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Work Done By Variable Force - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main
Quick Facts
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Work done by variable force is considered one the most difficult concept.
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38 Questions around this concept.
Solve by difficulty
A time-dependent force F=6t acts on a particle of mass 1 kg. If the particle starts from rest, the work (in Joule) is done by the force during the first 1 sec. will be :
A uniform chain of length 2 m is kept on a table such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg. What is the work (in Joule) done in pulling the entire chain on the table?
A force of variable magnitude is applied to an object and it moves a distance of 2 meters in the direction of the force. The work done by the force is:
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Choose the correct equation for work done by time-dependent force (W)
Arrange the four graphs in descending order of total work done; where $\mathrm{W}_1, \mathrm{~W}_2, \mathrm{~W}_3$ and $\mathrm{W}_4$ are the work done corresponding to figure $\mathrm{a}, \mathrm{b}, \mathrm{c}$ and d respectively.
A force $\vec{F}=2 \hat{i}+b \hat{j}+\hat{k}$ is applied on a particle and it undergoes a displacement $\hat{i}-2 \hat{j}-\hat{k}$. What will be the value of $b$, if work done on the particle is zero.
Work done by static friction on an object:
A body of mass $m$ dropped from a height $h$ reaches the ground with a speed of $0.8 \sqrt{g h}$. The value of work done by the air friction is :
A block of mass $100 \mathrm{~kg}$ slides over a distance of $10 \mathrm{~m}$ on a horizontal surface. If the co-efficient of friction between the surfaces is 0.4 , then the work done against friction (in $J$ ) is :
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Try NowChoose correct statement regarding work done by frictional force.
Concepts Covered - 2
Work done by variable force
- Force is a vector quantity. So it has a magnitude as well as direction. A variable force means when its magnitude or its direction or both varies with position.
And work done by the variable force is given by -
$$
W=\int \vec{F} \cdot \overrightarrow{d s}
$$
Where $\vec{F}$ is a variable force and $\overrightarrow{d s}$ is a small displacement
- When Force is time-dependent
And we can write $d \vec{s}=\vec{v} d t$
${ }_{\text {So, }} W=\int \vec{F} \cdot \vec{v} d t$
Where $\vec{F}$ and $\vec{v}$ are force and velocity vector at any instant.
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Work Done Calculation by Force Displacement Graph
The area under the force-displacement curve with the proper algebraic sign represents work done by the force.
Work done by the frictional force
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Work done by the frictional force is zero -
When the force applied on a body is insufficient to overcome the friction.
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Work done by the frictional force is negative
When the force is large enough to overcome the friction
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Work done by the frictional force is positive
When force is applied on a body, which is placed above another body ,the work done by the frictional force on the lower body
maybe positive.
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