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Unformatted text preview: Thevalingam, Donald – Homework 7 – Due: Nov 6 2006, midnight – Inst: Eslami 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. You want to master physics? Solve more problems. You want to solve problems but you cannot? Ask for help after you think about the problem. You do not want to learn physics? Tough luck! 001 (part 1 of 2) 10 points A car of mass m , initially at rest at time t = 0, is driven to the right as shown along a straight, horizontal road with the engine caus- ing a constant force ~ F to be applied. While moving, the car encounters a resistance force equal to- k~v , where ~v is the velocity of the car and k is a positive constant. Use a dot to represent the center of mass of the car. And on the figure, draw and label vectors to represent all the forces acting on the car as it moves with a velocity ~v to be the right. car v g O + Determine the horizontal acceleration of the car. 1. a = F + k m v 2. a = k v m 3. a = F- k m v 4. a = F + k v m 5. a = F- k v m correct Explanation: F k v N mg F net = m a . But F net = F- k v , so F- k v = m a a = F- k v m . 002 (part 2 of 2) 10 points Derive the equation expressing the velocity of the car as a function of time t . 1. v = F k ‡ 1 + e- k t/m · 2. v = F k ‡ 1- e- k m/t · 3. v = F k ‡ e- k t/m · 4. v = F k ‡ 1 + e- k m/t · 5. v = F k ‡ 1- e- k t/m · correct Explanation: a = d v dt Using the equation from the previous part d v dt = F- k v m (1) Re-arrange and integrating Z d v F- k v = Z 1 m dt (2) Let : u = F- k v du =- k dv- 1 k Z d u u = Z 1 m dt ln( F- k v )- ln C =- k m t , Thevalingam, Donald – Homework 7 – Due: Nov 6 2006, midnight – Inst: Eslami 2 where C is a constant. v = 1 k ‡ F- Ce- k t/m · . To evaluate C , use initial conditions t = 0, v = 0: C = F , so v = F k ‡ 1- e- k t/m · Equation (2) can also be integrated using limits 0 and v for the left-hand side and 0 and t for the right-hand side to obtain the same answer for full credit....
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