A 521 N box is sitting on a 33.5° incline. Find the force of gravity parallel (Fp) to the surface of
the incline, and the force of gravity perpendicular to the surface of the incline (FN).
a. If the coefficient of static friction is 0.227, find the Ff
.
b. Will the box slide down the hill?
To find the force of gravity parallel (Fp) to the surface of the incline and the force of gravity perpendicular to the surface of the incline (FN), we need to break down the weight of the box into its components.
1. Force of gravity parallel (Fp) to the surface of the incline:
Fp = mg sin(θ)
where m is the mass of the box and g is the acceleration due to gravity (9.8 m/s^2). In this case, the weight of the box is given as 521 N, which is equal to mg. So, we have:
Fp = (521 N) * sin(33.5°)
2. Force of gravity perpendicular to the surface of the incline (FN):
FN = mg cos(θ)
Similarly, we can calculate FN using the given weight of the box:
FN = (521 N) * cos(33.5°)
Now, let's move on to finding the force of friction (Ff) using the coefficient of static friction (μs = 0.227):
a. Force of static friction (Ff):
Ff = μs * FN
Substitute the value of FN into the formula:
Ff = 0.227 * [(521 N) * cos(33.5°)]
b. To determine if the box will slide down the hill, we compare the force of static friction (Ff) with the force of gravity parallel to the incline (Fp). If Ff is less than or equal to Fp, the box will not slide down the hill. If Ff is greater than Fp, the box will slide down the hill.
Therefore, compare the calculated values of Ff and Fp to determine if the box will slide down the hill.