Physics, Energy

Romar M. Cabinta EXERCISES 15 WORK, ENERGY, AND POWER A. conceptual QUESTIONS 1. Is make believe d peerless when you dissemble a admit from the top of the desk to the floor? why? Yes. It is because the fracture of the book from the top of the desk to the floor and the vehemence that is utilize to the book is parallel with one a nonher. 2. State the faithfulness of Conservation of mechanical Energy in two slipway? The law of conservation of postal code states that zippo may neither be created nor destroyed. thence the sum of all the energies in the carcass is a unvaried. TMEinitial=TMEfinal 3. Explain the basic ideas that govern the design and operation of a rolling coaster.A roller coaster is operated and designed through the cover of Physics. The law of Conservation of Energy governs the changes in a coasters zip and height. Simply put, the high an object is off the ground, the much durability zip it has that is, potency to polish off make haste as it fal ls. As it falls toward the ground, that potential energy changes to energizing energy, or energy of relocation. The sum of the two types of energy is constant, scarce a roller coaster must fight back an adequate balance of potential and energising energies to deliver a thrilling ride. . An wasteful pee is say to waste energy. Does this mean that energy is actually confounded? Explain. Energy is never lost. An in efficacious machine wastes energy by converting it to an un productionive state. A machine, such as a ride car engine has the primary business of converting the energy in the fuel to motion of the car. It is unproductive because a large comparison of the fuels chemical energy is dissipated in the form of noise, heat, vibration etc. so that only a small ana put downy is actually used for its prime purpose. 5.Is it assertable for a unsubdivided machine to cipher some(prenominal) army and travel rapidly at the comparable epoch? Why? It is hopeless for a simple machine to reckon both squelch and gain stop number at the aforementioned(prenominal) time. It is because the gain in bucket a unyielding of a machine is the case of an defendion of a lot more nip back and therefore do not take place at the same time. One best example is a bicycle crossing a imbibe hill requires a great force to be exerted to be able to gain speed. B. PROBLEMS 1. Starting from rilievo, 5-kg slides 2. 5 m down(p) a rough 30 tip. The coefficient of kinetic friction amongst the block and the incline is 0. . Determine the work done by (a) the force of gravity (b) the friction amidst the block and incline (c) the normal force and (d) the net force on the block. W=5kg9. 8kgs2 W=49 N a. ) W=Fd W=Wsin30(2. 5m) W=49sin30(2. 5m) W=61. 25 J b. ) W=-Fd W=-? kNd W=-(0. 4)(42. 44N)(2. 5m) W=-42,44 J c. ) W=0 Normal force does not exert work because it is perpendiuclar with the displacement. d. ) WT=49Nsin302. 5m-0. 442. 44N2. 5m+0 WT=18. 81 J 2. Car A has twice the aggregative of car B, but only fractional as much kinetic energy.When both cars increase their speed by 5m/s, then they have the same kinetic energy. What were the pilot light speeds of the two cars? gondola car A CAR B mass=2mB mass=mB KEA=12KEB KEB =KEB VA=5ms VB =5ms VA=2KEAmA KEA=KEB VA=2(12KEB)2mB 12mAv=12mBv 2122mB5=12mB5 VA=KEB2mB 10mB4=5mB2 VB=KEBmB 5mB2=5mB2 3. A 400-g fall slides on a curved frictionless cable, starting from rest at advert A. have the speed of the bead at channelize B and point C. 400g? 1kg kibibyteg=0. 4 kg PEA=mgh PEA=(0. 4 kg)(9. 8)(5m) PEA=19. 6 J PEB=(0. 4)(9. 8)(0) PEB=0 J KEA=12mv2=120. 4kg02=0 J TME=PEA+KEA=19. 6 J+0 J=19. 6 J KEB=TME-PEB=19. 6-0=19. 6 J KEB=12mvB2 19. 6 J=120. 4 kgVB2 VB=39. 2 J0. 4 lg=9. 90 m/s PEC=mgh=(0. 4)(9. 8ms22m=7. 84 J KEC=TME-PEC=19. 6 J-7. 84 J=11. 76 J KEC=12mv2C 11. 76=120. 4kg) (v2C Vc=23. 2 J0. 4 kg=76. 67 m/s 4. A tandem (two-person) bicycle team must overcome a force of 34 lbs. to maintain a speed of 30 ft. /s. Find the power take per rider, assuming they contribute equally. Express your declaration in horsepower. F=34 lb F1=17 lb=F2 P1=F1v=17 lb30fts=510 ftlbs? 1hp550 ftlbs=0. 93 hp P2=F1v=17 lb30fts=510 ftlbs? 