pulling on it before taking any measurements.
  2. Find the amount of mass in coins so that the IOLab just barely doesn’t move when the coins are hung over the edge of the smooth surface.
  3. Click Record and give the IOLab a brief push towards the right, and release. Let the IOLab move to the right for a few seconds, and then click Stop.
  4. Change the scale of the velocity vs. time graph if necessary to display it as clearly as possible.
Question 2-6: Is the velocity constant after the IOLab is released? How do you know?
  1. If the velocity is not constant, experiment by changing the hanging coins until you get a constant velocity graph.
  2. When you have a constant velocity graph, measure the average force and average acceleration over the time interval when the IOLab was moving after it was released.
Average acceleration: Average force:

Activity 2-2: Net Force and Newton’s First Law


Question 2-7: In Activity 2-1, the IOLab came to rest sometime after it was released because of the frictional force acting to the left. In this activity, the IOLab continues to move at a constant velocity. Why? What two forces are acting on the IOLab as it moves at a nearly constant velocity to the right?
Question 2-8: What can you say about the magnitudes of the frictional force (to the left) and the force applied by the fishing line (to the right)? What can you say about the magnitude of the net force acting on the IOLab? Explain.

Activity 2-2: Net Force and Newton’s First Law


Question 2-9: In the previous lab, you found that the force applied to an object is proportional to the acceleration of the object (Newton’s second law). In this activity, you found that the acceleration of the IOLab was nearly zero. What net force produces zero acceleration (results in motion of an object at a constant velocity)? (This is Newton’s first law.)
Question 2-10: State Newton’s first law in words in terms of the net force on an object that moves with a constant velocity.
Question 2-11: Based on your measurements, what is the magnitude of the frictional force? Explain how you found this value.

INVESTIGATION 3: FORCE, MASS, AND ACCELERATION


In the previous lab you applied different forces to an IOLab of fixed mass, and examined its motion (its acceleration). But when you apply a force to an object, you know that the object’s mass has a significant effect on its acceleration. For example, compare the different accelerations that would result if you pushed a 1000-kg (metric ton) automobile and a 1-kg cart, with the same force!

In this Investigation you will explore the mathematical relationship between acceleration and mass when you apply roughly the same constant force to objects of different mass.

You will need

Activity 3-1: Acceleration and Mass


You can easily change the mass of the IOLab by placing masses on top of it, and you can apply approximately the same force to the IOLab each time by using a piece of fishing line attached to the same hanging mass. By measuring the acceleration of different mass IOLabs, you can find a mathematical relationship between the acceleration of the IOLab and its mass, with the force applied by the fishing line kept nearly constant.

First a prediction.

Prediction 3-1: You apply a force to the IOLab and measure its acceleration. Now, you double the mass of the IOLab, and apply the same force to it. Predict what will happen to the acceleration.

Test your prediction.

Activity 3-1: Acceleration and Mass


In order to be able to double and triple the mass of the IOLab, you will need two masses that are equal to the IOLab’s mass. You can accomplish this by weighing the IOLab with its own force sensor, and then weighing other masses to find ones equal to that of the IOLab. Here’s a suggestion of how to do it.

  1. Be sure that the IOLab force sensor is calibrated.
  2. With the IOLab on the table with the screw eye pointed upward, zero the force sensor by clicking on Rezero sensor.

Activity 3-1: Acceleration and Mass

  1. Click Record, lift the IOLab by the screw eye, and record for a few seconds before clicking Stop.
  2. Measure the average value of the force while the IOLab was held above the table. This is the weight of the IOLab.
Average force (weight of IOLab):
  1. Hook the paper clip through the side of the cardboard box so that it can be hung from the IOLab screw eye.
  2. Hold the IOLab with the screw eye pointing down, and Rezero the force sensor.
  3. Hang the box from the screw eye, and add masses to the box until its weight is about the same as the IOLab (as measured in 4). Measure the average force.
  4. Alternatively, you can use the water bottle, by filling it with water, to make it have about the same weight as the IOLab. Use the other bottle to make it about twice the weight of the IOLab. Squeeze the air out while you screw on the caps. Tape the bottle to the IOLab. You will end up with something like in the image below.
Average force (weight of box with masses or a bottle with about 200 mL water in it):
  1. Repeat by adding masses to the plastic bag placed in the box until the weight of the box is about twice that of the IOLab. Measure the average force.
Average force (weight of box with coins plus plastic bag of masses or the other bottle with about 400 mL water in it):

