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Chapter $6,$ Team Problem $1$ WORKSHEET SOLUTION $[$T$1][$Easy$,$ Team, Worksheet$]$ A Runaway Sled You and your team are on the top of an icy slope that has a steep grade $($i$.$e$.,$ angle of ascent$)$ of $24\mathrm{.}0$o$,$ and need to pull up a heavy sled loaded with supplies. You fasten a pulley into the ice at the top of the slope through which you thread a $150\mathrm{.}0$ft rope $($which is just long enough to reach the sled$)$ and tie it to the sled. The rope has a strict tension rating of $450\mathrm{.}0$ lbs and a warning sticker on one end claims that it will break if this limit is exceeded by just $10\mathrm{.}0$ lbs $.$ Lined up like a tug$-$o$-$war team, you and six others in your group steadily pull on the rope with a nearly constant force, resulting in a constant rate of ascent. However, after exactly $45\mathrm{.}0$ s of pulling, the rope suddenly snaps, and the sled and its crucial supplies plummet down the hill and disappear into a snowbank. You measure the length of rope pulled through the pulley before it failed to be $85\mathrm{.}0$ ft $.($a$)$ Neglecting friction, how fast was the sled going when it reached the bottom of the slope? $($b$)$ For the next attempt to pull the sled up the slope, you get a stronger rope and want to use a motor$-$driven winch $($it was tiring work by hand$).$ What should be the minimum power rating of the motor $($in horsepower$)$ in order that the winch pulls the sled at the same rate as vour team had been pulling it by hand? $($Note: $1$ horsepower $=745\mathrm{.}7$ watts$).$

$[1]$ What is the approximate tension in the rope when it breaks?

$[2]$ Draw the free$-$body diagram of the forces acting on the sled as it is being pulled up the slope at a constant rate.

$[3]$ What is the total work done by the team just before the rope breaks?

$[4]$ What is the mass of the sled?

$[5]$ What is the speed of the sled at the bottom of the hill?

$[6]$ What is the power output of the team $($in watts$)$ while they are pulling the sled up the slope?

$[7]$ What should be the minimum power rating of the motor $($in horsepower$)$ in order that a