Work Done by a Variable Force

A force $\overrightarrow{F}=\left(3x^2\mathrm{N}\right)\hat{\mathrm{i}}+\left(4 \mathrm{N}\right)\hat{\mathrm{j}}$, (where $x$ is in meters), acts on a particle. Assuming that only kinetic energy is changed the net work done on the particle as it moves from position $\left(2\hat{\mathrm{i}}+3\hat{\mathrm{j}}\right) \mathrm{m}$ to $\left(3\hat{\mathrm{i}}+1\hat{\mathrm{j}}\right) \mathrm{m}$

What will be the position at time $t=5 \mathrm{s}$ if the particle starts from rest at origin and the force on the particle of mass $10 \mathrm{g}$ is $\left(10\widehat{\mathrm{i}}+5\widehat{\mathrm{j}}\right) \mathrm{N}$. 

A woman pushes a trunk on a railway platform which has a rough surface. She supplies a force of $100 \mathrm{N}$ over a distance of $10 \mathrm{m}$. Thereafter, she gets progressively tired and her applied force reduces linearly with distance to $50 \mathrm{N}$. The total distance by which the trunk has been moved is $20 \mathrm{m}$. Calculate the net work done by the two forces over $20 \mathrm{m}$.

A force $F$ acting on an object varies with distance x as shown in the figure. The work done by the force in moving the object from $x=0$ to $x=20 \mathrm{m}$ is

Starting from rest, a particle is moving along x-axis. The variation of force with position is shown in figure. Find the Kinetic energy $\left(KE\right)$ of particle when it is at $x=3\text{m}\text{.}$

A position dependent force $F=4-2x+6x^2$ Newton acts on a body and displaces it from $x=0$ to $x=\mathrm{4 }m$. Work done in the process is

A force $\overrightarrow{\mathit{\text{F}}}=\left(\text{3}\mathit{\text{t}}\widehat{\text{i}}+5\widehat{\text{j}}\right)\text{N}$ acts on a body due to which its displacement varies as $\mathit{\text{S}}=\left(2{\mathit{\text{t}}}^2\widehat{\text{i}}-5\widehat{\text{j}}\right)\text{m}$. Work done by this force in $2 \mathrm{s}$ is

The force on a particle as the function of displacement $x$ (in $x$ -direction) is given by $F=10+0.5x$ . The work done corresponding to displacement of particle from $x=0$ to $x=2$ unit is

A force $\overrightarrow{\mathrm{F}}=\left(2\mathrm{t}\widehat{\mathrm{i}}+6\widehat{\mathrm{j}}\right)\mathrm{N}$ . acts on a particle whose position varies as $\overrightarrow{\mathrm{s}}=\left(4{\mathrm{t}}^2\widehat{\mathrm{i}}-8\widehat{\mathrm{j}}\right)$ . Work done by this force in initial 1s is:

The spring extends by $x$ on loading, then energy stored by the spring is: (If $T$ is the tension in spring and $k$ is spring constant)

Which one of the following physical quantities is represented by the shaded area in the given graph?

A particle moves under the effect of a force $F=Cx$ from $x=0$ to $x=x_1$ . The work done in the process is (treat $c$as a constant)

A force $F$ acting on a particle varies with the position $x$ as shown in the graph. Find the work done by the force in displacing the particle from $x=-a$ to $x=+2a$

A block of mass $5 \mathrm{kg}$ initially at rest at the origin is acted on by a force along the positive $x$-direction represented by $F=(\mathrm{ }20\mathrm{ }+5x)\mathrm{ }\mathrm{N}$ . Calculate the work done by the force during the displacement of the block from $x=0$ at $x=4\mathrm{ }\mathrm{m}$

A particle of mass $m$ moves along the quarter section of the circular path whose centre is at the origin. The radius of the circular path is $a$. A force $\overrightarrow{F}=y\hat{\mathrm{i}}-x\hat{\mathrm{j}}$ $\mathrm{N}$ acts on the particle, where $x,y$ denote the coordinates of the position of the particle. Calculate the work done by this force in taking the particle from point $\mathrm{A}(\mathrm{a}, 0)$ to point $\mathrm{B}(0, \mathrm{a})$ along the circular path.

Which of the following is not a conservative force(s)?

A variable force $F$ acts along the $X\mathit{-}$axis given by $F=\left(3x^2-\mathrm{ }2x+1\right)\mathrm{ }\mathrm{N}$ . The work done by the force when a particle of mass $100\mathrm{ }\mathrm{g}$ moves from $x=50\mathrm{ }\mathrm{c}\mathrm{m}$ to $x=100\mathrm{ }\mathrm{c}\mathrm{m}$ is -

A particle moves along the $\mathrm{x}\text{-}\mathrm{a}\mathrm{x}\mathrm{i}\mathrm{s}$ from $\mathrm{x}=0$ to $\mathrm{x}=5\mathrm{m}$ under the influence of a force given by $\mathrm{F}=7-2\mathrm{x}+3{\mathrm{x}}^2$ . The work done in the process is-

The relationship between the force $F$ and position $x$ of a body is as shown in figure. The work done in displacing the body from $x=1 \mathrm{m}$ to $x=5 \mathrm{m}$ will be-

Force acting on a particle moving in a straight line varies with the velocity of the particle as $\mathrm{F}=\frac{\mathrm{K}}{\mathrm{v}}$ . Here $\mathrm{K}$ is constant. The work done by this force in time $\mathrm{t}$ is -