1hp550 ftlbs=0. 93 hp 5. A pump is required to burn up 200 L of water per jiffy from a well 10 m deep and eject it with a speed of 20m/s. (a) How much work is done per flash in lifting the water? (b) How much in giving its kinetic energy? What horsepower engine is needed if it is 80% efficient? a. ) W=mgh+12mv2=200kg? 0m? 9. 81kgm2+12? 200kg? 20ms2=59620Js=993. 67J/min b. ) W=12mv2=12200kg20ms2=40000 J c. ) HP=59620js? 0. 8? 746js=99. 899 hp EXERCISES 16 LINEAR pulsation A. CONCEPTUAL QUESTIONS 1. Which has greater pulsation, a ten cyclist truck at rest or a paltry motorcycle? Why? A moving motorcycle has a greater impetus than the truck. A truck at rest has zero momentum because an object has to be moving in couch to have a momentum. 2. How does im petus differ from force? Impulse is the product of force and the time interval of the application of force while force is bonnie a factor that affects an objects impulse when it is at motion. 3.Why is it incorrect to claim that impulse equals momentum? It is not serious to say that impulse is equal to momentum because impulse is the measure of the change in momentum and therefore an object with constant and non-changing momentum has zero impulse. 4. What is the function of seatbelts and airbags in car? The function of seatbelts and airbags in an automobile is to increase the time of a force to r individually its destination, which results to a lesser carry on of objects that end collide to a passenger and therefore will have a higher chance for his/her life to be saved. 5. Distinguish amid an lively impact and springless collision.In flexile collision, the momentum and the kinetic energy ar hold and its coefficient of coming back is equal to one. However in in lively collision, the kinetic energy is not conserved and the coefficient of restitution is zero. B. PROBLEMS 1. A 10,000-kg truck has a speed of 100 km/h? (a) what is its momentum? What speed must a 5,000-kg truck attain in order to have (b) the same momentum? (c) the same kinetic energy? a. ) P=mv=10000 kg27. 78ms=2. 78? 105kg? m/s b. ) P=mv 2. 78? 105kg? ms5000kg=5000 kgv5000 kg v=55. 6 m/s c. ) KE=12mv2 KE=121000027. 782 KE=3. 86? 106J KE=12mv2 3. 86? 106J=125000kgv2 v=7. 72? 106J500kg v=39. 29 m/s . A car is stopped for a traffic signal. When the light turns green, the car accelerates, change magnitude its speed from 0 to 60 km/h in 0. 8 s. What are the magnitudes of the linear impulse and the average innate force experienced by a 70-kg passenger in the car during the time the car accelerates? J=m? v J=(70 kg)(16. 67ms) J=1166. 9 kg? m/s J=Ft=Jt F=1166. 9 kg? ms0. 8s=1458. 63 N 3. A 5-g object moving to the right at 20cm/s makes expansibleised head on collision with a 10-g object that is initially at rest. Find (a) the velocity of each object afterwardwards the collision and (b) the fraction of the initial kinetic energy transferred to the 10-g object.PT=PT mAvA+mBvB=mAvA+mBvB 5g20cms+10g0=5g-vA+(10g)(vB) 100=-5vA+10vB 20=-vA+2vB 20=-vB+20 +2vB vB=0 cm/s e=(vB-vA)/(vA-vB) 1=(vB-vA)/(20 cm/s-0cm/s) 20=vB-vA vA=vB-20 vA=0-20 vA=-20 cm/s 4. After a completely inelastic collision between two objects of equal mass m, each having initial speed v, the two move off together with speed v/3. What was the angle between their initial directions? P1x + P2x = Pfx = Pf,P1y+P2x = 0. 2mv cos lettuce? = 2mv/3, cos? = 1/3, ? = 70. 5o. The angle between their initial directions is 2? =141 5. A cavity whose mass is 100 g rest on a frictionless even surface.A bullet of mass 2. 5 g, travel naiantly at 400 m/s, strikes the stone and rebounds horizontally at nighttime angles to its lord direction with a speed of 300 m/s. (a) Compute the magnitude and direction of the velo city of the stone after it is struck. (b) Is the collision holyly elastic? a. ) have on that the bullet is traveling in the overbearing x-direction and that the stone has components ofvelocityvx and vy after the collision. equivalence momentum before and after in these directions. 0. 0025 kg x 400ms=0. 1 kg vx vx = 10 m/s 0. 1 vy= 0. 0025 x 300 vy = 7. 5 m/s Magnitude of velocity = v(102+7. ) = 10. 37 m/s Angle =tan-1(vy/vx) = 36. 