Answer
given,
total mass = 18.3 Kg
inclined at = 19.8°
distance = 19.7 m
coefficient of friction = 0.5
a) Horizontal component of force forward,
![F_x = F cos \theta](https://tex.z-dn.net/?f=F_x%20%3D%20F%20cos%20%5Ctheta)
Horizontal force backward = force of friction, f =μN.
Normal force, N = mg - F sinθ
Since the velocity is uniform, acceleration, a = 0
Net force, ΣF = 0
F cos θ+ -μ(mg -F sinθ) = 0
F (cosθ + μsin θ) = μmg
![F = \dfrac{\mu m g}{cos \theta + \mu sin \theta}](https://tex.z-dn.net/?f=F%20%3D%20%5Cdfrac%7B%5Cmu%20m%20g%7D%7Bcos%20%5Ctheta%20%2B%20%5Cmu%20sin%20%5Ctheta%7D)
![F = \dfrac{0.5\times 18.3\times 9.8}{cos 19.8^0 +0.5\times sin 19.8^0}](https://tex.z-dn.net/?f=F%20%3D%20%5Cdfrac%7B0.5%5Ctimes%2018.3%5Ctimes%209.8%7D%7Bcos%2019.8%5E0%20%2B0.5%5Ctimes%20sin%2019.8%5E0%7D)
=80.76 N
(b) Work done by the rope on the sledge,
W = F.S cosθ = 80.76 x 19.7 x 0.9360
= 1497 J
(c) Mechanical energy lost due to friction,
E = W done against friction,
W' = f x S =F x S = 80.76 x 19.7 x0.9360
= 1497 J
we know velocity is uniform,.
W done by the applied force = W done against friction.
= 1440 J