Question

The box shown on the rough ramp above is sliding up the ramp.calculate the force of friction on the box

Answer 1

We are given a box that slides up a ramp. To determine the force of friction we will use the following relationship:

$F_f=\mu N$

Where.

$\begin{gathered} N=\text{ normal force} \\ \mu=\text{ coefficient of friction} \end{gathered}$

To determine the Normal force we will add the forces in the direction perpendicular to the ramp, we will call this direction the y-direction as shown in the following diagram:

In the diagram we have:

$\begin{gathered} m=\text{ mass}_{} \\ g=\text{ acceleration of gravity} \\ mg=\text{ weight} \\ mg_y=y-\text{component of the weight. } \end{gathered}$

Adding the forces in the y-direction we get:

$\Sigma F_y=N-mg_y$

Since there is no movement in the y-direction the sum of forces must be equal to zero:

$N-mg_y=0$

Now we solve for the normal force:

$N=mg_y$

To determine the y-component of the weight we will use the trigonometric function cosine:

$\cos 40=\frac{mg_y}{mg}$

Now we multiply both sides by "mg":

$mg\cos 40=mg_y$

Now we substitute this value in the expression for the normal force:

$N=mg\cos 40$

Now we substitute this in the expression for the friction force:

$F_f=\mu mg\cos 40$

Now we substitute the given values:

$F_f=(0.2)(10\operatorname{kg})(9.8\frac{m}{s^2})\cos 40$

Solving the operations:

$F_f=15.01N$

Therefore, the force of friction is 15.01 Newtons.