Question

A block is at rest. The coefficients of static and kinetic friction are s = 0.81 and k = 0.69, respectively. The acceleration of gravity is 9.8 m/s^2.

Required:
a. What is the largest angle which the incline can have so that the mass does not slide down the incline?
b. What is the acceleration of the block down the incline if the angle of the incline is 44°?

Answer 1

Step-by-step explanation:

a ) The angle required = angle of repose = θ

Tanθ = .81

θ = 39⁰

b ) when angle of incline θ = 44

Net force on the block = mg sinθ - μ mg cosθ where μ is coefficient of kinetic friction

acceleration = gsinθ - μ g cosθ

= 9.8 ( sin44 - μ cos44 )

= 9.8 ( .695 - .69 x .72 )

= 9.8 ( .695 - .497 )

= 1.94 m /s²