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midterm1-practice

# midterm1-practice - Name(print clearly Signature ID Number...

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Unformatted text preview: Name (print clearly!): Signature: ID Number: Discussion TA: Discussion Day: Hour: Date: Midterm 1 Physics 7C Tait (version 1) Closed book; you may use a calculator, but no other electronic devices, including cell phones, iPods, etc. For full credit, you must show your reasoning and/or work in obtaining the solution. Score: Useful(?) Formulae – Midterm 1 Kinematics A particle under constant acceleration ￿ with initial position ￿0 and vea r locity ￿0 at time t = 0 has position and velocity at later time t: v ￿ (t) = ￿0 + ￿ t v v a 1 ￿(t) = ￿0 + ￿0 t + ￿ t2 r r v a 2 A particle moving with uniform speed v in a circle of radius R feels centripetal acceleration of magnitude ac : v2 ac = R Dynamics ￿ A particle of mass m feeling external forces F experiences acceleration ￿ : a 1 ￿￿ ￿= a F m Forces Force of gravity: F = m￿ . At the surface of the Earth, |￿ | = 9.8 m/s2 . g g Force of kinetic friction: F = µK |￿ | where ￿ is the normal force n n perpendicular to the surface responsible for the friction. Force of static friction: F ≤ µS |￿ | where ￿ is the normal force n n perpendicular to the surface responsible for the friction. ￿ Force of ﬂuid/air resistance (1): F = −b￿ where b depends on the v object and the medium through which it moves. ￿ Force of ﬂuid/air resistance (2): |F | = 1 DρAv 2 where D is the drag 2 coeﬃcient, ρ is the density of the medium, A is the cross-sectional area of the object and v is its speed. 1. A spider of mass 1.00 g hangs from two equal length strands of spidersilk attached to the ceiling. The strands are attached to the ceiling at points 5.0 cm apart from each other. The strand on the left makes an angle of 30◦ with respect to the horizontal and the strand on the right makes an angle of 60◦ with respect to the horizontal. (See ﬁgure below). (A). Draw a free-body diagram for the spider. (B). If the spider is stable and unmoving, determine the tensions in each of the strands of spidersilk. (C) A sudden wind blows horizontally from the left to the right (see the ﬁgure), exerting a force which breaks one of the two strands of spidersilk by exceeding its maximum tension. Explain why it is the strand on the left that breaks. (D) Startled by its web breaking, the spider lets go of the still attached strand and falls to the ﬂoor, with the broken strand acting like a parachute. We will make the approximation that it reaches terminal velocity immediately. If the spider takes 1 s to fall 3.5 m to reach the ﬂoor below, compute the coeﬃcient b in the expression for the force due to the air resistance, ￿ F = −b￿ . v 2. A skier (of mass 70.0 kg) is at the top of a ski run, which for our purposes is a smooth plane inclined at an angle of 20◦ with respect to the horizontal. From where the skier stands at the top of the run, it is a distance of 200.0 m along the run to its end at the bottom. Do not ignore the force of friction between her skis and the snow. (A). Draw the free-body diagram for the skier. (B). If the skier is initially stable (not moving), compute the minimum coeﬃcient of static friction between the skis and the snow. (C). The skier pushes oﬀ and starts sliding down the hill (but with an initial speed of close to zero). The coeﬃcient of kinetic friction between skis and snow is µK = 0.01. How long does it take her to reach the bottom of the run? (D) What is her speed when she reaches the bottom of the run? 3. A merry-go-round is a large disk which rotates at a constant angular speed such that any point on its surface takes a time T to make a single revolution. (A) Consider a child of mass m standing on the merry-go-round at radial distance R from its center. At any given instance in time, describe the child’s velocity (both magnitude and direction) in terms of R and T as measured by an observer standing on the ground next to the merry-goround. (B) For an observer on the merry-go-round standing next to the child (so measuring no relative velocity or acceleration between the child and himself), what ﬁctitious force (magnitude and direction) accounts for this observer’s observations? (C) If the period of the merry-go-round is T = 3.00 s and the coeﬃcient of static friction between the child’s shoes and the surface of the merry-goround is µS = 0.700, determine which values of the radius allow the child to stand easily in equilibrium, and for which values the child slips oﬀ of the merry-go-round and goes ﬂying. ...
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