87 deg to the x-axis b. ) No. EXERCISES 16 LINEAR MOMENTUM A. CONCEPTUAL QUESTIONS 1. What is Hookes Law? Hookes lawofelasticityis an approximation that states that the extension of a spring is in direct remainder with theloadapplied to it. Many physicals heed this law as long as the load does not exceed the materialselastic curb. Materials for which Hookes law is a useful approximation are known aslinear-elasticor Hookean materials. Hookean materials are a necessarily panoptic term that may include the work of muscular layers of the heart.Hookes law in simple terms says that tuneisdirectly proportionatetostrain. Mathematically, Hookes law states that 2. When is a material said to be elastic? A material is called elastic if the deformation produced in the bole is completely recovered after the remotion the load. For ideally elastic materials, a superstar valued (linear) and time independent coincidence exists between the forces and the deformations. Although it is hard to begin an ideally elastic material, i. e. , A Hookean solid, most of the materials can be considered elastic at to the lowest degree for a specific range. 3.Which is more elastic, a rubber band or coil brand name spring? Why? roll make spring is more elastic than rubber band because it has greater elastic limit and ultimate loudness than a rubber band because it has greater elastic limit and ultimate strength than a rubber. 4. What is the difference between the elastic limit of a material and its ultimate strength? Why are these concepts of specia l sizeableness to construction engineers? Elastic limit is the supreme stress that can be applied to a material without being for good deformed while ultimate strength is the stress required to cause actual fracture to a material.These concepts are principal(prenominal) to construction engineers because it gives them the idea of what materials are perfect for the construction and those that are fragile. 5. Which is more compressible, intoxicant or water? Why? Alcohol. It is because alcohol has higher compressibility and accepts a greater pressure than on water. B. PROBLEMS 1. A nylon rophy used by mountaineers elongates . 5 m to a lower place the weight of an 80-kg climber. (a) If the rope is 50 m in length and 9 mm in diameter, what is the Youngs Modulus for this material? (b) If Polsons ratio for nylon is 0. , find the change in diameter under this stress. a) y=F? LoA? L y=(784N)(50m)Pi4. 510-32(1. 5 m) y=4. 11108 Pa b) ? tto=- LL0 ?t=- LtoLo=-0. 21. 5910-3m50m=-5. 4? 10-5 2. The elastic limit of blade elevator cable is 2. 75108 N/m2 Find the maximum upward speedup that can be given a 900-kg elevator when supported by a cable whose cross-section is 3 cm2, if the stress is not to exceed ? of the elastic limit. supreme stress allowed14(2. 75? 108=6. 875? 104 Pa blackmail force this stress=stress ? scene of action=6. 875? 104 x0. 0003=20. 625 N=Fup Fup=mg+ma 20. 625=900(9. 81)+900(a) a=13. 11 m s-2 . The deepest pint in the ocean is the Mariana trench, about11 km deep. The pressure at this depth is huge, about 1. 13? 108 Pa. (a) channelise the change in volume of 1000 L of saltwater carried from the surface to this deepest point in the Pacific Ocean. (b) The compactness of seawater at the surface is 1. 025g/cm3. Find its density at the bottom. 4. If the shear stress in steel exceeds 4108 N/m2, the steel ruptures. Determine the shearing force necessary to (a) shear a steal style 1. 0 cm in diameter and (b) punch a 1. 0-cm diameter muddle in stee l plate 5mm thick. a. ) FA= 4x108Nm2= F/R2 = F/*0. 1m2 F = 125663. 706143592N b. ) FA= 4x108Nm2= F/2RT= F/2*0. 005 m*0. 005m F = 63,000 N 5. In the figure below, 103 kg unvaried log hangs by two steel wires, A and B, both of diameters 2. 4 mm. initially, wire A was 2. 5 m long and 2. 0 mm shorter than wire B. The log is now horizontal. a) What are the tensions in wires A and b? Since the log is not moving FA + FB mg = 0 Since the log is horizontal LA + DLA = LB + DLB = LA + l + DLB, DLA = DLB + l, where l = 2 mm is the original difference in lengths between A and B. Which gives b) What is the ratio of distance a and b?