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Physics Chapter 7 : Topic 6
Work from Force–Extension Graph
1 / 40
The work done in stretching a wire is represented by:
Reasoning: Work done is the product of force and displacement. On a force-extension graph, the area represents this product.
2 / 40
The area under a force-extension graph represents:
Reasoning: The area under the graph gives the energy transferred as work during stretching.
3 / 40
The unit of the area under a force-extension graph is:
Reasoning: Force $\mathbf{\times}$ extension has units $\mathbf{N \times m}$, which is equal to joule.
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If a constant force of $\mathbf{10\ N}$ stretches a spring by $\mathbf{0.5\ m}$, the work done is:
Reasoning: Work done $\mathbf{=}$ Force $\mathbf{\times}$ extension $\mathbf{= 10 \times 0.5 = 5\ J}$
5 / 40
On a force-extension graph, the extension is represented on the:
Reasoning: Force-extension graphs normally plot extension on the $\mathbf{x}$-axis and force on the $\mathbf{y}$-axis.
6 / 40
For a spring obeying Hooke’s law, the force-extension graph is:
Reasoning: Hooke’s law states that force is directly proportional to extension.
7 / 40
The work done in stretching a spring following Hooke’s law is calculated by:
Reasoning: The average force during stretching is half the final force.So, Work $\mathbf{= 1/2 \times}$ final force $\mathbf{\times}$ extension
8 / 40
A spring is stretched gradually from zero to a force $\mathbf{F}$. The average force acting during stretching is:
Reasoning: For a linear force-extension relationship, force increases uniformly from $\mathbf{0\ }$to $\mathbf{F}$.
9 / 40
The triangular area under a force-extension graph represents:
Reasoning: The work done in stretching an elastic object is stored as elastic potential energy.
10 / 40
A larger area under a force-extension graph means:
Reasoning: The area represents work, so a larger area indicates more energy transferred.
11 / 40
If the extension of a spring is doubled within the elastic limit, the work done becomes:
Reasoning: Work done $\mathbf{= W =}$ $\frac{\mathbf{1}}{\mathbf{2}}\mathbf{\ k}\mathbf{x}^{\mathbf{2}}$, so doubling extension makes work four times.
12 / 40
The area under a force-extension graph gives work because:
Reasoning: Work done is calculated by adding small amounts of force multiplied by displacement.
13 / 40
A force-extension graph is curved. The work done is found by:
Reasoning: For variable force, the area under the graph gives total work done.
14 / 40
When stretching an elastic wire, the work done is stored as:
Reasoning: Energy supplied during stretching is stored in the deformed material.
15 / 40
If no force is applied to stretch an object, the work done is:
Reasoning: Work requires an applied force causing displacement.
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The area under a force-extension graph from zero extension to $\mathbf{x}$ represents:
Reasoning: The entire area represents accumulated work during stretching.
17 / 40
Two springs have identical extensions. Spring $\mathbf{A}$ requires greater force than Spring $\mathbf{B}$. The work done is greater for:
Reasoning: A larger force-extension area means greater work done.
18 / 40
The slope of a force-extension graph represents:
Reasoning: According to Hooke’s law $\mathbf{(F = k}\mathbf{x}\mathbf{)}$, so slope equals spring constant.
19 / 40
A force-extension graph has a straight line with a steeper slope. This means the spring:
Reasoning: A steeper slope means greater spring constant and stiffness.
20 / 40
The work done in stretching a spring depends on:
Reasoning: Work depends on both force and extension, represented by the area.
21 / 40
A force-extension graph forms a rectangle. The work done is:
Reasoning: For constant force, the area of rectangle gives work done.
22 / 40
For a non-linear elastic material, the work done is:
Reasoning: The area method works even when force does not increase linearly.
23 / 40
A spring with spring constant $\mathbf{200\ N/m}$ is stretched by $\mathbf{0.1\ m}$. The stored energy is:
Reasoning: $\mathbf{W =}$ $\frac{\mathbf{1}}{\mathbf{2}}\mathbf{k}\mathbf{x}^{\mathbf{2}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{(200)}\mathbf{(0.1)}^{\mathbf{2}}\mathbf{= 1\ J}$
24 / 40
The area below the force-extension curve is zero when:
Reasoning: No extension means no displacement and therefore no work done.
25 / 40
If a spring is stretched beyond its elastic limit, the area under the graph represents:
Reasoning: Beyond the elastic limit, some energy may not be recovered.
26 / 40
During unloading of an elastic material, the area under the unloading curve represents:
Reasoning: The stored elastic energy is released during unloading.
27 / 40
The difference between loading and unloading areas for a plastic material represents:
Reasoning: Plastic deformation converts some energy into internal energy and heat.
28 / 40
If the force-extension graph doubles in size vertically while extension remains the same, the work done:
Reasoning: The area under the graph increases proportionally with force.
29 / 40
The force-extension graph is useful because it allows determination of:
Reasoning: The graph directly provides energy through its area.
30 / 40
The energy stored in a stretched wire is equal to:
Reasoning: Elastic energy stored equals the work done in stretching the wire.
31 / 40
A spring requires increasing force as it stretches. The work done is not simply $\mathbf{(F}\mathbf{x}\mathbf{)}$ because:
Reasoning: Variable force requires using the area under the graph.
32 / 40
A straight-line force-extension graph indicates:
Reasoning: A straight line shows a constant ratio of force to extension.
33 / 40
If the final force and extension of a spring are both doubled, the work done becomes:
Reasoning: Area of triangular graph $\mathbf{=}$ $\frac{\mathbf{1}}{\mathbf{2}}\mathbf{F}\mathbf{x}$, so doubling both gives four times the area.
34 / 40
The force-extension graph is preferred over a force-distance graph because:
Reasoning: Extension is the displacement involved in deformation work.
35 / 40
The work done while stretching an elastic object is positive because:
Reasoning: Positive work occurs when force acts in the direction of displacement.
36 / 40
If a force-extension graph encloses a larger area, the material has:
Reasoning: The area represents energy stored during stretching.
37 / 40
For a spring stretched by a constant force, the graph shape is:
Reasoning: Constant force gives a rectangular area equal to work done.
38 / 40
The work done in stretching an elastic wire can be recovered because:
Reasoning: Elastic deformation stores recoverable energy.
39 / 40
A force-extension graph is used instead of only measuring final force because:
Reasoning: The graph accounts for changing force throughout the process.
40 / 40
The physical meaning of the area under a force-extension graph is:
Reasoning: The area represents the work done, which is the energy transferred to deform the material.
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