Physics 50 Winter 2018 Final Exam

Transcription

1 Physics 50 Winter 018 Final Exam Name: Mar 9, 018 Please show your work! Answers are not complete without clear reasoning. When asked for an expression, you must give your answer in terms of the variables given in the question and/or fundamental constants, like g. Answer as many questions as you can. Do not forget to include appropriate units when giving a number as an answer. Calculators are allowed. If you detach any pages from the test, please write your name on every loose page. If you are not asked for a hypothesis, you do not need to give one. g = 9.8 m/s Equations v f = v 0 + at v avg = v 0+v f x = v 0 t + 1 at x = v f t 1 at v f = v 0 + a x x = v avg t ω = π T v = πr T a c = v r f k = µ k n f s,max = µ s n F = kx K = 1 mv U g = mgy U s = 1 kx W = F d P = W = F v t p = mv Trigonometric Identities sin θ + cos θ = 1 sin(θ) = sin(θ) cos(θ). cos(θ) = cos θ sin θ sin(α ± β) = sin α cos β ± cos α sin β cos(α ± β) = cos α cos β sin α sin β cos α cos β = 1 [cos(α β) + cos(α + β)] sin α sin β = 1 [cos(α β) cos(α + β)] sin α cos β = 1 [sin(α + β) + sin(α β)] sin ( θ + π ) = cos θ cos ( θ + π ) = sin θ sec θ := 1 cos θ csc θ := 1 sin θ cot θ := 1 tan θ 1

2 1. [11pts total] In a grocery store, you push a 13.0-kg shopping cart with a force of 11.0 N. If the cart starts at rest, how far does it move in 1.60 s? HYPOTHESIS: [1pt] SKETCH: [3pts] SOLUTION: [6pts] ANSWER REASONALE / AGREES WITH HYPOTHESIS?: [1pt]

3 . [1pts total] A bicycle moves according to the velocity-versus-time graph shown. (a) Find the average acceleration of the bicycle during each of the segments of the motion A,, and C. [4pts] (b) Sketch the acceleration-time graph for this motion. (Label axes!) [6pts] (c) Find the displacement of the bicycle during each of the segments of the motion A,, and C. [4pts] (d) Sketch the displacement-time graph for this motion. (Label axes!) [7pts] 15 1 Velocity, v (m/s) A C O 5 10 Time, t (s)

4 3. [13pts total] A passenger on a train car moving at a constant speed in a straight horizontal line tosses a coin. He tosses it up with a speed.45 m/s so that relative to the train car it travels directly up and lands back down in his hand. A woman standing on the ground next to the track sees the train car (and his hand with it) move a horizontal distance of 6.00 m between the moment he tosses the coin and the moment he catches it. (a) How long is the coin in the air? [5pts] (b) What is the launch angle (measured upward from the horizontal) of the coin as seen by the woman? [5pts] SKETCH the woman s view of the coins trajectory: [3pts] SOLUTION (for (a) and (b)): [10pts] 4

5 4. What are Newton s three laws of motion? (Label which is which. e as complete and specific as you can be, and include equations where you can, but say in words what each symbol in your equation means.) [10 pts] 5

