Question

Force F acts such that it is always tangential to surface of hill(rough). Find work done by force.

Answer 1

Final Answer : $mg (\mu l+ h)$

Steps : 1)
Assuming body moves with constant velocity.

Let us consider a very small part of journey where mass m travels 'ds' along hypotenuse with its base 'dl' and perpendicular 'dh'.

For small part, trajectory is approximately straight / flat without curve.
f = friction force

2) Now, Force balance :

$F_t - f - mg sin(\alpha) = 0 \\ N = mg cos(\alpha) \\ => F_t = \mu mg cos(\alpha) + mg sin(\alpha)$

3) Now,
Work done by Tangential Force :
$\int F_t . ds = \int mg (\mu cos(\alpha )+ sin(\alpha) ) ds \\ => mg \int (\mu cos(\alpha) ds + sin(\alpha) ds) \\ => mg \int ( \mu dl + dh) \\ => mg (\mu l + h)$

Hence, Work done by Tangential Force =
$mg (\mu l + h)$ .

Answer 2

Answer:

hey dear

here is your answer

i have assumed complete suraface to be a inclined plane and then solved it

bt it is better for you to assume small part of the given figure as a inclined plane and then solve it bt answers will come same so dont worry and go through the attached explanation

BEST OF LUCK