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Work done by variable force is considered one the most difficult concept.
38 Questions around this concept.
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:
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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 :
Choose correct statement regarding work done by frictional force.
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.
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 is zero -
When the force applied on a body is insufficient to overcome the friction.
Work done by the frictional force is negative
When the force is large enough to overcome the friction
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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