sing the variables from the problem statement together with the acceleration due to gravity, g , write an equation for the magnitude of the acceleration of the system. hint: based upon the numeric choices, block 1 will accelerate up the incline while the suspended block, block 2, accelerates vertically downward.

The equation for the magnitude of the acceleration of the system is equals to the

a = g (m₂ - m₁μ꜀ cosθ - m₁sinθ )/(m₁ + m₂ ).

We have, two blocks with masses say m₁ = 3.8 kg and m₂ = 8.6 kg inclined on the plane at angle θ=39° above the horizontal. Also, cofficient of friction, μ=0.39. According to problem, In case of block 1 , accelerate up the inclined plane, Then forces along y-axis,

Net force during vertical motion = 0

=> Fₙ - m₁gcosθ = 0 --(1)

On horizontal direction,

Again net force = 0

=> T - f꜀ - m₁gsinθ = m₁a --(2) ( using Newton's second law)

For block 2, Vertical motion

So, net vertical force = 0

=> - T + m₂g = m₂a --(3)

Now, f꜀ = μ꜀ Fₙ= μ꜀ m₁g cosθ

so, T - μ꜀ m₁g cosθ - m₁gsinθ = m₁ a --(4)

Using the equation (4) and (3), we have to determine the equation for acceleration, a.

Adding (3) from (4),

m₁ a + m₂a = -μ꜀ m₁g cosθ - m₁gsinθ + m₂g + T - T

=> (m₁ a + m₂a) = g ( -m₁cosθ - m₁ sinθ + m₂)

=> a ( m₁ + m₂ ) = g (-m₁μ꜀ cosθ - m₁ sinθ + m₂)

=> a = g (- m₁μ꜀ cosθ - m₁sinθ + m₂)/(m₁ + m₂ )

by plugging all the above values we can calculate the magnitude of acceleration.

Hence, required equation is a = g (m₂ - m₁μ꜀cosθ - m₁sinθ)/(m₁ + m₂) .

To learn more about inclined plane, refer:

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Complete question:

Referring to the image to the above figure , the mass of block 1 is m1=3.8 kg while the mass of block 2 is m2=8.6 kg. The coefficient of friction between m1 and the inclined surface is μ=0.39. The inclined surface is at an angle θ=39∘ above the horizontal. Using the variables from the problem statement together with the acceleration due to gravity, g , write an equation for the magnitude of the acceleration of the system. hint: based upon the numeric choices, block 1 will accelerate up the incline while the suspended block, block 2, accelerates vertically downward.

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