Experimenting with Force Vectors

Size: px

Start display at page:

Download "Experimenting with Force Vectors"

Linette Johnston
6 years ago
Views:

1 Name Hr: Date: Experimenting with Force Vectors Purpose/Goals Apply the laws of vector addition to resolve forces in equilibrium. (Part 1) Determine the equilibrant necessary to balance a resulting force. (Part 2) Evaluate experimental error. Background Describing Vectors A vector is a quantity which has both magnitude and direction. Examples of vectors include displacement, velocity, acceleration, and force. To fully describe one of these vector quantities, it is necessary to tell both the magnitude and the direction. For instance, if the velocity of an object were said to be 25 m/s, then the description of the object's velocity is incomplete; the object could be moving 25 m/s south, or 25 m/s north, or 25 m/s southeast. To fully describe the object's velocity, both magnitude (25 m/s) and direction (e.g., south) must be stated. In order for such descriptions of vector quantities to be useful, it is important that everyone agree upon how the direction of an object is described. The convention upon which we can all agree is sometimes referred to as the CCW convention - "counter-clockwise" convention. Using this convention, we can describe the direction of any vector in terms of its counter-clockwise angle of rotation from due east. The direction north would be at 90 degrees since a vector pointing east would have to be rotated 90 degrees in the counter-clockwise direction in order to point north. The direction of west would be at 180 degrees since a vector pointing west would have to be rotated 180 degrees in the counter-clockwise direction in order to point west. One method of Adding Vectors Vectors are quantities which include a direction. As such, the addition of two or more vectors must take into account that the quantities being added have a directional characteristic. There are a number of methods for carrying out the addition of two (or more) vectors. The most common method is the "head-to-tail" method of vector addition. Using such a method, the first vector is drawn to scale in the appropriate direction. The second vector is then drawn such that its "tail" is positioned at the "head" (vector arrow) of the first vector. The sum of two such vectors is then represented by a third vector which stretches from the tail of the first vector to the head of the second vector. This third vector is known as the "resultant" - it is the result of adding the two vectors. The resultant is the vector sum of the two individual vectors. Of course, the actual magnitude and direction of the resultant is dependent upon the direction which the two individual vectors have. An Example to Test Your Understanding A pack of five Arctic wolves are exerting five different forces upon the carcass of a 500-kg dead polar bear. A top view showing the magnitude and direction of each of the five individual forces is shown in the diagram at the right. The counterclockwise convention is used to indicate the direction of each force vector. Remember that this is a top view of the situation and as such does not depict the gravitational and normal forces (since they would be perpendicular to the plane of your paper); it can be assumed that the gravitational and normal forces balance each other.

2 With your lab partner(s) - 1. Use a scaled vector diagram to determine the net force acting upon the polar bear. 2. Then compute the acceleration of the polar bear (both magnitude and direction). The task of determining the vector sum of all the forces for the polar bear problem involves constructing an accurately drawn scaled vector diagram in which all five forces are added head-totail. The following five forces must be added. Use your protractor to trace these vectors head-to-tail onto the paper provided to construct your scaled vector diagram. To find the resultant, draw a line connecting the base of the first vector with the head of the last vector. Measure it's angle for direction and it's length for magnitude. Then compute the Polar Bear's acceleration given it's mass and the force acting upon it. See next page for workspace for the Polar Bear problem.

3 Use this page to answer the polar bear problem. (Group Work) Construct your scaled diagram below using the head-to-tail method of vector addition. Net Force = Direction = (in degrees from due east) Compute the acceleration of the bear carcass. Acceleration = After your group is in agreement about the solution to this problem, check your answer with another group or with Mr. G then proceed to the next part of the lab - force table problems.

4 Answer to Polar Bear Problem Acceleration = Force/Mass = 39.4 N/500 kg = m/s/s

Using the Force Board. A force board (or force table) is a common physics lab apparatus that has three (or more) chains or cables attached to a center ring.

5 Using the Force Board. A force board (or force table) is a common physics lab apparatus that has three (or more) chains or cables attached to a center ring. The chains or cables exert forces upon the center ring in three different directions. Typically the experimenter adjusts the direction of the three forces, makes measurements of the amount of force in each direction, and determines the vector sum of three forces. Part 1. (Group work) 1. Place a piece of paper on the force board below and secure it with one or more of the clips. 2. Set up the apparatus as shown in the diagram attaching three spring scales to the force table so that each scale registers a force at approximately mid-range. The scales can be placed at any angle. 3. Using a sharp pencil, mark several points along the line of action of each force. Also mark the middle of the central ring. 4. Record the force of each spring scale next to it's corresponding line of action. (see Figure a.) 5. Disconnect the spring scales and remove the paper from the force table. Repeat steps 1-5 so that each lab partner has a set of data to analyze. Independent Work 6. Using the points you drew on the paper, construct lines A, B, and C, representing the three different lines of force that were acting on the ring. 7. Convert your lines to vectors by adding a suitable number scale to each line such as 1 N = 1 cm. (see Figure b.) 8. Add vector A to vector B by using the head-to-tail method. (see Figure c). 9. Draw a vector representing the vector sum of A + B, the resultant. Part 1 - Analysis (Independent Work) 1. Compute the resultant A + B using the number scale you selected. 2. a. Compare the magnitude and direction of the computed resultant force A + B with the measured or known magnitude of force C. b. Explain your findings. c. Calculate the relative error in the magnitudes using force C as the reference value.

6 Part 1 - Analysis continued 3. a. Use the head-to-tail method to add vectors A, B and C. Do this by placing this page over your first diagram and tracing the vectors in order. Label your vectors. b. What is the resultant of the three vectors? c. How does this resultant make sense? 4. Now add your three vectors in the order C + B + A. What result do you obtain? (Group Work) Compare your analysis with that of your group members before moving on to part 2

7 Part 2. (Independent Work) 1. a. Using graph paper and a protractor, draw two force vectors acting on the same point. Vector A is 5 N at an angle of 0 degrees. Vector B is 10 N at an angle of 120 degrees. b. Draw a resultant force vector R on your diagram. 3. The equilibrant force is the force required to balance the resultant net force. It is equal in magnitude and opposite in direction to the resultant. Add the equilibrant vector E to your diagram. Record in newtons the force that will be required for the equilibrant to balance out the resultant. Compare your drawings with those of your lab partners. (Group Work) 4. Now place a vector diagram from your group on the force table. Set up spring scales for vectors A and B. The spring scales should be anchored in slots on the force board that correspond to the angle of the vector they represent on your diagram. (0 degrees and 120 degrees). 5. Now place the third spring scale onto the slot which corresponds to the equilibrant angle and pull it until it brings scale A and B into line with your diagram. Record the newtons required to balance the resultant force by the equilibrant scale on the diagram. Show your group's final setup to Mr. G before disassembling the force Table.

8 Analysis part 2 (Independent work) 1. Calculate your percent error in part 2 using vector R on your diagram as the expected value. 2. Other than "human error", what do you consider to be some of the major sources of error in this experiment? 3. Which source listed in the previous question is, in your opinion, the largest contributor to error? How could it be eliminated or at least minimized?

VECTORS & EQUILIBRIUM Experiment 4

Physical Science 14 VECTORS & EQUILIBRIUM Experiment 4 INTRODUCTION: Pictures are often more descriptive than words. In physics it is useful to represent some quantities by an arrow, called vector, where