PHY131 Midterm 1

University Physics with Modern Physics with Mastering Physics (11th Edition)

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PHY 131 MIDTERM 1 Version Put FULL NAME, ID#, and EXAM VERSION on the front cover of the BLUE BOOKLET! Do all problems, and show all work for partial credit ! Note: make sketches where appropriate and show your axis conventions. Do not forget units, number of significant digits, and check your results for consistency. This exam will last 1.5 hr. Success! 1. Consider the vectors A = 2.00 i – 1.00 j and B = –2.00 i + 2.00 j (20 points) a. Make an x-y sketch of vectors A , B , and C = B – A b. Calculate the magnitude of vector C and the angle it makes with the positive x -axis. c. Calculate the angle between vectors A and B 2. A late commuter student bursts running onto the Long Island train platform. Upon arrival on the platform the nearest open train door is still 32 m away from her, and the train just starts to move (from rest) away from her, with constant acceleration 0.50 m/s 2 ; she keeps running at her top speed of 6.0 m/s along the train towards the door… (20 points) a. Calculate if she will make it to the door. A simple yes/no is not accepted; prove your answer! b. Graph x ( t ) vs. t for both the student and the train in the same plot; and label the curves and axes. Indicate what types of curves you have drawn (e.g. sine, straight line, hyperbola, parabola, etc.). 3. A projectile is launched from a cliff 18.0 m above sea level, under an angle of +30° with respect to the horizontal. After 6.00 s it lands out in the water. Ignore drag and friction. In any convenient order , calculate the following (Show all work!): (20 points) a. The initial speed of the projectile. b. The maximum height (with respect to sea level) of the projectile. c. The horizontal range of the projectile. 4. A block of mass M is held on a horizontal table against a compressed horizontal (massless) spring. When released from rest, the block is launched along the tabletop and eventually comes to a stop after sliding a total distance L . The initial spring compression is x 0 , and the spring constant is k . Calculate the coefficient of kinetic friction between the block and the table top in terms of the variables M , L , k , and x 0 . (10 points) 5. A 5.00 kg block is placed on a long straight plank. One end of the plank is slowly raised, to the point where the block just begins to slip. The angle at that point is 17.0°. (30 points) a. Make a sketch showing all forces acting on the block. b. Calculate the coefficient of static friction. c. The block is observed to accelerate down the plank, reaching a speed of 1.50 m/s after slipping a distance of D = 2.25 m (measured parallel the plank). Calculate the total work done on the block over that distance. d. Calculate the work done by gravity over the distance D . e. Why is there no work done by the normal force? Argue! f. Calculate the coefficient of kinetic friction.
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Formulae and Definitions: Vectors: A = A x i + A y j + A z k Scalar Product (“Dot” Product) A · B = A x B x + A y B y + A z B z = AB cos θ A , B Kinematics: the “motion” r = r ( t ) (position) [m] velocity v d r / dt (speed | v |) [m/s] acceleration a d v / dt [m/s 2 ] Linear Kinematics for CONSTANT a v = v 0 + a t, r = r 0 + v 0 t + ½ a t 2 ; eliminating t : v 2 = v 0 2 + 2 a ·( r
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PHY131 Midterm 1 - PHY 131 MIDTERM 1 Version A Put FULL...

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