Minimum Force (roller over step)

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SUMMARY

The discussion focuses on calculating the minimum force (P) required to pull a roller over a step on an inclined plane with an angle of 12° and a roller radius of 0.685m. The initial calculations provided by the user resulted in a force of 255.17 N, which was later identified as incorrect. The correct equation to consider includes the term P sin(θ), indicating that the user overlooked this component in their moment force balance. The correct approach involves ensuring all forces acting on the roller are accounted for in the equilibrium equation.

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On an inclined plane (φ = 12°), calculate the minimum force P required to pull the roller over the step. The radius of the roller, r = 0.685m

My attempt

The sum of the Moment force about the system = 0

0 = mg(sin(φ)*(r-h) + mg(cos(φ)*√[r2-(r-h)2] - P(cos(θ)*r-h)

P(cos(θ)*r-h) = mg(sin(φ)*(r-h) + mg(cos(φ)*√[r2-(r-h)2]

P(cos(32.9)*0.575m) = (26kg)(9.8)(sin(12)*(0.575) + (26)(9.8)(cos(12)*√[0.6852 - (0.575)2]

0.483*P = 30.46 + 92.79

P = 255.17



This answer appears to be wrong. Any help on this? I can't seem to figure out where I went wrong.
 
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BMcC said:
0 = mg(sin(φ)*(r-h) + mg(cos(φ)*√[r2-(r-h)2] - P(cos(θ)*r-h)
I guess you meant ##0 = mg\sin(φ)(r-h) + mg\cos(φ)\sqrt{r^2-(r-h)^2} - P\cos(θ)(r-h)##.
What about P sin(θ)?
 

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