We are given a box that slides up a ramp. To determine the force of friction we will use the following relationship:
Where.
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:
Adding the forces in the y-direction we get:
Since there is no movement in the y-direction the sum of forces must be equal to zero:
Now we solve for the normal force:
To determine the y-component of the weight we will use the trigonometric function cosine:
Now we multiply both sides by "mg":
Now we substitute this value in the expression for the normal force:
Now we substitute this in the expression for the friction force:
Now we substitute the given values:
Solving the operations:
Therefore, the force of friction is 15.01 Newtons.
