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the coefficient of kinetic friction between the block and the inclined surface of the figure below is 0.3 and the coefficient of static friction is 0.9. each block is 1 kg. the pulley is frictionless and the string is massless. what is the magnitude of the acceleration of the blocks if the system is released from rest?

User Carl
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Final answer:

The magnitude of the acceleration of the blocks, when the system is released from rest, is 9.8 m/s².

Step-by-step explanation:

The magnitude of the acceleration of the blocks can be determined by analyzing the forces acting on the system. Since the pulley is frictionless and the string is massless, the tension in the string will be the same on both sides. Let's denote the acceleration of the blocks as 'a'. Applying Newton's second law to each block, we get:

m₁g - μs₁m₁gcosθ - T = m₁a

μk₂m₂g - T = m₂a

where m₁ and m₂ are the masses of the blocks, μs₁ is the coefficient of static friction between the block and the inclined surface, μk is the coefficient of kinetic friction, g is the acceleration due to gravity, and θ is the angle of the inclined surface.

Given that μk = 0.3, μs₁ = 0.9, m₁ = m₂ = 1 kg, and θ = 0 (since the system is released from rest), we can solve the equations to find the acceleration:

m₁g - μs₁m₁gcosθ - T = m₁a

μk₂m₂g - T = m₂a

Substituting the values, we get:

(1)(9.8) - (0.9)(1)(0) - T = (1)a

(0.3)(1)(9.8) - T = (1)a

9.8 - T = a

2.94 - T = a

So, the magnitude of the acceleration of the blocks when the system is released from rest is 9.8 m/s².

User BiagioF
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