When a constant force is applied to a body moving with constant acceleration, power does not remain

English

Gujarati

Hindi

5.Work, Energy, Power and Collision

normal

When a constant force is applied to a body moving with constant acceleration, power does not remain constant. For power to be constant, the force has to vary with speed as follows

A

$F \propto \frac{1}{\upsilon }$

B

$F \propto \frac{1}{\sqrt \upsilon }$

C

$F \propto {\upsilon }$

D

$F \propto {\upsilon ^2}$

Solution

As $a=\frac{d v}{d t}=\frac{F}{m}=$ constant, hence, on integration,

we get $;$

$\mathrm{v}=\frac{\mathrm{F}}{\mathrm{m}} \mathrm{t}$

So, power, $P=\mathrm{F} \mathrm{v}=\frac{\mathrm{F}^{2}}{\mathrm{m}} \mathrm{t}$

i.e., $p$ $\infty$ $t$ For power to be constant, $\mathbf{Fv} =$ constant, i.e.,

$\mathrm{F} \propto \frac{1}{\mathrm{v}}$

Standard 11

Physics

Share

Similar Questions

The total work done on a particle is equal to the change in its kinetic energy. This is applicable

normal

Answer the following :

$(a)$ The casing of a rocket in flight burns up due to friction. At whose expense is the heat energy required for burning obtained? The rocket or the atmosphere?

$(b)$ Comets move around the sun in highly elliptical orbits. The gravitational force on the comet due to the sun is not normal to the comet’s velocity in general. Yet the work done by the gravitational force over every complete orbit of the comet is zero. Why ?

$(c)$ An artificial satellite orbiting the earth in very thin atmosphere loses its energy gradually due to dissipation against atmospheric resistance, however small. Why then does its speed increase progressively as it comes closer and closer to the earth ?

$(d)$ In Figure $(i)$ the man walks $2\; m$ carrying a mass of $15\; kg$ on his hands. In Figure $(ii)$, he walks the same distance pulling the rope behind him. The rope goes over a pulley, and a mass of $15\; kg$ hangs at its other end. In which case is the work done greater ?

medium

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to

normal

A boy holds a uniform chain of length $2\,m$ which is kept on a smooth 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 done in pulling the entire chain on the table ………….. $\mathrm{J}$

normal

Power applied to a particle varies with time as $P = (4t^3 -5t + 2)\,watt$, where $t$ is in second. Find the change is its $K.E.$ between time $t = 2$ and $t = 4 \,sec.$ …………… $\mathrm{J}$

normal