The work done by a body on the application of a constant force is the product of the constant force and the distance travelled by the body in the direction of the force. Express this in the form of a linear equation in two variables (work w and distance d), and draw its graph by taking the constant force as 3 units. What is the work done when the distance travelled is 2 units? Verify it by plotting it on the graph.
Step-by-step solution
Idea: Work = constant force × distance. With force 3 this is w = 3d, a straight line through the origin with slope 3.
- Work = force × distance. With force 3 units: w = 3d, a linear equation in w and d.1 mark
- Table of values (distance cannot be negative, so take d ≥ 0):½ mark
d 0 1 2 4 w 0 3 6 12 - Plot (0, 0) and (4, 12) with d on the horizontal axis and w on the vertical axis, and join them (see the graph).1 mark
- d = 2: w = 3 × 2 = 6 units.½ mark
- Verify on the graph: go up from d = 2 to the line, then across to the w-axis: it reads 6. The point (2, 6) lies on the line ✓.1 mark
Check: The graph passes through the origin (no distance, no work) and rises 3 units of work for each unit of distance ✓.
Answer to write in the exam
Work = force × distance ⇒ w = 3d
d: 0, 1, 2, 4 → w: 0, 3, 6, 12
Graph of w = 3d drawn through (0, 0) and (4, 12)
d = 2: w = 3 × 2 = 6
∴ Work done = 6 units; (2, 6) lies on the graph
Common mistakes that cost marks
- Writing w = d + 3 (adding the force). Work is the product of force and distance.
- Putting w on the horizontal axis and reading the point as (6, 2).
- Drawing the line into negative distances without comment. Distance travelled is never negative, so the graph starts at the origin.
How this can come in the exam
If the constant force is 5 units, the work done in moving 7 units is
- 12 units
- 35 units
- 2 units
- 75 units
Show answer
(B) 35 units
w = 5 × 7 = 35.
A worker pushes a cart with a constant force of 4 units.
(i) Write the work w as a linear equation in the distance d. (ii) Find the work for d = 3. (iii) Find the distance for which the work is 26 units. (iv) Through which point do all such graphs pass, whatever the force?
Show answer
(i) w = 4d (1 mark). (ii) 12 units (1 mark). (iii) 4d = 26 ⇒ d = 6.5 units (1 mark). (iv) The origin (0, 0), since no distance means no work (1 mark).Try one yourself
Taking the constant force as 2.5 units, write the equation and find the work done for a distance of 8 units.
Show answer
w = 2.5d; w = 20 units.
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