Question

a forcce is acting on a mass at inclined rough surface upward direction tangentially to the surface of hill if the speed of mass of climbing upward is constant find work done by this force

Answer 1

Ref. image 1
According to work energy theorem we know
(W
A−B
​
)
net
​
=KE
B
​
−KE
A
​

Hence (W
A−B
​
)
net
​
= work done from A to B (net) and KE = kinetic energy
as V
B
​
=V
A
​
,KE
B
​
=KE
A
​

∴(W
A−B
​
)
net
​
=0
Now from acting on mass m are.
By FBD
Ref. image 2
So work done by all the forces
W
net
​
=D
Work done by F+ work done by mg+ work done by friction = 0
W
F
​
=−W
mg
​
−W
friction
​

W
f
​
=−(−mgh)−W
friction
​
taking upwind direction
=mgh−W
friction
​

Now for W
friction
​

Now for W
friction
​

ref. image 3
friction force = μmgcosθ as (N=mgcosθ)
Let the mass more ds.
ref. image 4 Then dW
friction
​
=−mumgcosθ
Ref. image 5
W
friction
​
=−μmg∫dscosθ
=−μmg∫dx
=−μmgl
∴W
f
​
=mgh+μmgl
=mg(h+μl)


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