Inclined Plane with Friction

At 6 [ m ] 6[m] from the floor a mass 5 [ k g ] 5[kg] is dropped on a inclined plane which form an angle θ \theta with the horizontal. If the base of the inclined plane is 8 [ m ] 8[m] long, and the coefficient of friction of the mass with the inclined plane is 0 , 6 0,6 , what is the absolute value of the work (in Joules) done by the friction force untill the mass get to the floor?

Details and Assumptions:

  • Take g = 10 [ m s 2 ] g=10[\frac{m}{s^2}]


The answer is 240.

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1 solution

At drawing an FBD with x x axis parallel to the surface where is falling the object we can realize that there is a normal force, gravity force and friction force; with N = c o s ( θ ) m g N=cos(\theta)mg and therefore f = μ c o s ( θ ) m g f=\mu \cdot cos(\theta)mg . We are given all these values, except θ \theta , but we can see that the inclined plane is a right triangle, so the hypotenuse equals 10 [ m ] 10[m] and then c o s ( θ ) = 8 10 = 0 , 8 cos(\theta)=\frac{8}{10}=0,8 , so replacing the values and using the fact that friction force opposes to the movement, we have: f = 0 , 6 0 , 8 50 [ N ] = 24 \vec{f}=-0,6\cdot 0,8 \cdot 50[N]=-24 W f = f r = 24 10 [ J ] = 240 [ J ] \Rightarrow W_{f}=\vec{f}\cdot \vec{r}=-24 \cdot 10[J]=-240[J]

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