Question 45 of 49advanced🔧 ApplyLong Answer5 marks

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 ww and distance dd), 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.

Correct Answer

Based on the given statement, work done is the product of the constant force and the distance travelled. This gives us the relation:

Work=Force×Distance\text{Work} = \text{Force} \times \text{Distance}

Expressing this as a linear equation in two variables (ww and dd), we write:

w=f×dw = f \times d

where ff is the constant force.

Given the constant force is 3 units, we substitute f=3f = 3 into the equation. This yields the specific linear equation:

w=3dw = 3d

To draw the graph of this equation, we need to identify at least two points on the line. When d=0d = 0, w=0w = 0, giving the point (0,0)(0, 0). When d=1d = 1, w=3w = 3, giving the point (1,3)(1, 3).

To find the work done when the distance travelled is 2 units, we substitute d=2d = 2 into our equation.

Calculation:

w=3×2=6w = 3 \times 2 = 6

Therefore, the work done is 6 units.

For verification by plotting, we locate the point corresponding to d=2d = 2 and w=6w = 6 on the graph, which is the coordinate (2,6)(2, 6). We observe that this point lies exactly on the straight line drawn through (0,0)(0, 0) and (1,3)(1, 3), confirming our calculated value.

Exercise: END-OF-CHAPTER EXERCISES | Q: 9 | (Page 22)
For More Understanding

Explanation

The question requires forming a linear equation from a real-world statement and then graphing it. The context provides the formula for work done as the product of force and distance, leading to w=fdw = fd. Substituting f=3f = 3 gives w=3dw = 3d, which is analogous to the y=3xy = 3x example found in the context.

The context also explains that plotting a linear equation requires identifying two points, such as (0,0)(0, 0) and (1,3)(1, 3). Finally, calculating work for d=2d = 2 gives w=6w = 6, and plotting (2,6)(2, 6) verifies it lies on the line.

Solution Steps

  1. Step 1: Formulate the equation based on the statement: Work=Force×Distance\text{Work} = \text{Force} \times \text{Distance}, so w=f×dw = f \times d.

  2. Step 2: Substitute the constant force (f=3f = 3) into the equation to get the linear equation: w=3dw = 3d.

  3. Step 3: Find two points to plot the graph. For d=0d = 0, w=0→(0,0)w = 0 \rightarrow (0, 0). For d=1d = 1, w=3→(1,3)w = 3 \rightarrow (1, 3).

  4. Step 4: Calculate work done for d=2d = 2 units: w=3×2=6w = 3 \times 2 = 6 units.

  5. Step 5: Verify by checking that the point (2,6)(2, 6) lies on the plotted straight line.

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