MATH - SCIENCE INTEGRATION

bullet1 UNITS OF WORK

bullet2 Calculating Work

"I did more work than you!"   "No way, I did more!"


bullet3 Work Equation

The equation to solve work problems looks like this:

work = force x distance  or   W = F x d
  • The SI unit for force is newton (N).
  • The SI unit for distance is meter (m).
  • The SI unit for work is joule (J).

Now let's look at the steps for calculating work.
If you need some review on calculating one step equations, click on the link below.




See also: Solving One Step Multiplication Equations

bullet3 Steps for Calculating Work

We will continue to use the same procedure to solve work problems as we have when working other physics problems.
 Remember to continue to work in a step by step manner by writing each step out.


Problem:  A fork lift moves 34m carrying a 1023N box across the warehouse floor. How much work is done by the fork lift.



Step 1:   Write down the equation needed to solve the problem.

W = F x d


Step 2:  Insert all known measurements into the equation.
W =
(1023N)(34m)


Step 3:  Solve.  Carefully enter numbers into your calculator.
W = 34,782 J
The forklift does 34,782J of work.
  • Make sure that all of your numbers have the correct SI unit label.
  • Always recheck your answers.

The next page will give you some sample problems with the answers.








bullet3 Sample Work Problem #1

Remember as you solve the following problems to keep following the steps shown on the previous page.


Problem #1:
How much work is done by a person who uses a force of 27.5N to move a grocery buggy 12.3m?



  • Equation
    W = F x d = (27.5N) (12.3m) =  ?



     
    • Answer
      W =  338.25J

      Did you get it correct?  Try another one!



       

bullet3 Sample Work Problem #2

Problem #2:
55, 000J of work is done to move a rock 25m. How much force was applied?


Many work problems give you the amount of work done, but want you to solve for distance or force.  

In that case the work formula can be rearranged to look for the other variables.  In this problem, we are looking for force, so the equation must be rearranged.


  • Equation
    F =  W  =  55,000J  =  ?
            d           25m



     
    • Answer
      F = 2200J

      Think you're pretty good at this?  Work one more sample problem before you complete the practice problems.



       

bullet3 Sample Work Problem #3

Let's try a problem where distance is the unknown.
Problem #3:
You and 3 friends apply a combined force of 489.5N to push a piano.  The amount of work done is 1762.2J.  What distance did the piano move?



  • Equation
    You need to rearrange the work formula to look for distance:
    d=  W  = 1762.2J  =
           F      489.5N



     
    • Answer
      d = 3.6m

      You've worked through all of the sample problems, now you need to try out your skills on the practice problems.  Good Luck!



       

bullet3 Practice Problems

Get your paper, pencil, and calculator ready for some work practice problems!  Make sure to label all numbers with SI units and show all of your work.

Practice Problems:
1.  Calculate the amount of work done when moving a 567N crate a distance of 20 meters.

2.  A fallen tree is lifted 2.75 meters.  How much work is done?

3.  If it took a bulldozer 567.6 joules of work to push a mound of dirt 30.5 meters, how much force did the bulldozer have to apply?

4.  A frontend loader needed to apply 137 newtons of force to lift a rock.  A total of 223 joules of work was done.  How far was the rock lifted?

5.  A young boy applied a force of 2,550 newtons on his St. Bernard dog who is sitting on the boy's tennis shoes.  He was unable to move the dog.  How much work did he do trying to push the dog?

6.  If it takes 68 joules of work to push a desk chair across a floor, what force would be needed?

7.  If a long distance runner with a weight of 596.82 newtons does 35,674.7 joules of work during a portion of a race, what distance will she cover during that portion?

8.  If a weight lifter raises a barbell with a mass of 125.7 grams doing 5,023 joules of work, what distance did he move the barbells?   Remember that you need a force, not a mass.  You must first calculate the force in order to complete your solution. HINT: Weight is a force.  Weight on earth is determined by multiplying an object's mass times earth's gravitational pull (9.8m/s2   ).

9.  Children are sled riding on a hill.  One little girl pulls her sled back up the hill and does 379.5 joules of work while pulling it back up the 17.3 meter hill.  What amount of force did she exert on the sled?

10.  A large semi-truck is moving a house from one lot to another. The amount of force required to move the house horizontally a distance of 73.2 meters is 3,500 newtons. How much work will be done on the house?