The minimum pulling force when the angle is 0 degrees = 0.675 kN
The minimum pulling force when the angle is 30 degrees = 0.54 kN
Given data :
Radius of roller = 25 cm
Height of curb = 5 cm
Force of Lawn roller = 900-N
First step : Determine angle made by the reaction force with the vertical axis
cos ∝ = ( 25 - 5 ) / 5
= 20 / 5 = 4
∴ ∝ = cos⁻¹ 4 = 36.87°
Step two : Determine the minimum pulling forces
applying the horizontal force balance equation
∑Fₓ = 0
Fcos ∅ + R sin ∝ = 0 --- ( 1 )
where R ( vertical force balance equation ) = ( W - Fsin∅ ) / cos ∝
Back to equation ( 1 )
The horizontal force balance equation Fₓ becomes
F = ( W sin ∝ ) / cos ( ∅ - ∝ )
Final step :
A ) When the angle ( ∅ ) = 0 degrees
F = ( 900 * sin 36.87 ) / cos ( 0 - 36.87
= 675 N = 0.675 kN
B) When the angle ( ∅ ) = 30 degrees
F = ( 900 * sin 36.87 ) / ( cos ( 30 - 36.87 )
= 540 N = 0.540 kN
Hence we can conclude that the minimum pulling force when the angle is 0 degrees = 0.675 kN and The minimum pulling force when the angle is 30 degrees = 0.54 kN
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