1 00:00:00,000 --> 00:00:05,000 How is algebra used to find a solution? 2 00:00:05,000 --> 00:00:08,000 How are arrays used in algebra? 3 00:00:08,000 --> 00:00:14,000 What algebraic equation shows that voltage is related to current? 4 00:00:14,000 --> 00:00:18,000 Hey guys, meet Leslie Curtis. She's an engineer here at NASA Marshall. 5 00:00:18,000 --> 00:00:21,000 Thanks, Van. Dr. Gilchrist is right. 6 00:00:21,000 --> 00:00:25,000 Mathematics is one of the most powerful tools that we have available to us at NASA. 7 00:00:25,000 --> 00:00:29,000 We use algebra almost every day to find solutions to our problems. 8 00:00:29,000 --> 00:00:32,000 This is the Icarus satellite that Jane told us about. 9 00:00:32,000 --> 00:00:35,000 It uses solar cells to charge its batteries. 10 00:00:35,000 --> 00:00:41,000 Solar cells, which convert sunlight into electricity, are arranged in a pattern called an array. 11 00:00:41,000 --> 00:00:47,000 One of the ways that equations can be written in algebra is also called an array or matrix. 12 00:00:47,000 --> 00:00:51,000 Actually, they look a lot alike. Let's compare them. 13 00:00:51,000 --> 00:00:57,000 Here's an example of an array used in algebra. Notice the pattern of rows and columns. 14 00:00:57,000 --> 00:01:02,000 Now here's a picture of a solar array. See the rows and columns again? 15 00:01:02,000 --> 00:01:10,000 Let's use the solar arrays on the Icarus satellite to do a simple math problem that the students at the University of Michigan were faced with. 16 00:01:10,000 --> 00:01:13,000 Then let's compare solar arrays with algebraic arrays. 17 00:01:13,000 --> 00:01:19,000 The Icarus satellite uses 12-volt batteries. Voltage is a measurement of electricity. 18 00:01:19,000 --> 00:01:24,000 And if we use a solar array to charge our batteries, we know from science that we need to have a solar array voltage 19 00:01:24,000 --> 00:01:29,000 that is slightly higher than the 12-volt batteries, so let's say 15 volts. 20 00:01:29,000 --> 00:01:34,000 To calculate the number of solar cells we need for the array, we use algebra. 21 00:01:34,000 --> 00:01:40,000 And since each Icarus solar cell provides 0.5 or a half a volt of charge, 22 00:01:40,000 --> 00:01:44,000 how many cells do we need for our solar array to produce the 15 volts? 23 00:01:44,000 --> 00:01:47,000 If we solve for C, which stands for the number of cells, 24 00:01:47,000 --> 00:01:53,000 we see that it will take 30 cells to give us 15 volts to successfully charge the batteries. 25 00:01:53,000 --> 00:01:58,000 From this information, we can arrange our solar cells in a solar array pattern. 26 00:01:58,000 --> 00:02:01,000 Cool! Like 10 cells wide by 3 cells high? 27 00:02:01,000 --> 00:02:04,000 Or 15 cells wide by 2 cells high. 28 00:02:04,000 --> 00:02:08,000 So you see, when scientists are trying to calculate complicated equations, 29 00:02:08,000 --> 00:02:11,000 we often write them in the pattern of an algebraic array. 30 00:02:11,000 --> 00:02:17,000 That's great! So you use patterns and algebra to determine the amount of solar cells in an array. 31 00:02:17,000 --> 00:02:24,000 But let me ask you this. How long does it take for solar cells to charge Icarus's batteries? 32 00:02:24,000 --> 00:02:27,000 Well, that question can be answered using algebra also. 33 00:02:27,000 --> 00:02:32,000 We know that the charge on the Icarus satellite batteries is related to current and time. 34 00:02:32,000 --> 00:02:38,000 Current is another measure of electricity, which is expressed in units called amperes, or amps for short. 35 00:02:38,000 --> 00:02:43,000 Now, to calculate the amount of time needed to charge the batteries, we use the following equation. 36 00:02:44,000 --> 00:02:47,000 Charge is equal to current times time. 37 00:02:47,000 --> 00:02:51,000 Since we want to know the length of time needed to charge the batteries, 38 00:02:51,000 --> 00:02:56,000 we can rewrite the equation as time is equal to charge divided by current. 39 00:02:56,000 --> 00:03:02,000 The Icarus satellite batteries have a maximum charge capacity of 2.5 amp hours. 40 00:03:02,000 --> 00:03:08,000 A typical charging current that we might use to charge the system is 0.5 amps. 41 00:03:08,000 --> 00:03:16,000 So if the charge is 2.5 amp hours and the current is 0.5 amps, the equation can be written this way. 42 00:03:16,000 --> 00:03:22,000 Time is equal to 2.5 amp hours divided by 0.5 amps. 43 00:03:22,000 --> 00:03:29,000 Solving for time, we can see that the time required to reach full charge on the system is 5 hours. 44 00:03:29,000 --> 00:03:31,000 Okay, let me see if I got this straight. 45 00:03:31,000 --> 00:03:36,000 We use voltage as a way of measuring electricity when we're talking about the solar array, 46 00:03:36,000 --> 00:03:43,000 and current to describe electricity when we're calculating the time it takes to recharge the batteries. 47 00:03:43,000 --> 00:03:46,000 But how are voltage and current related? 48 00:03:46,000 --> 00:03:51,000 Voltage and current are related by the simple equation V equals IR. 49 00:03:51,000 --> 00:03:55,000 V stands for voltage, which is usually measured in volts. 50 00:03:55,000 --> 00:03:58,000 I is the current, which is usually measured in amps. 51 00:03:58,000 --> 00:04:00,000 And R is called the resistance. 52 00:04:00,000 --> 00:04:03,000 The resistance is measured in units called ohms. 53 00:04:03,000 --> 00:04:10,000 And the equation V equals IR is actually called Ohm's Law after G.S. Ohm, a German scientist. 54 00:04:10,000 --> 00:04:13,000 And the unit of resistance was named in his honor. 55 00:04:13,000 --> 00:04:17,000 You just wouldn't believe the resistance I got. 56 00:04:17,000 --> 00:04:19,000 Shocking. 57 00:04:19,000 --> 00:04:26,000 You know, I think it's pretty sweet that the university students used algebra to work with NASA on the ProSense experiment. 58 00:04:26,000 --> 00:04:31,000 But I don't really get the volts and amps and resistance. 59 00:04:31,000 --> 00:04:32,000 Oh my. 60 00:04:32,000 --> 00:04:34,000 Volts and amps and resistance. 61 00:04:34,000 --> 00:04:35,000 Oh my. 62 00:04:35,000 --> 00:04:36,000 I get it, Dorothy. 63 00:04:36,000 --> 00:04:37,000 I get it. 64 00:04:37,000 --> 00:04:39,000 I just couldn't resist. 65 00:04:39,000 --> 00:04:46,000 Nor could we resist the chance to meet some students who teamed up with NASA Connect and are wired for today's web activity.