Physics_7A_-_Spring_2001_-_Stahler_-_Midterm_1

# Physics_7A_-_Spring_2001_-_Stahler_-_Midterm_1 - UNIVERSITY...

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Unformatted text preview: UNIVERSITY OF CALIFORNIA AT BERKELEY Physics 7A w Section 3 (Stahler) Spring 2001 FIRST MIDTERM EXAMINATION } Please do all your work on the front and back pages of this exam. Write your name on all pages. You should ﬁnd these problems to be at the same level as the homework — so relax! YOu must attempt all three problems. If you become stuck on one, go on to another and return to the ﬁrst one later. You should show all your reasoning, since partial credit will be allotted. Remember to circle your ﬁnal answer. 3< Problem 1 (35 points) The motion of a point mass is given by fl/Y Here= w is a constant and t is the time. We are interested in t 2 0. ‘ 3E9}; 869% CH): RCii‘fOJéU7l» 0 =' RC1 +605a’+) coda/t) (b) Write an algebraic expression for 17(t), the vector velocity as a function of time. Use the notation i and 5, respectively, to denote the :c- and y-unit vectors. z:(t) = R [out + sin (to 15)] |' y(t) = R [1 + cos (w (a) What is the ﬁrst time that y = 0? r}: (c) What is the ﬁrst time that Vr = 0? {(1) Write an algebraic expression for if (t), the vector acceleration as a function of time. 7r: Mix- by i. {j + f3 (it _ M40 +WCOJMJ); ##w SI‘ﬂagﬂ/J 7/" if t ~ I? (war 31 2mm) @ a 1 + (£05 Problem 2 (35 points) A block-of mass m is on an inclined plane, with inclination angle 6. It is prevented from sliding down the plane by application'of a horizontal force F and by friction between the block and plane. Let us be the coefficient of static friction. (a) Draw a free-body diagram for the block, carefully labeling all of the forces. (b) After choosing a convenient set of coordinate axes, apply Newton’s Second Law in the two orthogonal directions. (c) What is the minimum horizontal force needed to prevent sliding? Problem 3 (30 points) T .(_. (.53 Suppose you are looking out your window, which has a height h and is located some distance above the ground. A friend on the groand tosses 'up a ball, which passes in front of the window along a curved path, as shown. Using a stopwatch, you ﬁnd that it takes a time T for the ball to do this. (a) What is Voy, the hall’s vertical velocity when you ﬁrst see it? (b) How long after the ball passes above the window wi]l_it reach its maximum height? _ _. as w m In “st/.9»- big“ U0y50°A7;”q'g/‘1/sz h ,4. :2.“ V013 I, L: dime. 'iﬁﬂ Now I £30m 6‘4"???" ti}! t: 75% Raﬁ/max 75(0/‘4 fag! {if Wew ...
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