# On a planet where g 10 ms 2 a football is kicked from

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6. [7 Points] On a planet where g = 10 m/s2, a football is kicked from the origin (point A) at a speed of 6.0 m/s, directed θA= 53.13° above the horizontal (so cos θA= 3/5, sin 4/5). At t = 0.75 s, what is the football’s: θA= (a)rate of change of speed; (b)normal component of acceleration; (c)radius of curvature.
Method 1: Method 2:
10 Method 3: Method 4: ´µ´µ´µ´µ´µ222222222222223.6 m/s,4.8103.64.81010 4.8103.64.81010 4.810 0.75At 0.75 s,6 m/s3.64.810 0.75100368 m/sAt 0.75 ,3.6 m/s,2.7 m/s/3.62xyxyttntxynvvtvvvttdvadtttaagatsvvvaU±³³±±±³±±±ªº¬¼³±ªº¬¼±±±³´µ2.7/ 82.53 m
11 7. [8 Points] The car travels along a circular path having a radius of 30 m at a speed of 0v= 5 m/s. At s= 0, it begins to accelerate with v±= dv/dt = (0.05 s) m/s2, where s is in meters. Determine its speed and the magnitude of its total acceleration when it has moved s18 m. = ´ µ´µ002220222022222220.050.050.05220.050.0525/186.42/0.05180.9/6.421.37/301.64/tsvvtnnta dsvdvsdsvdvsdsvdvvvsv ssvsmsvmsamsvamsaaamsU±³³u³³³
12 8. [8 Points] Consider the system shown. Both blocks move at a constant speed. The relative velocity of Bwith respect to A, vB/A, is directed downwards towards the right at an angleEas measured from the usual positive x±axis (a) Does Bmove up or down the incline? Circle . one answer. Up Down If the speed of Bis 3 m/s determine: (b) the velocity of A, expressed as a magnitude and direction with respect to the nearest horizontal; and (c) the angle Ethat vB/Amakes with respect to the nearest horizontal. (b) Placing datum at the centre of the top pulley: 2constant20.ABABsslvv³³3Bvm/s down the incline 3Bv³m/s relative to the datum. So 26ABvv±±m/s = 6 m/s towards the datum: 6 m/s Av. (c) 6 m/s6An vj´µ3 m/s3 cos60sin60B±vij2´µ|3cos603sin6061.58.598 .B ABA?±±±±vvvijjijAngle :E18.598tan80.10 .1.5E±§·¨¸©¹D
13 9. [6 Points] Two stacked blocks are traveling horizontally along a rough horizontal surface as shown when the bottom block encounters a spring anchored on one side to a wall. The surface between the two blocks is also rough. While the spring is being compressed and while the top block remains at rest relative to the bottom block (figure on the right), draw the complete free-body and kinetic diagrams for both blocks. Be sure to clearly indicate the correctdirectionsof any vectoron each diagram. All symbols shown in your diagrams are assumed to take on positive values. In addition, YOU MUST USE the following symbols for forces (IF APPLICABLE): mig for gravitational forces fkfor kinetic frictional forces Nijfor normal forces i acting on j fsfor static frictional forces Fspringfor elastic restoring forces Tijfor tensional forcesFree Body Diagram for A: Kinetic Diagram for A: Free Body Diagram for B: Kinetic Diagram for B:
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