Question

The propelling force of a rocket increases uniformly from zero to N in the first
12 m and remains constant for the next 40 m. Find the total work done​

Answer 1

Question:

The propelling force of a rocket increases uniformly from zero to 1 N in the first in the first 12 m and remains constant for the next 40 m. Find the total work done.

Answer:

Force $\propto$ Height

F $\propto$ h

F = p.h

F = Force

h = height

p = constant

p = $\dfrac{F}{h}$

p = $\dfrac{1}{12}$

For first 12 m Force is increased from 0 to 1 N (as you have not given i am considering according to it)

$W_{1}$ = $\int F dx$

$W_{1}$ = $\int p.h dx$

$W_{1}$ = $p \int h dx$ -- {p is constant}

$W_{1}$ = $\dfrac{1}{12}\times\Big[\dfrac{h^{2}}{2}\Big]_{0}^{12}$

$W_{1}$ = $\dfrac{1}{12}\times\dfrac{12^{2}}{2}$

$W_{1}$ = 6 Joule

$W_{2}$ = F × $h_{2}$

$W_{2}$ = 1 × 40

$W_{2}$ = 40 Joule

$W_{1}\: + \: W_{2}$ = 40 + 6 = 46 Joules

Answer is 46 Joules