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A string wraps around a wheel with mass mW = 6.5 kgand radius r = 0.15 m . The wheel is mounted on a frictionless horizontal axle at the top of an inclined plane tilted at the angle θ = 37∘ below the horizontal. The free end of the string is attached to a block with mass of mB = 3.0 kg that slides down the incline without friction. The block's acceleration while sliding down the incline is a = 3.0 m/s2 .

Draw a force diagram for the block. Use x-axis parallel to the inclined surface with the positive direction pointing downhill, and the y-axis perpendicular to the inclined surface with the positive direction pointing upward.

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Answer

given,

mass of wheel = 6.5 kg

radius = 0.15 m

inclined plane tilted at the angle θ = 37∘

mass of block = 3 kg

acceleration due to friction = 3 m/s²

acceleration in y-direction is zero

[tex]a_y = 0[/tex]

[tex]\sum {F_y} = 0[/tex]

N = mg cos 37°

N = 6.5 × 9.8 ×cos 37°

N = 50.87 N

acceleration on x- direction is given as a = 3 m/s²

[tex]mg sin 37^0 - T = ma_x[/tex]

[tex]6.5 \times 9.8 \times sin 37^0 - T = 6.5 \times 3[/tex]

T = 38.33 - 19.5

T = 18.83 N

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