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Q 29PE

Expert-verifiedFound in: Page 318

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

**Question: A device for exercising the upper leg muscle is shown in ****Figure ****, together with a schematic representation of an equivalent lever system. Calculate the force exerted by the upper leg muscle to lift the mass at a constant speed. Explicitly show how you follow the steps in the Problem- Solving Strategy for static equilibrium in ****Applications of Statistics,**** ****Including Problem-Solving Strategies****.**

The force exerted by the upper leg muscle is 1715 N.

A force is an external factor that can change the rest or motion of a body. It has a size and a general direction.

The diagram for the leg muscles is shown below:

The perpendicular distance of the weight from the pivot point is ${\text{r}}_{\perp}=\text{35}\text{cm}$.

The perpendicular distance of the applied force from the pivot point is ${{\text{r}}_{\perp}}^{\text{'}}=\text{2.0}\text{cm}$.

As the upper leg muscle lifts the mass at a constant speed, the net force is zero. So, we can write,

$\begin{array}{rcl}T& =& mg\\ & =& 10\times 9.8\\ & =& 98\text{N}\end{array}$

The torque about the pivot point is zero. So, we can write,

$\begin{array}{rcl}{F}_{M}{r\text{'}}_{\perp}-T{r}_{\perp}& =& 0\\ {F}_{M}& =& \frac{T{r}_{\perp}}{{r\text{'}}_{\perp}}\\ & =& \frac{98\times 35}{2}\\ & =& 1715\text{N}\end{array}$

Hence, the force is 1715 N.

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