Now your IOLab can have three different masses: (1) the IOLab alone, (2) 2X the IOLab: with the box of masses on top of it (without the plastic bag) and (3) 3X the IOLab: with the box of masses on top of it (including the plastic bag).

Activity 3-1: Acceleration and Mass



  1. Set up the IOLab and fishing line on the smooth surface, this time with the 60 g mass hanging from the fishing line.
  2. Zero the force sensor (Rezero sensor) with nothing pulling on it.
  3. Click Record, release the IOLab, and allow it to move across the surface for several seconds before stopping it and clicking Stop.
  4. Measure the average force and average acceleration during the time interval that the IOLab was accelerating across the surface. Write the values down to record them in the table when you move to the next slide.
  5. Place the box of equal mass to the IOLab on top of the IOLab, and repeat these measurements. Again write the values down, and record them in the table on the next slide.

Activity 3-1: Acceleration and Mass


Question 3-1: Did the acceleration agree with your prediction? Explain.
  1. Add the plastic bag of masses to the box on top of the IOLab or replace the bottle with the heavier one, and again repeat these measurements. Record the average values in the table.

Mass added to IOLab (in IOLab masses) Total mass of IOLab (in IOLab masses) Average force (N) Average acceleration (m/s2)
0 1
2
3

Activity 3-1: Acceleration and Mass


Question 3-2: Does the acceleration of the IOLab increase, decrease, or remain the same as the mass of the IOLab is increased?

Activity 3-2: Relationship Between Acceleration and Mass


  1. Use the graphical analysis software to plot a graph of average acceleration vs. IOLab mass (with constant force applied to the IOLab).
  2. Use the fit routine in the software to fit the data on your graph of average acceleration vs. mass of the IOLab. Select different linear and power relationships and test them.
  3. When you have found the best fit, save the graph along with the fit equation.

Comment: We are interested in the nature of the mathematical relationship between average acceleration and mass of the IOLab with the force applied to the IOLab kept constant. As always this can be determined from the graph by drawing a smooth curve which fits the plotted data points.

Some definitions of possible mathematical relationships when y decreases as x increases are shown in the sketches on the next slide. In these examples, y might be the average acceleration, and x the mass of the IOLab.

Activity 3-2: Relationship Between Acceleration and Mass



y is a linear function, which decreases linearly as x increases according to the mathematical relationship , where the slope m is a negative constant and b = const. y is a function of x, which decreases as x increases. The mathematical relationship might be , where n is an integer. When b = 0 and n = 1, the relationship becomes , and y is said to be inversely proportional to x.

Note that these are not all the same. y can decrease as x increases, and the relationship doesn’t have to be linear or inversely proportional. Inverse proportionality refers only to the special relationship where , where c is a constant. The graphical analysis software allows you to determine the relationship by trying various curves to see which best fits the plotted data.

Activity 3-2: Relationship Between Acceleration and Mass


Question 3-3: What appears to be the mathematical relationship between acceleration and mass of the IOLab, when the force applied to the IOLab is kept constant? Question 3-4: In Lab 4, you found that the acceleration of the IOLab was proportional to the force applied to the IOLab when the mass of the IOLab was not changed. State in words the general relationship between the net force, the mass, and the acceleration of the IOLab that you have found in these two labs. If the net force is , the mass is m, and the acceleration is , write a mathematical relationship that relates these three physical quantities.

ALL DONE!

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.


Copyright © 2018 John Wiley & Sons, Inc. and David Sokoloff, Erik Jensen, and Erik Bodegom.
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