Unit $3$ section $3$ problems $$ equilibrium and elasticity

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A $35$ kg child is supported on a $55$ kg plank $($of length $80\mathrm{.}0$ cm$)$ by his parents on the left and right end of the plank. The child is located at $20\mathrm{.}0$ cm from the left edge. Find the forces exerted by each parent.

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A $5\mathrm{.}00$ m long diving board is supported by $2$ pillars $($one on the left end and the

$$ other $1\mathrm{.}50$ m away from the left end$).$ Find the forces exerted by the pillars when a$$

$90\mathrm{.}0$ kg diver stands at the far right end of the board.

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A cat walks along a plank $($length $=4\mathrm{.}00$ m and mass $=7\mathrm{.}00$ kg$).$ The plank is

$$ supported by $2$ sawhorses $($one $\mathrm{.}440$ m from the left end and $1\mathrm{.}50$ m from the right$$

$$ end$).$ When the cat reaches the right end, the plank just begins to tip. What is the

$$ mass of the cat?

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A person carries a $21$ kg suitcase in one hand. If the upper arm bone $($length $=33$

$$ cm and area $=5\mathrm{.}2$ x $10-4$ m$2)$ supports the suitcase, by what amount will this bone$$

$$ stretch? Assume a modulus of steel for the bone.

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A helicopter is using a steel cable to lift a $2100\mathrm{.}0$ kg jeep. The unstretched length$$

$$ of the cable is $16$ m and its radius is $5\mathrm{.}0$ x $10-3$ m$.$ By what amount does the cable$$

$$ stretch when the jeep is hoisted upward at a rate of $1\mathrm{.}5$ m$/$s$2?$

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