6 5. [1pts total] Two blocks are connected by a light string, as shown. The smooth inclined surface makes an angle of 38 m =.50 kg with the horizontal, and the block on the incline has a mass of 5.8 kg. FIGURE (The6 7 pulley Problems is assumed 31 and to53be ideal.) (a) Find the 3. mass Two blocks of theare hanging connectedblock by a string, that as will shown cause in Figure the system 6 8. to be in equilibrium. [6pts] The smooth inclined surface makes an angle of 4 with the hor- F! and F! 3, izontal, and the block on the incline has a mass of 6.7 kg. Find the (b) If the mass mass of of the the hanging hanging block that is m will = 3.0 cause kg, thefind system the to direction be in and magnitude of the acceleration of the hanging block. [9pts] total force equilibrium. (The pulley is assumed to be ideal.) FIGURE 6 30 Pr 35. IO The Russell Tractio tured femur (the thigh bone), traction system illustrated in force is applied directly to the are applied to the bine to give a force F! + F! 3 lower leg to the knee. The resu F! total = system is to have F! F! 1 + F! total directl at an angle of 0.0 above th required to produce this align tude of the force, F! total that is (Assume the pulleys are idea 6.7 kg 5.8 kg m 38º 4 FIGURE 6 8 Problem 3 SKETCH (free body diagrams, as needed): [6pts] F SOLUTION (for (a) and (b)): [15pts] F 3 Contact force 1 mg Contact force 4.5 kg FIGURE 6 9 Problem 33 FIGURE 6 31 Problem 35 Section 6 4 Connected Obj 36. Find the acceleration o ure 6 3, given that m 1 = 3.0 kg. Assume the table is f freely. 6

7 and (b) contact force. Contact force 1 mg 0 FIGURE 6 37 Problem 65 Center line 6. [15pts total] A kg 70. IP Referring toy to airplane Problem 49, issuppose tied the toferris thewheel ceiling rotateswith a string. When the fast enough to make you feel weightless at the top. (a) How airplane s motor is started, many seconds itdoes moves it take with to complete a constant one revolution speed in this in a horizontal circle of case? (b) How does your answer to part (a) depend on your radius 0.50 m, making one full revolution every 1. s, as illustrated in the diagram. Contact Find force g box rests on a plank that is inclined at an angle of the horizontal. The upper end of the box is attached g with a force constant of 360 N/m, as shown in 8. If the coefficient of static friction between the box ank is 0., what is the maximum amount the spring tched and the box remain at rest? (a) the angle the string makes with the vertical and (b) the tension in the string. as shown in Figure 6 4. The tension in string is 1.7 N. (a) Is the tension in string 1 greater than, less than or equal to 1.7 N? Explain. (b) Verify your answer to part (a) by calculating the tension in string 1. (c) What is the mass of the picture? mass? Explain. (c) What is the direction and magnitude of your acceleration when you are at the bottom of the wheel? Assume that its rotational speed has remained constant. 71. A Conical Pendulum A kg toy airplane is tied to the ceiling with a string. When the airplane s motor is started, it moves with a constant speed of 1.1 m/s in a horizontal circle of radius 0.44 m, as illustrated in Figure Find (a) the angle the string makes with the vertical and (b) the tension in the string. FIGURE 6 40 Problem 71.0 kg A tugboat tows a barge at constant speed with a 3500-kg cable, as shown in Figure If the angle the cable makes with the horizontal where it attaches to the barge and the tugboat is, find the force the cable exerts on the barge in the forward direction. SKETCH (a free body diagram for the airplane): [3pts] E 6 38 Problem 66 blocks shown in Figure 6 39 are at rest. (a) Find the orce exerted on block A given that the mass of block A the mass of block is.5 kg, and the coefficient of on between block A and the surface on which it rests ) If the mass of block A is doubled, does the frictional ed on it increase, decrease, or stay the same? Explain. A 45 FIGURE 6 41 Problem IP Two blocks, stacked one on top of the other, can move without friction on the horizontal surface shown in Figure 6 4. The surface between the two blocks is rough, however, with a coefficient of static friction equal to (a) If a horizontal force F is applied to the 5.0-kg bottom block, what is the maximum value F can have before the.0-kg top block begins to slip? (b) If the mass of the top block is increased, does the maximum value of F increase, decrease, or stay the same? Explain. SOLUTION (for (a) and (b)): [1pts].0 kg F 5.0 kg FIGURE 6 4 Problem Problems 67 and Find the coefficient of kinetic friction between a 4.5-kg block and the horizontal surface on which it rests if an 85 N/m 7

