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Physics Chapter 5 : Topic 2
Work from Force–Displacement Graphs
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Work done by a force is defined as:
Reasoning: Work is $\mathbf{W = Fs}$. When force and displacement are in the same direction.
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The SI unit of work is:
Reasoning: The $\mathbf{SI}$ unit of work is joule $\mathbf{(}$J$\mathbf{)}$.
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Work done can be determined from a force-displacement graph by finding:
Reasoning: The area under an $\mathbf{F -}\mathbf{x}$ graph represents work done.
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The area under a force-displacement graph represents:
Reasoning: $\mathbf{W = Fs}$ ; Area $\mathbf{=}$ force $\mathbf{\times}$ displacement.
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In a force-displacement graph, force is plotted on:
Reasoning: Usually displacement is on $\mathbf{x}$-axis and force on $\mathbf{y}$-axis.
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For a constant force, the force-displacement graph is:
Reasoning: Constant force has the same value for all displacements.
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The work done by a constant force is equal to the area of:
Reasoning: Area $\mathbf{= F \times s}$
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If the area under a force-displacement graph is larger, the work done is:
Reasoning: Work is directly proportional to the area.
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A force-displacement graph is useful because it can show:
Reasoning: Variable forces cannot be calculated simply by $\mathbf{W = Fs}$, so graph area is used.
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The area under an $\mathbf{F -}\mathbf{x}$ graph has dimensions of:
Reasoning: $\mathbf{Force \times displacement = Work}$
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When force and displacement are in the same direction, work done is:
Reasoning: Force assists motion, producing positive work.
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In a force-displacement graph, area above the displacement axis represents:
Reasoning: Positive force produces positive work.
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Area below the displacement axis in an $\mathbf{F -}\mathbf{x}$ graph represents:
Reasoning: Negative force acts opposite to displacement.
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Friction acting on a moving object produces:
Reasoning: Friction opposes displacement.
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If the net area under a force-displacement graph is zero, the total work done is:
Reasoning: Positive and negative areas cancel.
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A force of $\mathbf{10\ N}$ acts on an object through a displacement of $\mathbf{5\ m}$. Work done is:
Reasoning: $\mathbf{W = Fs = 10(5) = 50\ J}$
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A force-displacement graph is a rectangle with force $\mathbf{20\ N}$ and displacement $\mathbf{4\ m}$. Work done is:
Reasoning: $\mathbf{W =}\mathbf{Area}\mathbf{= 20 \times 4 = 80\ J}$
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A triangular region under a force-displacement graph has base $\mathbf{6\ m}$and height $\mathbf{10\ N}$. Work done is:
Reasoning: Area of triangle: $\mathbf{W =}$ $\frac{\mathbf{1}}{\mathbf{2}}\mathbf{\times base \times height}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{(6)(10) = 30\ J}$
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A force increases linearly from $\mathbf{0\ N}$ to $\mathbf{20\ N\ }$over $\mathbf{5\ m}$. Work done is:
Reasoning: Area is triangular: $\mathbf{W =}$ $\frac{\mathbf{1}}{\mathbf{2}}\mathbf{(5)(20) = 50\ J}$
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A force of $\mathbf{15\ N}$ acts opposite to displacement of $\mathbf{3\ m}$. Work done is:
Reasoning: Opposite direction: $\mathbf{W = - \ Fs = - \ 15}\left( \mathbf{3} \right)\mathbf{= - \ 45\ J}$
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If force remains constant while displacement increases, the graph will show:
Reasoning: Constant force gives constant height on graph.
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The area under a curved force-displacement graph is found by:
Reasoning: Variable forces require area calculation.
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The slope of a force-displacement graph represents:
Reasoning: Slope $\mathbf{=}$ $\frac{\mathbf{\Delta F}}{\mathbf{\Delta}\mathbf{x}}$
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A decreasing force-displacement graph indicates:
Reasoning: Height of graph represents force.
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The total work done from a force-displacement graph is obtained by:
Reasoning: Areas above and below axis have opposite signs.
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According to the work-energy theorem:
Reasoning: $\mathbf{W = K\ .E}$
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Positive work on an object causes its kinetic energy to:
Reasoning: Positive work adds energy to the object.
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Negative work on an object causes:
Reasoning: Opposing forces remove kinetic energy.
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If the force-displacement graph has greater area, the object gains:
Reasoning: Greater work means greater energy transfer.
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The area under a force-displacement graph is equal to:
Reasoning: By definition, area represents work.
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A horizontal force-displacement graph above $\mathbf{x}$-axis means:
Reasoning: Constant height above axis represents constant positive force.
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If the force-displacement graph crosses the displacement axis:
Reasoning: Force changes sign when it crosses the axis.
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Two objects have the same displacement. The one with greater area under $\mathbf{F -}\mathbf{x}$ graph has:
Reasoning: Area directly represents work.
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A force-displacement graph is preferred for variable force because:
Reasoning: Graph allows calculation of work for changing forces.
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If displacement is zero, the area under $\mathbf{F -}\mathbf{x}$ graph is:
Reasoning: No displacement means no work.
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Which statement is correct?
Reasoning: Work is calculated from the area under the $\mathbf{F -}\mathbf{x}$ curve.
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The area under a force-displacement graph with a curved line is calculated by:
Reasoning: Work equals area under the graph.
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If the area under a force-displacement graph is doubled, the work done:
Reasoning: Work is directly proportional to area.
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A force-displacement graph is a straight line parallel to $\mathbf{x}$-axis. This means:
Reasoning: Constant height represents constant force.
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Which graph gives maximum work?
Reasoning: $\mathbf{W = 10 \times 10 = 100\ J}$
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The force-displacement graph is mainly used because:
Reasoning: Variable forces require graphical area calculation.
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