Question

Two Masses, a Pulley, and an Inclined Plane

(Eigure 1)Block 1, of mass m₁ = 0.700 kg, is connected
over an ideal (massless and frictionless) pulley to block
2, of mass m₂, as shown. For an angle of 30.0°
and a coefficient of kinetic friction between block 2 and
the plane of 0.350, an acceleration of magnitude a =
0.350 m/s² is observed for block 2.
Part A
Find the mass of block 2, m₂.
Express your answer numerically in kilograms.
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[5] ΑΣΦ
m₂ -0.350
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Answer 1

The mass of block 2 is approximately 0.457 kg

Mass of block 1 (m₁= 0.700 kg

Angle of the inclined plane (θ)= 30.0°

Coefficient of kinetic friction (μ_k) = 0.350

Acceleration of block 2 (a) = 0.350 m/s²

Normal force (N)= m₂g * cosθ). we will apply Newton's second law to each block:

Block 1:

ΣF_y = m₁a_y

T - m₁g = m₁ * 0

T = m₁g

Block 2:

ΣF_x = m₂a_x

m₂g * sinθ - f = m₂a

m₂g * cosθ - N = 0 (

we Combine the equations:

m₂g * sinθ - μ_k * (m₂g * cosθ) = m₂a

m₂g * (sinθ - μ_k * cosθ) = m₂a

m₂ = a / (g * (sinθ - μ_k * cosθ))

m₂ = 0.350 m/s² / (9.81 m/s² * (sin 30.0° - 0.350 * cos 30.0°))

m₂ = 0.457 kg