physics solved questions

NAME: _ Physics 116 Quiz #3 TA: John Read 20 points You have 30 minutes to complete the following problems. Please write clearly and explain your reasoning. You may define new quantities, but yow answers should be in terms of given quantities only. You must show your work to receive full credit. Problem 1 [14 points) A ball ofmass m is thrown upwards through a viscous material that subjects the ball to a resistive viscous force with magnitude F, = C v (C is a constant). The ball then begins falling back towards the Earth.. (a) [2 points) Draw a diagram of the ball when it is traveling upwards and when it is traveling downwards Label the upwards direction positive in both cases and include the following in yow diagrams: (i) all forces acting on the ball, (ii) the velocity ofthe ball Upwards Travel Downwards Travel • (b) [6 points) Now consider the ball's motion when it is falling back down toEarth. Assume that the ball starts from rest and use separation of variables to fwd the speed of the ball as a function oftime (c) [4 points) Integrate your expression from part (a) to find the height of the ball as a function of time. The ball reaches a height ofYo before it begins to fall. (d) [2 points) Consider short times, specifically when t « (m I C) and expand your function from part (c) in a Taylor series to show that the time dependence ofthe gosition at short times is exactly what you already knew: y (t «(m/C» > - (112) g t [Hint: your function from part (c) has three terms: constant + linear term + exponential term. Expand the exponential term to three terms and plug it back into your function in part (c)] To check your answer: y (t« (m/C) ) = Yo - (m2 gtc;2) - (112) g • • Problem 2 [6 points) (a) [4 points) A block of mass m is attached to one end ofa spring (spring constant k) and can oscillate on a frictionless horizontal surface. Considering the horizontal oscillations, fmd a general solution for the block's x position as a function oftime +x ----c~ k (b) [2 points) The block is pulled to a position ofc and then released with speed v. Use these initial conditions to solve for the position ofthe block. (vs.,t/.''1U )