Slanted surfaces with friction: A 200 g hockey puck is launched up a metal ramp that is inclined at a 30° angle. The coefficients of static and kinetic friction between the hockey puck and the metal ramp are μ_s = 0.40 and μ_k = 0.30, respectively. The puck's initial speed is 4.9 m/s. What speed does it have when it slides back down to its starting point? A) 2.8 m/s B) 3.5 m/s C) 4.2 m/s D) 4.9 m/s

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Explanation:The correct answer is A.The work done by friction on the way up is:$$W_f = -f_kd = -\mu_k m g d \sin	heta$$The work done by gravity on the way up is:$$W_g = m g d \sin	heta$$The change in kinetic energy on the way up is:$$\Delta K = K_f - K_i = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2$$The work-energy theorem gives:$$W_f + W_g = \Delta K$$$$-\mu_k m g d \sin	heta + m g d \sin	heta = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2$$$$v_f = \sqrt{v_i^2 - 2\mu_k g d \sin	heta}$$$$v_f = \sqrt{(4.9 m/s)^2 - 2(0.30)(9.8 m/s^2)(d \sin30^\circ)}$$$$v_f = 2.8 m/s$$

Slanted Surfaces with Friction: a 200 G Hockey Puck Is