কাজ

A time dependent force F = 10 t is applied on 10 kg block. Find out the work done by F in 2 seconds.

হানি নাটস

$10\, \times\, \displaystyle \dfrac{dv}{dt}\, =\, 10\, t$

$\int_0^v \ dv =\int_{0}^{t} tdt$

$\Rightarrow\, v\, =\, \displaystyle \dfrac{t^2}{2}$ ..........(1)

$dW\, =\, \vec{F}\, .\, \vec{ds}$

$dW\, =\, 10 t. dx$

$dW\, =\, 10 t. v. dt$ .......... (2) $\because\, dx\, =\, vdt$

from (1) & (2)

$dW\, =\, 10\, t\, .\, \left ( \displaystyle \dfrac{t^2}{2} \right )dt\, \quad\, dW\, =\, 5t^3dt$

$W\, =\, \displaystyle \dfrac{5}{4}\, [t^4]_0^2\, =\, 20\, J$

কাজ টপিকের ওপরে পরীক্ষা দাও

এখনো না বুঝতে পারলে ডাউটস এ পোস্ট করো

পোস্ট করো

Related question

Water is dragged from a well of hepth 30 m using bucket of weight 50kg with water If the weight of the rope is 0.4 kg per metre, the amount of work done is ;

The force constant of a wire is k and that of another wire is $2k$ When both the wires are stretched through same distance, then the work done.

By applying a force $F=(3xy-5z) j +4zk$ a particle is moved along the path $y=x^2$ from point $(0,0,0)$ to the point $(2,4,0)$ . The work done by the F ;on the particle is (all values are in SI& ;units)

The distance $(x)$ converted by a body of $2\ kg$ under the action of a force is related to time $t$ as $x=t^{2}/4$ . What is the work done by the force in first $2$ seconds?