For the remainder of questions, assume that the slide does have kinetic friction

Question

For the remainder of questions, assume that the slide does have kinetic friction (mu_k 0). Which of the following equations gives W_friction on Adam, triangle 1 for JUST the downward trip (going down triangle 1), assuming that Adam has mass m? - mu_k mgL_1 sin theta_1 + mu_k mg L_1 sin theta_1 - mu_k mg L_1 cos theta_1 +mu_k mg L_1 cos theta_1 -mu_k mg L_1 Present your reasoning. Now derive an equation for W_friction on Adam, 2, the work done by friction during Adam's slide up the smaller ramp (Triangle 2)? Present your reasoning. Let W_frinction on Adam be the total work done by sliding friction on Adam, from top of the larger ramp to the top of the smaller ramp. (It will be the sum of the answers to the last two questions) Which of the following equations accurately states the conservation of energy for Adam's motion from the start to the end, the top of the smaller ramp? (v is his speed at the top of the smaller ramp) Which of the following equations accurately states the conservation of energy for Adam's motion from the start to the end, the top of the smaller ramp? (v is his speed at the top of the smaller ramp) mgh_1 = 1/2 mv^2 + mgh_2 + W_by friction on Adam mgh_1 = 1/2 mv^2 + mgh_2 - W_by friction on Adam Neither of the above two equations gets it right! Briefly, present your reasoning. (If your answer is C, what should it be and whty?)

Explanation / Answer

5) C

W = F.s = -umgCos theta1 *L1    negative because friction opposite to the direction of motion,

F=uN=mgCos theta1

6)W = F.s

W= -umg Cos theta2 *L2

negative because friction opposite to the direction of motion,F=uN=umgCos theta2,

as N is normal raction =mgCos theta2

7)B,

by energy conservation

Initial Potential Energy = final potential energy + kinetic energy gained + energy lost due to friction

mgh1 = mgh2 + 0.5mv2 + umg Cos theta2 *L2   + umg Cos theta2 *L2  

mgh1 = mgh2 + 0.5mv2 - (- umg Cos theta2 *L2   - umg Cos theta2 *L2 )

mgh1 = mgh2 + 0.5mv2 - Wfriction    as work done by friction is negative

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