Name: _____________________ Period: _____________________ Unit 6:S1 How to Solve Word Problems Variable Sheet Step 1: Use the Variable Sheet to Assign Variables The units tell you what variable to use. Variable Units Variable Name Problem: A spring pulls with 30 N on a 6 kg metal cart. Find the acceleration that occurs. d m (meters) distance v m/s velocity t sec time F = 30 N m = 6 kg a = ____ Always assign variables here! This is your unknown. It MUST be included in your variables! Make sure your variables are in STANDARD UNITS (convert centimeters to meters, for instance). Most equations will only work with standard units! a m/s F N (newtons) force m kg mass p kgm/s momentum W J (joules) work Find an equation that contains all the variables in your variable list INCLUDING your unknown. Equations Equations d t v f − vi W = Fd v= Problem: A spring pulls with 30 N on a 6 kg metal cart. Find the acceleration that occurs. F = ma acceleration Equation Sheet Step 2: Use the Equation Sheet to Select a Formula. F = 30 N m = 6 kg a = ____ 2 a= ALWAYS put your formula here: WITHOUT NUMBERS! P= t F = ma W t PE = mgh p = mv KE = 1 mv 2 2 Step 3: Put in the Numbers and Do the Math. (See “Algebra Help”, if you need help with the math.) Sometimes it is easier to solve for the unknown BEFORE putting in the numbers. Problem: A spring pulls with 30 N on a 6 kg metal cart. Find the acceleration that occurs. F = 30 N m = 6 kg a = ____ F = ma 30 = 6a 30 6a = 6 6 a=5 Big Hint Variable Sheet Step 4: Make Sure the Answer Has the Correct Units. In science, the answer is not completely correct without units. Problem: A spring pulls with 30 N on a 6 kg metal cart. Find the acceleration that occurs. F = 30 N m = 6 kg a = 5 m/s2 F = ma 30 = 6a 30 6a = 6 6 a = 5 m/ s2 The chart shows that acceleration has the units of m/s2. Put your answer back in your variable list, where it will be easy to find if you need it for another problem or step. cstephenmurray.com Variable Units Variable Name d m (meters) distance v m/s velocity t sec time 2 a m/s F N (newtons) force m kg mass p kgm/s momentum W J (joules) work Legal copying of this worksheet requires written permission. acceleration Copyright © 2008, C. Stephen Murray Name: _____________________ Unit 6:S1 Period: _____________________ How To Do the Algebra Addition and subtraction are notated the same in physics equations as in basic mathematics, but not so for multiplication or division. Notation Two letters or numbers next to each other show multiplication. F = ma = m x a A letter below another letter means division. Correct, but confusing Still correct, but less confusing 2 PE = (25)(10)(5) PE = (25kg )(10m/s )(5m ) Equations are Equal Not Equal d = d ÷t t Use units to assign variables and to be sure you are using standard units (meters instead of centimeters, for instance), then put in just the numbers—no units! Make sure, though, to put the units back on the answer at the end. Do Not Keep Units Equal v= The equal sign means that both sides are equal. Therefore, anything done to one side must be done to the other or the equation is no longer equal. 35 = v f − 10 35 = v f − 10 + 10 Equal 35 = vf −10 Still Equal 35 +10 = vf −10 +10 The following shows only the four most common algebraic operations. There are many more. They will be presented to you as necessary. The Algebra Division Moves Multiplication Multiplication Moves Division Variables Numbers Variables Numbers F = ma F ma = m m F =a m 35 = 7a W t W Pt = t t Pt = W W 3 W 12(3) = 3 3 36 J = W 35 7 a = 7 7 5m/s 2 = a Subtraction Moves Addition P= 12 = Addition Moves Subtraction Variables Numbers Variables Numbers Fnet = F1 + F2 15 = F1 + 6 ∆V = V f − Vi 24 = V f − 8 Fnet − F2 = F1 + F2 − F2 15 − 6 = F1 + 6 − 6 ∆V + Vi = V f − Vi + Vi 24 + 8 = V f − 8 + 8 Fnet − F2 = F1 9 N = F1 ∆V + Vi = V f 32m/s = V f “Please Excuse My Dear Aunt Sally” will help you remember you order of operations: Parenthesis; Exponents; Multiply; Divide; Add; Subtract. Order Matters! Correct Incorrect 2(4 − 2) + 3 = 2(2) + 3 = 4 + 3 = 7 2(4 − 2) + 3 = 2(2) + 3 = 2(5) = 10 cstephenmurray.com Legal copying of this worksheet requires written permission. Copyright © 2008, C. Stephen Murray Name: _____________________ Period: _____________________ A bike moves 30 m in 5 seconds. Calculate the speed of the bike. Variables: Unit 6:S2 Practice with Word Problems A car starts at rest. After 4 seconds it is going 24 m/s. What was the car’s acceleration? Solve: Variables: Equation: Solve: Equation: A 12 N force pushes on a 3 kg object. Find the object’s acceleration. Variables: A 10 N force pushes for 3 m. How much work was done on the object? Solve: Variables: Equation: Solve: Equation: Using the same procedure as above, solve the following word problems. Challenge problems: A person walks 240 meters at 3 m/s. How long did it take? A bike goes 10 m/s for 20 seconds. Calculate how far the bike traveled. A 2 kg object is moving 12 m/s. How much momentum does the object have? Grandma lives 120 miles away. Dinner is at 5 p.m. The speed limit is 60 mph. What time do you need to leave to be on time? If a person pushes with 3 N and does 18 J of work. How far did they push the object? Position vs. Time 50 45 40 0:00.0 Constant Speed Position (m) 0:04.0 35 30 25 20 15 10 5 0 0 2 4 6 8 10 12 14 16 18 20 Tim e (sec) How fast is Nigel moving, if he is at constant speed? Find the slope of the graph (including units). cstephenmurray.com Legal copying of this worksheet requires written permission. Copyright © 2008, C. Stephen Murray Name: _____________________ Period: _____________________ cstephenmurray.com Legal copying of this worksheet requires written permission. Copyright © 2008, C. Stephen Murray