A force of $10 \mathrm{N}$ is acting on a block of $20 \mathrm{kg}$ on a horizontal surface with coefficient of friction $\mu =0.2.$ Calculate the work done by the force.

An inclined plane is moving up with constant velocity $v.$ A block kept on an incline is at rest. Calculate the work done by gravity, friction force, and normal reaction on the block in a time interval of $t.$

A block of mass $m$ is kept over another block of mass $M$ and the system rests on a horizontal surface. A constant horizontal force $F$ acting on the lower block produces an acceleration $\frac{F}{2(m+M)}$ in the system. The two blocks always move together. Consider displacement $d$ of the system.

(a) Find the work done by friction on a bigger block.

(b) Find the coefficient of kinetic friction between the bigger block and the horizontal surface.

(c) Find the frictional force acting on the smaller block.

(d) Find the work done by the force of friction on the smaller block by the bigger block.

(e) Find the work done by static friction on a bigger block.

A block of mass $m$ is placed on the block of mass $M$ as shown in Figure. The horizontal force $\overrightarrow{F}$ acts on $M$ during time interval $t.$ If the horizontal surface is smooth, assuming no relative sliding between the blocks, find the

(a) work done by friction on the blocks

(b) work done by $\overrightarrow{F}$ on the lower block

A $10-\mathrm{kg}$ block is placed on a rough horizontal floor. The block is being pulled by a constant force $100 \mathrm{N}$ acting at angle $37°$ over displacement of $5 \mathrm{m}.$ If the coefficient of kinetic friction between the block and the floor is $0.4,$ find the work done by

(a) work done by the gravity

(b) the normal reaction

(c) the applied force

(d) the force of kinetic friction

A block of mass $2.0 \mathrm{kg}$ is pushed down an inclined plane of inclination $37°$ with a force of $F=20 \mathrm{N}$ acting parallel to the incline. It is found that the block moves down the incline with an acceleration of $10{ \mathrm{m} \mathrm{s}}^{-2}.$ If the block started from rest, find the work done

(a) by the applied force in the first second.

(b) by the weight of the block in the first second.

(c) by the frictional force acting on the block in the first second.

A block of mass $m_1$ moves with an acceleration $a_{12}$ relative to a trolley as shown in the figure. The block is being observed by two observers $\left(2\right)$ and $\left(3\right)$. The observer $\left(2\right)$ is at rest with respect to the trolley which is moving with acceleration $a_2$ while the observer $\left(3\right)$ is moving on the ground with acceleration $a_3$. What is the work done by the pseudo force as observed by the observers $\left(2\right)$ and $\left(3\right)$ on the block during the time $t$? Assume zero initial velocities of the bodies and observers.

A smooth block of mass $m$ moves up from the bottom to the top of a wedge which is moving with acceleration $a_0$. Find the work done by the pseudo force measured by the person sitting at the edge of the wedge.

The only force acting on a $2.0$$\mathrm{kg}$ body as it moves along the $x$-axis varies as shown in figure. The velocity of the body at $x=0$ is $4.0{ \mathrm{m} \mathrm{s}}^{-1}$.

(a) What is the kinetic energy of the body at $x=3.0 \mathrm{m}$?

(b) At what value of $x$ will the body have a kinetic energy of $8.0 \mathrm{J}$?

(c) What is the maximum kinetic energy attained by the body between $x=0$ and $x=5.0 \mathrm{m}$?