Answer:
[tex]1270.64\ \text{J}[/tex]
Explanation:
m = Mass of object = [tex]\dfrac{mg}{g}[/tex]
mg = Weight of object = 20 N
g = Acceleration due to gravity = [tex]9.81\ \text{m/s}^2[/tex]
v = Final velocity = 15 m/s
u = Initial velocity = 0
d = Distance moved by the object = 150 m
[tex]\theta[/tex] = Angle of slope = [tex]30^{\circ}[/tex]
f = Force of friction
fd = Work done against friction
The force balance of the system is
[tex]\dfrac{1}{2}m(v^2-u^2)=(mg\sin\theta-f)d\\\Rightarrow \dfrac{1}{2}mv^2=mg\sin\theta d-fd\\\Rightarrow fd=mg\sin\theta d-\dfrac{1}{2}mv^2\\\Rightarrow fd=20\times \sin 30^{\circ}\times 150-\dfrac{1}{2}\times \dfrac{20}{9.81}\times 15^2\\\Rightarrow fd=1270.64\ \text{J}[/tex]
The work done against friction is [tex]1270.64\ \text{J}[/tex].
