Mass Part III. In the front of the room is a large spring balance of the type you may have seen before.

Transcription

1 Mass Part III The spring balance (also known as the spring scale) In the front of the room is a large spring balance of the type you may have seen before. 1) Why is this device called a spring balance? What quantities are being balanced? 2) Imagine that you were given a spring and asked to calibrate (yes there s that word again) it so that it could be used to measure mass. Write down a detailed procedure for calibration below. 1

2 The Equi-arm balance The equi-arm balance consists of a beam supported at the center with two identical pans suspended at the same distance from the support. The support point is called the pivot, because the beam can rotate about it. You may have seen such a balance in action at a grocery store, a jeweler s store, or at a chemist s. If you put identical objects, one in each pan, the beam balances and we say that the two objects have identical mass. 1) Will the equi-arm balance work on the moon? Explain. 2) Will it work in a space-ship under weightless conditions? Explain. Balancing masses a detailed look Your instructors should have available for you the following equipment - a wooden stand with a nail to serve as a pivot, a peg board to serve as the beam for your balance and several identical nuts, and paper-clips. Below is a picture of the peg board with labels that will help you understand instructions on the following pages Top Row Bottom Row L R L denotes left of the pivot, and R denotes right of the pivot point. 2

3 First, place the beam on the wooden-stand so that it is pivoted at hole-0. 3) Is the beam balanced? After you have discussed this with your partners, your instructors will lead a discussion. Write down what you learned from this discussion below. 4) Next using a paper-clip, hang one nut on the 8 th hole from the center on the left (hence forth called L8) and two nuts using one paper-clip on the 8 th hole on the right (R8). Is the beam balanced? Now that we know what balance is, let us do some more investigations by loading the beam (or lever) with masses at various points. Please indicate your prediction (and the result of your measurement) with a "YES" for balance and a "NO" for will not balance. You must predict, before you place the nuts on the beam. For your prediction, it is alright to say, don t know. Mass Combination* Prediction Observational Result One into L6 One into R6 One into L8 One into R4 Three into L1 One into L3 *One on L8 means one nut in the eighth hole to the left of the pivot. One on R4 means one nut in the fourth hole to the right of the pivot hole. Q: Do you see a pattern i.e. a number formed by the hole-number and the number of nuts that gives a balanced beam? Talk with your partners about this. Once your group has decided on an answer, predict how many nuts, and where you will hang them from to make the following arrangement balance: One on L8. There are many possibilities, but you should be able to come up with at least four. Make up 3-4 of your own combinations that you think will balance. Write them down and try them out. 3

4 Now try out these slightly more complicated ones and see which combinations balance. You could try predicting, but you don t have to. Note that the combination on the left is fixed for this exercise. Mass Combination Prediction Result One into L6, One into L8 One into R6, One into R8 One into L6, One into L8 Two into R4, One into R6 One into L6, One into L8 Two into R3, One into R8 Can you find a pattern - i.e. a number formed by the hole-number and the number of nuts that gives a balanced beam in this case? After you discuss this with your group and have an answer, find one more combination that will balance: One into L6, One into L8 Try another definition of mass and then check with an instructor: 4

5 End of Module Questions: 1. In ancient Mediterranean cultures, coins were made out of pure metal and the value of a coin was determined by the mass of the metal used to make the coin. Once upon a time, three merchants from different cultures met to buy and sell goods. Merchant #1 had a pocket full of Nara coins, Merchant #2 had a pocket full of Filsa coins, and Merchant #3 had a pocketful of Mac coins. The first thing they needed to do was figure out how many Nara in a Filsa, how many Filsa in a Mac, and so on. a) Explain in words (and pictures if you like) how the three merchants could have determined the relative values of their coins using only a few sticks, some cloth, and some string. b) It turns out that four Filsas have the same mass as one Mac. Three Macs have the same mass as two Naras. i) How many Filsa would have the same value as 1 Nara? (Show your work) ii) Hoping that Merchant #3 didn't pass IDS 101, Merchant #2 decides to try and fool her. He quickly demonstrates that he can balance one Mac with one Filsa. How did he do it and where did he have to hang the two coins to pull of his trick? 2. The following questions all refer to a set of experiments with the balance shown below. A meter stick is balanced on a pivot point. Four pieces of aluminum metal are then placed 22 cm from the balance point. Each piece of aluminum has dimensions of 1 cm x 1 cm by 1 cm. 22 cm a. If you remove just one of the four pieces of aluminum, where will you have to place it on the other side to balance the remaining three pieces? Show your work or explain your reasoning. b. Next you are going to try balancing all four pieces of aluminum (in the original position shown in the diagram) with one piece of lead. Lead is 4 times as dense as aluminum. If you use a 1 cm x 1cm x 1 cm piece of lead, where will you have to place the lead to balance the four pieces of aluminum? Show your work or explain your reasoning. 5

6 If you use three of pieces of lead, where will they need to be placed in order to balance the four pieces of aluminum (in their original position)? Show your work or explain your reasoning. Finally, imagine repeating the experiment with a 2 cm x 2 cm x 2 cm piece of lead. Where should this piece of lead be placed in order to balance the four pieces of aluminum? Show your work or explain your reasoning. 3. Consider the lever shown below. If there are no weights on the lever it will be perfectly balanced on the fulcrum shown in the center. A B a) Block B has the same width and thickness as block A, but block B is twice as tall. The lever balances when blocks A and B are the same distance from the center. How does the density of block B compare to the density of block A? (Be quantitative and explain your reasoning.) 6

7 b) The two blocks labeled C in the diagram below have masses of 30 g each. The lever is balanced when one block C is 20 cm from the center and the other block C rests on block D 5 cm from the center. What is the mass of block D? (Be quantitative and explain your reasoning and/or show your work.) C C D c) Two identical 12 g blocks are placed on the lever, 20 cm and 25 cm from the center. Where would one have to place a single 60 g block to balance the lever? (Be quantitative and explain your reasoning and/or show your work 60 g 12 g 12 g? 7