A wheel of radius 1 m is being lifted over a cerb of height 0.5 m by applying a horizontal force of 50 N on the axle of radius 0.2 m.
(a) Calculate the weight of the wheel.
(b) If the force is applied in other direction at another point of the wheel, the force needed can be reduced. Find the minimum force required to lift the wheel.

Question

A wheel of radius 1 m is being lifted over a cerb of height 0.5 m by applying a horizontal force of 50 N on the axle of radius 0.2 m.
(a) Calculate the weight of the wheel.
(b) If the force is applied in other direction at another point of the wheel, the force needed can be reduced. Find the minimum force required to lift the wheel.

lollylau · Answer

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sachintha · Answer

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sachintha · Answer

$\sf\underline{Moment~of~a~couple}$

$\begin{array}{ccc}&R\cdot cos\;\theta\times0.5&=&50\times0.2\&R\times\large\frac{0.86}{1}\normalsize\times0.5&=&50\times0.2\&R&=&23.3N\end{array}$

$\sf\underline{Resolution~of~forces}$

$\begin{array}{ccc}&R\cdot sin\;\theta&=&mg\&23.3N\times\large\frac{0.5}{1}&=&W\&W&=&11.65N\end{array}$

perl · Answer

@Sachintha Can you explain how you derived R cos theta *0.5.
I presume you are calculating Moment = F*distance = F cos theta
R is the reaction force when the wheel presses against the curb?

sachintha · Answer

Well, tbh I don't know whether I have done it correctly. Just gave it a try. Since the horizontal resolution of the resultant force is R cos theta, I used moments of a couple of forces to calculate R. Then I resolved R for vertical position(taking upward direction as positive) and solved for weight.