How to Solve Work Problems

Two Methods:Approaching a ProblemSolving an Example

Work in physics is the measurement of the result of transferring energy from one system to another to cause an object to move. Work is commonly used to described activities in which there is force and displacement along the line of the force exerted. For example, a man standing with a briefcase actually does no work if he is merely standing and holding his briefcase. However, the moment he picks his briefcase from the floor and rises to his standing position, he performed work. When a force, "F", moves in the course of displacement (or distance), "s", this is called work, "W". Therefore, W = F • s.

Method 1
Approaching a Problem

  1. Image titled Solve Work Problems Step 1
    Determine what type of units the given is measured in. Before attempting any calculations, make sure to understand if the given (a number provided in the problem) is referring to force (a push or pull upon an object resulting from the object's interaction with another object), displacement (how far out place the object is), or work (when a force acts upon an object to cause a displacement of the object).
    • When the units of the given are Newtons, dynes, or pounds, the given is a measurement of force.
    • When the units of the given are meters, centimeters, or feet, the given is a measurement of displacement.
    • Lastly, if the unit is given as a joule, erg, or foot-pound, then it is a measurement of work.
    • The equation for work is: W = F • s.
  2. Image titled Solve Work Problems Step 2
    Analyze the problem to begin solving it. Once you have established the classification of the given, you can analyze the problem.
    • Write out the formula for work (W = F • s) and plug in your givens.
    • Determine if there are any additional givens provided by the problem, and input them.
    • Then, you can figure out how to find the other missing numbers.
    • Once the numbers are found, you can solve for what you are looking for.
  3. Image titled Solve Work Problems Step 3
    Know that you must alter the work equation if the displacement is not a straight line. The equation W = F(s) assumes that force and displacement travel in a straight line together.
    • If the displacement has a different direction from the force, then the equation is W = F • s • cos(theta).
    • When solving work problems, theta is the angle between the force and the displacement which it causes. For example:
      • If the force goes in the same direction as the displacement, then the angle is 0 degrees.
      • If the force is in the opposite direction as the displacement, then the angle is 180 degrees.
      • If the force is up and the displacement is to the right, then the angle is 90 degrees.

Method 2
Solving an Example

  1. Image titled Solve Work Problems Step 4
    Practice finding the givens in a problem. Using a practice problem, find the givens and see how you can incorporate them into the equation.
    • For example, find the givens in the problem: "What work is performed by dragging a sled 50 feet (15.2 m) horizontally without acceleration when the force of 60lbs, is transmitted by a rope at an angle of 300 degrees with the ground."
  2. Image titled Solve Work Problems Step 5
    Find the given for displacement. We are given 50 feet (15.2 m) horizontal displacement without acceleration.
    • This means the sled moved 50 feet (15.2 m) after work was performed.
    • So, you now have s = 50 feet (15.2 m).
    • Next, the problem says that the force that displaced the sled was 60 lbs, meaning the force exerted was 60 lbs.
    • You now know that f= 60lb at 30 degrees with the ground.
  3. Image titled Solve Work Problems Step 6
    Use these givens to fill in the equation for work. Now, analyze what you are being asked to look for, based on the givens.
    • Based on the question, you know you need to find the value of work.
    • You know that the formula for determining the value of work is: W = F • s • cos(theta).
  4. Image titled Solve Work Problems Step 7
    Solve the equation. Use the givens you plugged in to continue solving and find the value of work.
    • W = 60 (cos30) (50)
    • W = 60lbs (0.866) (50)
    • W = 2.6x10^3ft-lb
    • Therefore, work is equal to 2.6x10^3ft-lb.

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