AP Physics - Chapter 7 - #24

• https://openstax.org/books/college-physics-2e/pages/7-problems-exercises

• https://www.dropbox.com/scl/fo/qwrrlm0nkwtci7g8r8vsn/h?rlkey=w8esl193zfvshy2n2npt8py0f&dl=0

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Work Energy Theorem

• Conservative Forces :

  • $W_{\text{net}}=\mathrm{\Delta }KE$$W_{\text{net}} = \Delta KE$

• Non-Conservative Forces :

  • $W_{\text{non-conservative}}+W_{\text{conservative}}=\mathrm{\Delta }KE$$W_{\text{non-conservative}} + W_{\text{conservative}} = \Delta KE$

  • $W_{\text{non-conservative}}=\mathrm{\Delta }KE+\mathrm{\Delta }PE$$W_{\text{non-conservative}} = \Delta KE + \Delta PE$

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A 60.0-kg skier with an initial speed of 12.0 m/s coasts up a 2.50-m-high rise as shown in Figure 7.37. Find her final speed at the top, given that the coefficient of friction between her skis and the snow is 0.0800. (Hint: Find the distance traveled up the incline assuming a straight-line path as shown in the figure.)

• The work done by friction = negative value

  • $\therefore$$\therefore$ $W_{nc}=-f\ast d$$W_{nc} = - f * d$

  • equation 7.59

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• Let $(-f)$$\left(-f\right)$ :

  • be replaced by $(-\mu \ast m\ast g\ast cos(\theta ))$$\left(- \mu * m * g * cos(\theta)\right)$

• Let $d$$d$ :

  • be replaced by $\left(\frac{h}{sin(\theta )}\right)$$\left(\frac{h}{sin(\theta)}\right)$

• Trig Identity Substitution :

• Isolate the term with $v_f$$v_f$ :

• Simplify the right-hand side :

• Divide Each Term by $(\frac{1}{2}\ast m)$$\left( \frac{1}{2} * m \right)$ :

• Simplify :

• Combine and Rearrange :

• Take Square Root of Both Sides :

• Plug In Numbers :