Question

How much work does it take to push an object with a mass of `1 kg` up a `6 m` ramp, if the ramp has an incline of `(5pi)/12` and a kinetic friction coefficient of `8`?

Answer 1

Work done to displace the object of `1 kg` mass upward on a plane of length `l=6 m` inclined at an angle of `\theta={5\pi}/12`
`=\text{opposing force }\times \text{displacement against the direction of force}`
`=(mg\sin\theta+\mu mg\cos\theta)\times l`
`=(1\cdot 9.81\sin \frac{5\pi}{12}+0.8\cdot 1\cdot 9.81 \cos\frac{5\pi}{12})\times 6`
`=58.86(\frac{\sqrt3+1}{2\sqrt2}+0.8\cdot \frac{\sqrt3-1}{2\sqrt2})`
`=58.86(\frac{1.8\sqrt3+0.2}{2\sqrt2})`
`=69.04166533116205\ J`