Work

A particle being acted on by constant forces $\left(4 \hat{i}+\hat{j}-3 \hat{k}\right)$ and $\left(3 \hat{i}+\hat{j}-\hat{k}\right)$ is displaced from the point $\left(\hat{i}+2 \hat{j}-3 \hat{k}\right)$ to the point $\left(5 \hat{i}+4 \hat{j}-\hat{k}\right)$. Find the total work done by the forces.

A force $F=\left(20+0.5 \mathrm{x}\right)$ acts on a particle in the $x$-direction where $F$ is in newton and $x$ in metre. Find the work done by this force during a displacement from $x=0$to $x=2.0 \mathrm{m}$.

A particle of mass $5 \mathrm{g}$ is initially moving along a straight line with a velocity of $10 {\mathrm{cms}}^{-1}$ and then a force of $10\sqrt{2}$ dyne is applied to it an angle of $45°$ to the initial direction of motion. Calculate the change in its kinetic energy during the first second.

A certain force performed $112 \mathrm{J}$ of work in raising a mass of a $4 \mathrm{kg}$ vertically through $1 \mathrm{m}$ from the ground. With what acceleration had the body moved up?

When a rubber-band is stretched by a distance $x$, it exerts a restoring force of magnitude $F=ax+b{x}^2$ where $a$ and $b$ are constants. The work done in stretching the unstretched rubber band by $L$ is:

A body moves a distance of $10 \mathrm{m}$ along a straight line under the action of a force of $5 \mathrm{N}$. If the work done is $25 \mathrm{J}$, the angle which the force makes with the direction of motion of the body is.

Prove that if a piston moves in a cylinder due to a constant pressure, the work done in each stroke is equal to the product of the pressure and the volume swept out by the piston.

How would you find out the work done by a variable force, varying both in magnitude and direction?

What do you mean by 'work done by a couple'? If a body makes $n$ complete rotations, show that work done$=2 \mathrm{\pi n\tau }$ where $\tau$ is the torque applied.

A particle of mass $100 \mathrm{g}$ is thrown vertically upward with a speed of $5 {\mathrm{ms}}^{-1}$. The work done by the force of gravity during the time the particle goes up is

State the sign of the work done in the following cases: Work done by the resistive force of air on a vibrating pendulum in bringing it to rest.

State the sign of the work done in the following cases: Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity.

State the sign of the work done in the following cases: Work done by friction on a body sliding down an inclined plane.

State the sign of the work done in the following cases: Work done by the force of gravity when a man pulls a bucket up from the well.

State the sign of the work done in the following cases: Work done by a man lifting a bucket out of a well by means of a rope tied to the bucket.

A uniform chain of length $L$ and mass $M$ is lying on smooth table and one-third of its length is hanging vertically down over the edge of the table. If $g$ is the acceleration due to gravity, the work required to pull the hanging part on to the table is

A force$\overrightarrow{F}=-k(y\hat{i}+x\hat{j})$  (where $k$ is positive constant) acts on a particle moving in the $xy$ plane. Starting from the origin, the particle is taken along the positive $x$-axis to the point ($a, 0$) and then parallel to the y-axis to the point ($a, a$). The total work done by the force $F$ on the particle is

Give an example of a force acting on a moving body, yet doing no work.

A block of mass $50 \mathrm{kg}$ just slides over a distance of $1 \mathrm{m}$. If the coefficient of friction between their surfaces is $0.2$, the work done against friction is

A force $\overrightarrow{F}=5\hat{i}+6\hat{j}-4\hat{k}$ acting on body produces a displacement $\overrightarrow{S}=6\hat{i}+5\hat{k}$. The work done by the force is