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UMass Amherst PHYSICS 131 - final exam study guide 131

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Conversions: 1 inch=.0254 meters 1Pa=9.86E-6 atm 1 g=.001 kg 1cm^3=(1/100)^3 m 1 second= 1000 milliseconds 1 m=100 cm 1 inch=2.54 cm Wave Motion Amplitude:Max of the wave Period (T): Time to make 1 cycle of motion Frequency: # of cycles per second (1/T) T=2pi*sqrt(L/g) v=Wavelength*frequency Wavelength= 2L/n Transverse (string; electromagnetic) Longitudinal (sound, spring, slinky) Torsional ( twisting as in Tacoma Narrows Bridge) Combinations ( surface water waves) Constructive interfernce: two peaks/two toughs meet Deconstructive interference: One peak one trough meet Speed of sound=sqrt(140*P/p P=Air pressure p=Air densitiy Ex. People with very good pitch discrimination can very quickly determine what note they are listening to. The note on the musical scale called C6 (two octaves above middle C) has a frequency of 1050 Hz. Some trained musicians can identify this note after hearing only 12 cycles of the wave. T=1/f 1/1050=9.52E-4 seconds*12 cycles=.00114 s=> 11.4 ms Fluids and Pressure Pressure=Force/Area (Pa or N/m^2) Fi/Ai=Ff/Af Weight of fluid column m=p*A*H*g (p=density) P=pHg Pressure+Atmospheric pressure: P = Po + Dgh Where d = density of water = 1030 kg / m^ 3 Po= 1 atm density of salt water = 1.028 g/L density of fresh water = 1 g/L the volume of fresh water with an equal mass x will satisfy the following equation l*w*h1*1.028 =l*w*h2*1 M=Density*Volume In freshwater Mg = [L*W*h(total) - h(above)1*g h(total)-h(above)=M/L*W Same for salt but with 1.03 instead of 1 Tension on a string T=g*V(Density of liquid-Density of object on the string) Ex. What is the maximum mass that can hang without sinking from a 70-cm diameter Styrofoam sphere in water? Assume the volume of the mass is negligible compared to that of the sphere. Find mass of sphere Density*Volume (4/3pi*r^3) Find mass of displaced water: Volume of sphere*1000kg Mass of water-Mass of sphere=Answer If the rectangular barge is 3.5 m by 22.0 m and sits 0.90 m deep in the harbor, how deep will it sit in the river? Harbor: 3.5*22*.9*1027=71171.1 River: 3.5*22*h*1000=77000h 71171.1=77000h h=.924 A 10cm×10cm×10cm wood block with a density of 740 kg/m3 floats in water. Fresh: 10*10*h/10*10*10=740/1000 Salt: 10*10*h/10*10*10=740/1030Conversions: 1 inch=.0254 meters 1Pa=9.86E-6 atm 1 g=.001 kg 1cm^3=(1/100)^3 m 1 second= 1000 milliseconds 1 m=100 cm 1 inch=2.54 cm Old Material Exam 1 Constant velocity=0 acceleration Fcosx=m*a Initial v=Final v-at vf^2-v0^2=2(-g)h d = (1/2) g t^2 F=m/a v2 - u2 = 2as Apparent weight=m(a+g) Can an object accelerate and have a constant speed at the same time? Yes, Because a change in direction will result in a change in velocity and may or may not result in a change in speed If a rocket initially at rest accelerates at a rate of 50 m/s2 for one minute, its speed will be 3000 m/s because 50 m/s*60 seconds=3000 It takes 6 seconds for a stone to fall to the bottom of a mine shaft. How deep is the shaft? 180 m =.5(9.8)(6^2) A 1000.0 kg car experiences a net force of while decelerating from to How far does it travel while slowing down? a=F/m 9500/1000=-9.5 19.8^2-30^2=2(-9.5)s s=18.5 A toy rocket is launched vertically from ground level (y = 0 m), at time t = 0.0 s. The rocket engine provides constant upward acceleration during the burn phase. At the instant of engine burnout, the rocket has risen to 64 m and acquired a velocity of The rocket continues to rise in unpowered flight, reaches maximum height, and falls back to the ground. The maximum height reached by the rocket is closest to: vi=90 vf=0 h=? g=-9.81 0^2-90^2=2(-9.81)h h=413 +64 m already traveled=477m Two identical stones are dropped from a tall building, one after the other. Assume air resistance is negligible. While both stones are falling, what will happen to the vertical distance between them? It will increase A child pulls on a wagon handle at an angle 37° above the horizontal with a force of 45 N. If the wagon accelerates at 6.2 m/s2 horizontally, what is the mass of the wagon? 45cos37=6.2*a a=5.7 The figure shows a block of mass M hanging at rest. The light wire fastened to the wall is horizontal and has a tension of 38 N. The wire fastened to the ceiling is also very light, has a tension of and makes an angle θ with the ceiling. Find the angle θ. 59cosx-38=> x=cos^-1(38/59)=50 Exam 2 W=f*d K.E=.5(m)(v)^2 Or .5(m)(vf^2-vi^2) Potential energy=m*g*h W=ma+mgh p=MV Impulse=m(vf-vi)/(tf-ti) Torque=m*g*d or F*d ● Sum of forces acting upward=sum of forces acting downward ● Net torque=0 F=mgL/2d M1R1=M2R2 (Mobile questions) A crane lifts a 425 kg steel beam vertically upward a distance of 59 m. How much work does the crane do on the beam if the beam accelerates upward at 1.8 m/s2? W=425*1.8+425*9.8*59=4.7E5 A bead is moving with a speed of 20 m/s at position A on the track shown in the figure. This track is friction-free, and there is no appreciable air resistance. What is the speed of the bead at point C? energy at A = energy at C (1/2)*m*(vA)^2+mg(hA) = (1/2)*m*(vC)^2+mg(hC) (vC)^2=(vA)^2+2*g*(hA-hC) =20^2+ 2*9.8*40 vC = 34.4 m/sec A meter stick balances at the 50.0-cm mark. If a mass of 50.0 g is placed at the 90.0-cm mark, the stick balances at the 61.3-cm mark. What is the mass of the meter stick? Lever arm(LA1) for m1= pivot point-center of mass=61.3cm-50cm=11.3cm lever arm(LA2) for m2=location of mass-pivot point=90cm-61.3cm=28.7cm Torque=m1g*LA1-m2g*LA2=0 m1g*LA1=m2g*LA2 solve for m1 m1=(m2g*LA2)/(g*LA1) m1=(0.05kg*9.8*28.7cm)/(9.8*11.3cm) m1=0.1269kg=126.9g=127g An athlete holds a 7.5-kg shot put in his hand with his lower arm horizontal, as shown in the figure. His lower arm has a mass of 2.8 kg and its center of gravity (or center of mass) is 12 cm from the elbow-joint pivot. How much force must the extensor muscle (which is M in the figure) in the upper arm exert on the lower arm? MGD(muscle)+MGD(ball)+MGDelbow=0 F=m*aConversions: 1 inch=.0254 meters 1Pa=9.86E-6 atm 1 g=.001 kg 1cm^3=(1/100)^3 m 1 second= 1000 milliseconds 1 m=100 cm 1 inch=2.54 cm A 1200 kg cannon fires a 100.0 kg cannonball at 35 m/s. What is the recoil velocity of the cannon? Assume that frictional forces are negligible and the cannon is fired


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