A rough inclined plane is placed on car moving with a constant velocity $u$ on horizontal ground. A block of mass $ M$ rests on the inclined plane. Is any work done by force of friction between the block and inclined plane ? Is there then a dissipation of energy ?
Yes, the friction,
$f=\mathrm{Mg} \sin \theta \quad(\because \mathrm{M}$ is at rest)
Since, block is not in motion so, no work is done by the friction no dissipation of energy takes place.
Under the action of a force, a $2 \,kg$ body moves such that its position $x$ as a function of time $t$ is given by $x=\frac{t^2}{3}$, where $x$ is in metres and $t$ in seconds. The workdone by the force in first two seconds is .......... $J$
A bullet of mass $200\,g$ having initial kinetic energy $90\,J$ is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to $40\,J$ within 1s, the minimum length of the pool, the bullet has a to travel so that it completely comes to rest is $.....m$
A small disk can slide in a circular path on a frictionless inclined plane inclined at an angle of $30^o $ with the help of a thread as shown. Mass of the disk is $m$ and acceleration due to gravity is $g$. If the disk is released, when the thread is horizontal, expression for the tension in the thread at the lowest point is :- ................. $\mathrm{mg}$
Two identical steel cubes (masses $50\,g$, side $1\,cm$) collide head-on face to face with a space of $10\,cm/s$ each. Find the maximum compression of each. Young’s modulus for steel $Y = 2 \times 10^{11}\,Nm^{-2}$.
A wedge of mass $M = 4\,m$ lies on a frictionless plane. A particle of mass $m$ approaches the wedge with speed $v$. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by