The roof on a house rises 1.50 m over a horizontal diestance of 3.50 m. A 72.9-kg roofer stands on the roof. Is the frictional force that keeps the roofer from slipping equal in magnitude to F perpendicular or F paralell?
What is its magnitude?
Neither. Friction force is parallel, but it is equal to mu*Fperpendicular which is mu*mg*CosineTheta
cosine theta= 3.5/(sqrt(1.5^2+3.5^2))
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To determine whether the frictional force that keeps the roofer from slipping is equal in magnitude to the perpendicular force (F perpendicular) or the parallel force (F parallel), we need to understand the components of the roofer's weight.
1. Vertical Weight Component (F perpendicular):
The weight of the roofer can be resolved into two components: the perpendicular force, acting vertically downward, which is equal to the roofer's weight (W = m * g), where m is the mass of the roofer (72.9 kg) and g is the acceleration due to gravity (9.8 m/s^2).
F perpendicular = W = m * g = 72.9 kg * 9.8 m/s^2
2. Horizontal Weight Component (F parallel):
The horizontal component of the roofer's weight is responsible for creating the frictional force. It can be calculated using trigonometry, as the roof rises at an angle.
The given information tells us that the roof rises 1.50 m over a horizontal distance of 3.50 m. Therefore, the angle of inclination can be determined as:
sin(angle) = opposite/hypotenuse = 1.50 m / 3.50 m
To find the angle, we can use the inverse sine function:
angle = sin^(-1)(1.50 m / 3.50 m)
Now we can find the horizontal weight component (F parallel) using this angle and the roofer's weight:
F parallel = W * sin(angle)
Once we have both the F perpendicular and F parallel, we can compare their magnitudes.
Finally, to calculate the magnitude of the frictional force, we can use either F perpendicular or F parallel, as the frictional force will be equal in magnitude to either of them.
To summarize:
- Calculate the perpendicular weight component (F perpendicular) using the formula: F perpendicular = m * g.
- Calculate the angle of inclination using the given information and trigonometry: angle = sin^(-1)(1.50 m / 3.50 m).
- Calculate the horizontal weight component (F parallel) using the angle and the roofer's weight: F parallel = W * sin(angle).
- Compare the magnitudes of F perpendicular and F parallel to determine if they are equal.
- Use either F perpendicular or F parallel as the magnitude of the frictional force.