Answer :
Final answer:
To determine if the construction worker will slip, compare the static friction force with the parallel component of the worker's weight on the sloped roof, using given values for mass, angle, and the coefficient of static friction.
Explanation:
To determine if a 112 kg construction worker walking down a roof with a pitch of 33 degrees to the horizontal will slip, we need to calculate the forces acting on the worker and compare the static friction force to the component of the worker's weight parallel to the slope of the roof. The coefficient of static friction (μ) between the worker's boots and the tar roof is 0.92.
The normal force (N) is given by μ∙N = mgcos(θ), where mg is the gravitational force acting on the worker (mass ∙ gravity), and θ is the angle of the roof. The force of static friction (μ∙N) that's preventing the worker from slipping is compared to the component of the worker's weight pulling him down the slope, which is mgsin(θ).
If μ∙N ≥ mgsin(θ), the worker does not slip. However, for a precise answer, numerical calculations should be done using the given values: mass (m) = 112 kg, gravity (g) = 9.8 m/s², θ = 33 degrees, and μ = 0.92. The conclusion depends on this calculation.
