Answer :
Substituting the given values of m, g, and θ into the equation, we can calculate the coefficient of static friction.
μ = 182 N / (m * g * cos(θ))
To find the coefficient of static friction, we need to consider the forces acting on the block on the inclined plane. The force pushing downhill, parallel to the slope, is the maximum force that can be exerted without causing the block to start moving. This force is given as 182 N.
The force pushing downhill can be resolved into two components: the force of gravity acting vertically downward and the force of static friction acting parallel to the slope. Calculations for the gravitational pull include:
F_gravity = m * g
where m is the mass of the block (59.1 kg) and g is the acceleration due to gravity (approximately 9.8 m/s²).
For the static friction force:
F_friction = μ * N
where μ is the coefficient of static friction we need to find, and N is the normal force exerted on the block by the slope.
The normal force can be calculated as:
N = m * g * cos(θ)
where θ is the angle of elevation of the slope (26.3°).
Since the block is in equilibrium, the force pushing downhill is equal to the force of static friction:
F_push = F_friction
Substituting the expressions for F_push and F_friction, we have:
182 N = μ * N
182 N = μ * (m * g * cos(θ))
Now we can solve for the coefficient of static friction (μ):
μ = 182 N / (m * g * cos(θ))
Substituting the given values of m, g, and θ into the equation, we can calculate the coefficient of static friction.
Make sure to use consistent units and convert angles to radians if necessary.
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