Net Work (Grade 12 NSC Matric Physical Sciences): Revision Notes
Net Work
What is net work?
When multiple forces act on an object at the same time, we need to consider the combined effect of all these forces. Net work is the total work done on an object when several forces are acting simultaneously.
Net work tells us about the overall energy transfer to or from an object. Even if multiple large forces are acting, the net work could be zero if some forces do positive work while others do negative work that cancels it out.
The concept of net work is fundamental because it connects forces to energy changes. Understanding how multiple forces combine their effects helps us predict whether an object will gain or lose energy overall.
Two approaches to calculating net work
There are two equivalent methods for calculating net work, and both will always give you the same answer.
Approach 1: Calculate individual forces then sum
This method involves calculating the work done by each force separately, then adding them together while being careful about signs.
Steps for Approach 1:
- Calculate the work done by each individual force using
- Take the signs into account (positive work increases energy, negative work decreases energy)
- Add all the individual work values together:
If one force does positive work and another does the same amount of negative work, they will cancel out completely. This is why understanding the direction of each force relative to motion is crucial.
Approach 2: Find resultant force first
This method involves finding the net force acting on the object first, then calculating work using that resultant force.
Steps for Approach 2:
- Add all the force vectors to find the resultant force:
- Calculate the work done using the resultant force:
- This approach is equivalent to Approach 1 but sometimes simpler to use
If the resultant force is parallel to the direction of motion, then and , making the calculation straightforward.
Worked examples
Worked Example 1: Using Approach 1
Question: A car is accelerating forwards. An applied force of 300 N acts forwards while friction of 100 N opposes the motion. The car travels 20 m forwards. Calculate the net work done.
Solution:
Step 1: Calculate work done by each force individually
Step 2: Add the individual work values
The positive answer shows that although energy was lost to friction, the total work done resulted in a net energy gain.
Worked Example 2: Using Approach 2
Question: Using the same scenario as above, calculate net work using the resultant force method.
Solution:
Step 1: Find the resultant force Taking forwards as positive direction:
Step 2: Calculate work using resultant force
This gives exactly the same answer as Approach 1, confirming both methods are equivalent.
Key considerations about signs and vectors
Understanding the relationship between force directions and work calculations is essential for solving problems correctly.
Important exam tips:
- Forces are vectors, but work is a scalar quantity
- The sign of work depends on whether the force helps or opposes motion
- Only force components parallel to the displacement do work
- Forces perpendicular to motion (like normal force) do zero work
- Always be consistent with your chosen positive direction
- When using vector addition, make sure to account for directions properly
Remember that work represents energy transfer. Forces doing positive work transfer energy to the object, while forces doing negative work remove energy from the object.
Key Points to Remember:
- Net work is the total work done when multiple forces act on an object simultaneously
- Two equivalent approaches: calculate individual works then sum, or find resultant force first then calculate work
- Signs matter: positive work increases energy, negative work decreases energy
- Both methods give identical answers when done correctly
- Only forces parallel to motion contribute to work - perpendicular forces do zero work