(B) The work done by a variable force is equal to the area under the $F-x$ graph.From the graph,the area is a trapezoid with parallel sides of length

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(B) The work done by a variable force is equal to the area under the $F-x$ graph.From the graph,the area is a trapezoid with parallel sides of length $3\,m$ (from $x=0$ to $x=3$) and $6\,m$ (from $x=0$ to $x=6$),and height $3\,N$.Alternatively,the area can be calculated as the sum of a rectangle (from $x=0$ to $x=3$) and a triangle (from $x=3$ to $x=6$).Area of rectangle = $3\,m \times 3\,N = 9\,J$.Area of triangle = $\frac{1}{2} \times (6-3)\,m \times 3\,N = \frac{1}{2} \times 3 \times 3 = 4.5\,J$.Total work done = $9\,J + 4.5\,J = 13.5\,J$.

Class 11 Physics Work, Energy, Power and Collision Work Done by Variable Force and Force-Displacement Graph

Medium

$A$ force $F$ acting on an object varies with distance $x$ as shown in the graph. The force is in newton $(N)$ and $x$ is in metre $(m)$. The work done by the force in moving the object from $x = 0$ to $x = 6\,m$ is......$J$.

AIPMT 2005 All AIPMT

A
$4.5$
B
$13.5$
C
$9$
D
$18$

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Class 11

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Work, Energy, Power and Collision

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Work Done by Variable Force and Force-Displacement Graph

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$A$ particle is acted upon by a force $F$ which varies with position $x$ as shown in the figure. If the particle at $x = 0$ has a kinetic energy of $25\,J$,then the kinetic energy of the particle at $x = 16\,m$ is .............. $J$.

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What does the area enclosed by the $F-x$ graph represent? (where $F$ is the external force and $x$ is the change in the length of the spring)

Medium

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The adjacent figure shows the force-displacement graph of a moving body. The work done in displacing the body from $x = 0$ to $x = 35\,m$ is equal to ........... $J$.

Easy

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$A$ body covers a distance of $2\,m$ under the influence of a force $F = 15 - 4x\,N$,where $x$ is the distance covered by the particle in meters. The work done by the force is ............ $J$.

Easy

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The figure shows the relationship between force and position. What is the work done by the force for the displacement of the object from $x = 1 \; cm$ to $x = 5 \; cm$ in ergs?

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$A$ force $F$ acting on an object varies with distance $x$ as shown in the graph. The force is in newton $(N)$ and $x$ is in metre $(m)$. The work done by the force in moving the object from $x = 0$ to $x = 6\,m$ is......$J$.

Similar Questions

$A$ particle is acted upon by a force $F$ which varies with position $x$ as shown in the figure. If the particle at $x = 0$ has a kinetic energy of $25\,J$,then the kinetic energy of the particle at $x = 16\,m$ is .............. $J$.

What does the area enclosed by the $F-x$ graph represent? (where $F$ is the external force and $x$ is the change in the length of the spring)

The adjacent figure shows the force-displacement graph of a moving body. The work done in displacing the body from $x = 0$ to $x = 35\,m$ is equal to ........... $J$.

$A$ body covers a distance of $2\,m$ under the influence of a force $F = 15 - 4x\,N$,where $x$ is the distance covered by the particle in meters. The work done by the force is ............ $J$.

The figure shows the relationship between force and position. What is the work done by the force for the displacement of the object from $x = 1 \; cm$ to $x = 5 \; cm$ in ergs?

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