A horizontally directed force of 100 N holds the body on an inclined plane. What is the maximum mass of a body if the angle

| February 28, 2021 | education

A horizontally directed force of 100 N holds the body on an inclined plane. What is the maximum mass of a body if the angle of inclination of the plane is 45 degrees and the coefficient of friction is 0.5?

F = 100 N.

∠α = 45 °.

g = 9.8 m / s2.

μ = 0.5.

m -?

Let us write down the condition for finding the body at rest in vector form: m * g + N + F + Ffr = 0.

ОХ: m * g * sinα – F * cos (90 ° – ∠α) – Ftr = 0.

ОУ: – m * g * cosα – F * sin (90 ° – ∠α) + N = 0.

N = m * g * cosα + F * sin (90 ° – ∠α).

The friction force Ffr is determined by the formula: Ffr = μ * N = μ * m * g * cosα + F * sin (90 ° – ∠α).

m * g * sinα – F * cos (90 ° – ∠α) = Ftr.

m * g * sinα – F * cos (90 ° – ∠α) = μ * m * g * cosα + F * sin (90 ° – ∠α).

m * g * sinα – μ * m * g * cosα = F * cos (90 ° – ∠α) + F * sin (90 ° – ∠α).

m = F * (cos (90 ° – ∠α) + sin (90 ° – ∠α)) / g * (sinα – μ * cosα).

m = 100 N * (cos (90 ° – 45 °) + sin (90 ° – 45 °)) / 9.8 m / s2 * (sin45 ° – 0.5 * cos45 °) = 40 kg.

Answer: the body can have a maximum mass m = 40 kg.



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