Physics 50 Test 2. Feb 25, Calculators are allowed. Notes and books are not allowed.

Transcription

1 Physics 50 Test 2 Name: Feb 25, 2016 Calculators are allowed. Notes and books are not allowed. Answer all the questions in any order you like. For full credit you must show your work and/or explain your logic. Scale symbols Scale Prefix Symbol 10 3 kilo- k deci- d 10 2 centi- c 10 3 milli- m g = 9.81 m/s 2 sin 2 θ + cos 2 θ = 1 sin(2θ) = 2 sin(θ) cos(θ) cos(2θ) = cos 2 θ sin 2 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)] 2 sin α sin β = 1 [cos(α β) cos(α + β)] 2 sin α cos β = 1 [sin(α + β) + sin(α β)] 2 sin ( θ + π 2 ) = cos θ cos ( θ + π 2 ) = sin θ sec θ := 1 cos θ csc θ := 1 sin θ cot θ := 1 tan θ Trigonometric Identities

2 37. On a hot summer day, a young girl swings on a rope above the local swimming hole (Figure 4 21). When she lets go of the rope her initial velocity is 2.25 m/s at an angle of On a hot summer above day, the horizontal. a young girl If she swings is flight on afor rope above s, how the high local swimming hole. When she letsabove go ofthe thewater ropewas her she initial when velocity she let go is of 2.50 the rope? m/s at an angle of 35.0 above the horizontal. If she is in flight for s, how high above the water was she when she let go of the rope? mum height of the ejected lava same as on Io? Explain. HYPOTHESIS: [1 pts] v FIGURE 4 21 Problem A certain projectile is launched with an initial speed v 0. At its highest point its speed is v 0 >4. What was the launch angle? A volcano on Io, the innermost the characteristic features of proje 46. IP A soccer ball is kicked w in a direction 25.0 above the and direction of its velocity (a being kicked. (c) Is the ball at i s? Explain. 47. A second soccer ball is kicke in Problem 46. After s it i its initial direction of motion? SOLUTION: [5 pts] ANSWER REASONABLE / AGREES WITH HYPOTHESIS?: [1 pt]

3 an elevator that is moving at constant velocity. Find the tension in each of the three strands of cord supporting each load the acceleration of the obj the string. 2. Find the tension in each of the three strands of cord supporting the load, which hangs at rest T 1 T 2 T T Figure P5.41 shows the spe does a chin-up. Assume the mass of the person s body force exerted by the chin-u 0, (b) t s, (c) t s, 30 T 3 T 3 a 5.00 kg 10.0 kg b SKETCH a Free-body Diagram: [2 pts] Figure P5.36 speed (cm/s) An object of mass m kg is observed to have an acceleration S a with a magnitude of 10.0 m/s 2 in a direction 60.0 east of north. Figure P5.37 shows a view HYPOTHESIS: of the object [3 pts] from above. The force S F2 acting on the object has a magnitude of 5.00 N and is directed north. Determine the magnitude and direction of the SOLUTION: [7 pts] one other horizontal force S F1 acting on the object.. A setup similar to the one shown in Figure P5.38 is often used in hospitals to support and apply a horizontal traction force to an injured leg. (a) Determine the force of tension in the rope supporting the leg. (b) What is the traction force exerted to the right on the leg? Figure P kg. A simple accelerometer is constructed inside a car by S F 2 m 60.0 S F 1 S a Figure P time Figure P 42. Two objects are connected light string that passes ov frictionless pulley as show Figure P5.42. Assume the in is frictionless and take m 2.00 kg, m kg, and (a) Draw free-body grams of both objects. (b) the magnitude of the a eration of the objects, (c) the sion in the string, and (d) speed of each object 2.00 s it is released from rest. 43. Two blocks, each of mass 3.50 kg, are hung from the c of an elevator as in Figure (a) If the elevator moves w upward acceler ation a S of m tude 1.60 m/s 2, find the ten T 1 and T 2 in the upper and strings. (b) If the string

4 ANSWER REASONABLE / AGREES WITH HYPOTHESIS?: [1 pt] 3. What are Newton s three laws of motion? (Be 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.) [9 pts]

5 4. A block sits on a frictionless incline. The angle θ = 20.0 and the mass of the block is 2.00 kg. m 1 (a) What is the magnitude of the normal force on the block and which way is it directed? Figure P5.46 (b) What is the block s acceleration and which way is it directed? 47. A block is given an initial velocity of 5.00 m/s up a fric- (c) If the block is given an initial velocity of 5.00 m/s up the slope, how far up the tionless incline of angle u (Fig. P5.47). How far incline does the block slide before coming to rest? up the incline does the block slide before coming to rest? θ Figure P5.47 SKETCH a Free-body Diagram for the block: [2 pts] 48. A car is stuck in the mud. A tow truck pulls on the car with the arrangement shown in Fig. P5.48. The tow cable is under a tension of N and pulls downward and to the left on the pin at its upper end. The light pin is held in equilibrium by forces exerted by the two bars A and B. Each bar is a strut; that is, each is a bar whose weight is small compared to the forces it exerts and which exerts forces only through hinge pins at its ends. Each strut exerts a force directed parallel to its length. Determine the force of tension or compression in each strut. Proceed as follows. Make a guess as to which way (pushing or pulling) each force HYPOTHESIS for (a), (b), and (c): [3 pts] Fig 50. In the Atwoo shown in Fig The masses o comparison. string does n with a sharp 2.40 m/s dow its initial leve 51. In Example 5 a fish in an el ing on a spri the elevator 1.20 m/s in 0 for the next 5 form accelera and comes to (a) before th first s, stant speed, a ing down? AMT M Section 5.8 Force 52. Consider a la steel beams. the load ma truck stops su Assume, for e SOLUTION: Part (a): [3 pts]

6 Part (b): [3 pts] Part (c): [5 pts] ANSWERS REASONABLE / AGREES WITH HYPOTHESIS?: [1 pt]