Vector Activity

The purpose of this activity is provide the students with an opportunity to explore the relationships between vectors that add to zero. This activity has been written as a “cookbook” lab, where students are somewhat directed through the activity by the lab sheet. It can just as easily be used as a demonstration.

Vector Activity

Before becoming a teacher, Mr. Reed used to work at a sign hanging shop … the only problem is that every sign that he hung fell on the customers’ heads. The last advice Mr. Reed’s boss gave him before giving him the boot was “Boy, you better learn yourself some Fizzicks!”. So, after four years of Physics in college, Mr. Reed finally learned how to hang a sign. Today, you will learn the concepts involved in hanging a sign in less than an hour!

At your computer station, there are two force probes set-up to look similar to the following:

Each force probe measures the tension in the string that connects the probe to the washer holding the wood block. The ultimate goal of this lab is to determine the tension forces and their respective components for each condition defined by the cases 1 – 6. Before doing this, however, it is important to determine the weight of the wood block. This weight value as well as the rest of the data collected should be placed on another sheet of paper.

1. For each case (1-6), record the force values from each probe – these are the tension forces in each respective string. Also measure the angle of each tension force.

2. Then, determine the horizontal and vertical components of the tension forces in both strings for cases #1 through #6. Hint: you will need the angles of the forces to determine these components.

3. Create a table for each case listing the value of the tension force, the angle of the tension force, and the components of each tension force. Also include a diagram illustrating the direction and magnitude of these components.

Follow-up questions (write the answers to these in a conclusions paragraph on a separate sheet):

1. For each case, what is the relationship between the x-components of the tension forces? Explain.

2. For each case, what is the relationship between the y-components of the tension forces? Explain.

3. If you were to hang a sign using two strings, what would be the best set-up to ensure that neither string breaks? With this in mind, what would you guess was Mr. Reed’s problem when he was hanging signs so long ago.

Vector Activity – Teacher’s Notes

Prior to this activity, the following needs to be set-up at each lab station:

The right-side probe is connected to a piece of wood with numbers 1 – 6 labeled and a hook that corresponds to each number. The students will then hook their string to each number as they perform the lab. The set-up is best when #1 is directly above the mass (allowing for slack in the string in the left-side probe when hooked at #1), and when #3 or #4 forms a 90 degree angle between the left and right probes.

Once completing this activity, the students should discover the following:

· Since the block is not accelerating, the net force on the system is zero. The vector sum of both tension forces and the weight force should therefore equal zero. Said another way: the x-components of both tensions forces should be equal and in opposite directions; where as, the sum of the y-components of both tension forces should be equal in value to the weight force (the y-components of the tensions are in an opposite direction as the weight force).

· The tension force measured by the left probe will initially read zero because the right probe should be supporting all of the weight of the block in position #1. As the right probe is moved through the cases 2-6, the tension in the string on the left probe continually increases as the tension in the string on the right probe decreases at first (because the second string now helps support the block) and then increases (as the angle between the two probes continues to increase) as well. As the angle between the left and right probes increases, the overall tension forces in both strings increase (because they are effectively pulling each other with stronger x-components as the angle increases).

· To answer follow-up question #3, students should be able to come to the conclusion that the best arrangement is to have two strings vertically hanging that support the wood block. Mr. Reed probably set the sign up the signs such that the angle between the two strings was too large causing a greater tension force which caused the string to break. That’s why he needed to learn him some more “fizziks”.

A cool extension of this lab (actually a better use of the technology of force probes) would be to replace the hooked number support above the right force probe with a slider. If the support for the right probe is slid from 1 to 6 in a continuous motion, then the data collected would show the change in the total force in each string. Superimposing these two sets of data and their respective curves might prove to be interesting and insightful.