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Some sliding rocks approach the base of a hill with a speed of 16.0 m/s . The hill rises at 36.0 ∘ above the horizontal and has coefficients of kinetic and static friction of 0.390 and 0.620, respectively, with these rocks. Start each part of your solution to this problem with a free-body diagram.

(a) Find the acceleration of the rocks as they slide up the hill.

User Aquila
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Final answer:

To find the acceleration of rocks sliding up a hill, subtract the frictional force from gravity's component along the slope and apply Newton's second law. Use the given angle and coefficient of kinetic friction in the equation a = g(sin θ - µk cos θ) to calculate the value.

Step-by-step explanation:

The question is asking to find the acceleration of sliding rocks as they slide up a hill with a given angle and coefficients of friction. To begin with, a free-body diagram would show the forces acting on the rocks: the force of gravity, the normal force perpendicular to the slope, and the frictional force opposing motion up the incline. Using Newton's second law, we can set up the equation for net force in the direction along the slope, which would be the force of gravity down the slope (mg sin θ) minus the frictional force (μk mg cos θ), where 'm' is the mass of the rocks, 'g' is the acceleration due to gravity, θ is the angle of the slope, and μk is the coefficient of kinetic friction. Solving for 'a', we get:

a = g(sin θ - μk cos θ)

Plugging in the given values for g (9.8 m/s²), the angle (36 degrees), and the coefficient of kinetic friction (0.390), we calculate the acceleration.