8 7. [1pts total] For an object moving along the x axis, the potential energy of the frictionless system is shown in the graph. Suppose the object is released from rest at the point A. PROLEMS 33 (a) What are the turning points of the system? [ pts] e dashed level, (1) ball 3 nonconservative work done on block by the tension in the lowest speed; (3) all three (b) What points are stable equilibrium points? [ pts] rope positive, negative, or zero? d of the balls depends on (c) What 16. points For an object are unstable moving equilibrium along the x axis, points? the potential [ pts] energy of (d) If the object the frictionless is at a position system is somewhere shown in Figure between points Suppose C and the D, is the force on a height h, its kinetic enuppose a second ball of the object in the positive x direction or the negative x direction? [1 pt] object is released from rest at the point A. Rank the other points in the figure in increasing order of the object s speed. Indicate. Just before ball lands, (e) Rank the ties where other appropriate. points in the figure in increasing order of the objects speed. /4? Indicate ties where appropriate. Explain briefly your logic. [5 pts] h decreasing speed. Your tant speed. (a) Ignoring U of your system (youthe same? (b) Does the stem increase, decrease, ntaining a constant speed he gravitational potential ncrease, decrease, or stay of you and your bike in- ) Has the mechanical end, or remained the same? stant speed. Is U i + K i U f + K f for this system? ive heat tiles become exof the shuttle-earth sysan, less than, or the same own in Example distance d, does its mestay the same? (b) Is the A O C FIGURE 8 16 Conceptual Exercises 16 and Referring to Conceptual Exercise 16, suppose the object is released from rest at a point halfway between the points F and G. Rank the other points in the figure in increasing order of the object s speed, if the object can reach that point. Indicate ties where appropriate. D E F G x titative problem. IO identifies problems of biological or medical interest. Red bullets (,, ) are used. conservative Forces ity as a 3.-kg object is re 8 17 along paths 1,, m 4.0 m A.0 m 8.0 m 3.0 m

9 FIGURE 8 3 Problem 84 (a) What is the speed of the block w compression of only.50 cm? (b) W after it leaves the spring? 89. IP Referring to Example 8 8 force constant of 955 N/m. (a) Supp 1.70 kg, but its initial speed can be v required to give a maximum spring Suppose the initial speed of the blo can be varied. What mass is required compression of 4.00 cm? 8. [14pts total] The diagram shows a block at rest on a ramp of height h = m. When the block 85. is released, Figure 8 33itshows slidesa without 1.50-kg block friction at rest to on the a ramp bottom of of the ramp, and height h. When the block is released, it slides without friction to then continues across a surface that is frictionless except for a rough patch of width the bottom of the ramp, and then continues across a surface 10.0 cm that has is frictionless a coefficient except offor kinetic a rough friction patch of µ width k. Find 10.0 cm µ k that such hasthat the blocks speed after crossing the a coefficient rough patch of kinetic is friction 3.00 m/s. m k = Find h such that the HYPOTHESIS: [1pt] block s speed after crossing the rough patch is 3.50 m/s. v Rough patch 10.0 cm FIGURE 8 33 Problem In Figure 8 34 a 1.-kg block is held at rest against a spring with a force constant k = 730 N/m. Initially, the spring is compressed a distance d. When the block is released, it slides h 90. Referring to Example 8 10 S landing speed of block to be increa the coefficient of kinetic friction bet top be increased or decreased? (b) F of kinetic friction for a landing sp m 1 =.40 kg, m = 1.80 kg, and d 91. IP Referring to Example 8 1 m 1 =.40 kg, m = 1.80 kg, d = (a) Does the mechanical energy of b stay the same as it moves from poi change in mechanical energy for blo i to point f. (c) What is the nonconse by the tension in the rope? (d) Wh (e) What is the nonconservative wo tension in the rope? SOLUTION: [1pts] ANSWER REASONALE / AGREES WITH HYPOTHESIS?: [1pt] 9