Question

Hi there,
How do you calculate the work done by friction given the coefficient of friction, mass, incline angle and distance?

Problem: A 12.2 kg mass Is moving down a rough incline plane with an initial speed Vo. The incline has a coefficient friction of 0.596 and is inclined at an angle of 33 degrees horizontally. The mass moves a distance of 2.77 m along a plane before stopping. calculate the work done by friction (in J).

Any info would be appreciated.

Answer 1

Here $\mathbf{F}_{fr}$ is frictional force, $\mathbf{N}$ is the normal force and $m\mathbf{g}$ is gravitational force. $\alpha = 33\degree$ is the angle of inclination.

By definition, $F_{fr} = \mu N$, where $\mu = 0.596$.

Let's write down Newton's second law in projection on y-axis.

$$N - mg\cos\alpha = 0\\ N =mg\cos\alpha$$

Subsitiuting the last expression into the definition of $F_{fr}$ , obtain:

$$F_{fr} = \mu N = \mu mg\cos\alpha$$

The work done by friction is given then as

$$A = F_{fr}\cdot d = d\mu mg\cos\alpha$$

where $d = 2.77m$. Thus, obtain:

$$A = 2.77\cdot 0.596 \cdot 12.2\cdot 9.81\cdot \cos33\degree \approx 165.7\space J$$

Answer. 165.7 J.