Presentation ~ above theme: "WORK In bespeak for job-related to be done, 3 things space necessary:"— Presentation transcript:
1 occupational In order for work to be done, three things are necessary: There have to be an applied force. The pressure must act with a specific distance, dubbed the displacement. The force must have actually a component follow me the displacement.
2 job-related is a scalar quantity equal come the product the the magnitudes of the displacement and the ingredient of the force in the direction of the displacement. W = F . X or W = F cos x UNITS: N.m this unit is referred to as a Joule (J)
3 As lengthy as this human being does not lift or reduced the bag of groceries, that is doing no work on it. The force he exerts has no ingredient in the direction the motion. Work-related done by forces that oppose the direction that motion, such together friction, will be negative.
4 Centripetal forces do no work, together they are constantly perpendicular come the direction the motion.
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5 If the pressure acting on an object varies in size and/or direction during the object’s displacement, graphical evaluation can be provided to determine the job-related done. The pressure is plotted on the y-axis and also the distance with which the object move is plotted ~ above the x-axis. The job-related done is stood for by the area under the curve.
7 Forces acting: Ff FA FG and also FN FN does NO work.5.1 A push of 200 N move a 100 N block increase a 30inclined plane. The coefficient that kinetic friction is 0.25 and also the length of the airplane is 12 m. A. Uncover the occupational done by each pressure acting top top the block. W FA = 200 N FG = 100 N θ = 30˚ μ = 0.25 x = 12 m forces acting: Ff FA FG and also FN FN go NO work.
8 WFG = FG x = -FGx x = - FG sin30˚x = - 100 sin 30˚ (12) = - 600 J FGy W FA = FA x = 200 (12) = 2400 J Ff = μ FN = μ FG cos 30˚ = 0.25 (100) cos 30˚ = 21.6 N WFf = - Ff x = (12) = J FN FA WFG = FG x = -FGx x = - FG sin30˚x = sin 30˚ (12) = J FGy θ Ff FG FGx
9 Net work: ΣW = 2400 - 259.2 - 600 = 1540.8 J FN The resultant force:b. Display that the net work done through these forces is the exact same as the work-related of the resultant force. Network work: ΣW = = J FN The resultant force: ΣFx = FA - Ff - FGx = = N WF = Fx . X = (12) = J FA FGy θ Ff FGx FG
10 energy Energy is that which have the right to be converted right into work. When something has actually energy, the is able to perform work or, in a general sense, to change some facet of the physical world.
11 In mechanics we are pertained to with 2 kinds that energy:KINETIC ENERGY: K, energy possessed by a body by virtue that its motion. Units: Joules (J) POTENTIAL ENERGY: PE, power possessed by a system by virtue of place or condition. PE = m g h Units: Joules (J)
12 WORK-ENERGY PRINCIPLE:The work of a resultant exterior force on a body is equal to the readjust in kinetic energy of the body. W = KUnits: Joules (J)
13 W = PE
14 5.2 What average pressure F is important to prevent a 16 g cartridge traveling in ~ 260 m/s as it penetrates into wood in ~ a distance of 12 cm? us W = ΔK vf = 0 m/s m = kg vo = 260 m/s x = 0.12 m = N
15 CONSERVATIVE and NON-CONSERVATIVE FORCESThe work done by a conservative pressure depends just on the initial and final position of the thing acted upon. An instance of a conservative force is gravity. The occupational done equates to the adjust in potential energy and depends just on the initial and also final positions over the ground and NOT ~ above the route taken.
16 Friction is a non-conservative force and also the work-related done in relocating an object against a non-conservative pressure depends top top the path. For example, the work-related done in slide a crate of books versus friction from one end of a room to the various other depends on the route taken.
17 For mechanically systems entailing conservative forces, the complete mechanical energy equals the amount of the kinetic and also potential energies of the objects that make up the system and also is always conserved.
19 A roller-coaster vehicle moving there is no friction illustrates the preservation of mechanical energy.
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21 In real life applications, few of the mechanical power is lost because of friction. The work due to non-conservative pressures is offered by: WNC = ΔPE + ΔK or WNC = Ef - Eo
23 5.3 A ballistic pendulum apparatus has a 40-g sphere that is recorded by a 500-g suspended mass. After ~ impact, the 2 masses increase a vertical distance of 45 mm. Discover the velocity of the combined masses just after impact. COE m1 = 0.04 kg m2 = kg h = m K0 = PEf
24 K0 = PEf PEf = (m1+m2) ghf = (0.04+0.500)(9.8)(0.045) = 0.24 Jm1 = 0.04 kg m2 = kg h = m K0 = PEf PEf = (m1+m2) ghf = ( )(9.8)(0.045) = 0.24 J K0 = PEf = 0.24 J = 0.94 m/s
25 A At suggest A: PEA + KA At allude B: KB PEA + KA= KB B = 42.9 m/s5.4 The tallest and also fastest roller coaster in the world is the stole Dragon in Japan. The ride has a upright drop the 93.5 m. The coaster has actually a rate of 3 m/s in ~ the height of the drop. A. Overlook friction and also find the speed of the riders at the bottom.? COE A At point A: PEA + KA At suggest B: KB PEA + KA= KB vA = 3 m/s hA = 93.5 m hB = 0 m B = 42.9 m/s (about 96 mi/h)
26 WNC = Ef - E0 = KB - (PEA + KA) = - 4416.5 Jb. Find the occupational done by non-conservative pressures on a 55 kg rider throughout the descent if the actual velocity at the bottom is 41 m/s. VA = 3 m/s vB = 41 m/s hA = 93.5 m hB = 0 m m = 55 kg WNC = Ef - E0 = KB - (PEA + KA) = J
27 5.5 A 20-kg sledge’s rests at the height of a 30˚ steep 80 m in length.If μk= 0.2, what is the velocity at the bottom the the incline? COE WNC = Ef - Eo = Kf - PE0 m = 20 kg θ = 30° r = 80 m μk= 0.2
28 PE0 = mgh0 = 20(9.8)(40) = 7840 J Ff = μkFN = μk Fgy = μk Fgcos30°m = 20 kg θ = 30° x = 80 m μk= 0.2 h = x sin θ h = 80 sin 30° = 40 m x h PE0 = mgh0 = 20(9.8)(40) = 7840 J Ff = μkFN = μk Fgy = μk Fgcos30° = (0.2)(20)(9.8)cos30° = 34 N WNC = - Ff r = - 34 (80) = J WNC= Kf - PE0 Kf = PE0 + WNC = = 5120 J
29 = 22.6 m/s
30 strength Is the price at which occupational is performed.P = work/time = Watt UNITS: The difference in between walking and running up these stairs is power. The adjust in gravitational potential power is the same.
31 = 23 m/s The average velocity is: 23/2 = 11.5 m/s p = Fv 5.6 A 1100-kg car starting from rest, increases for 5.0 s. The size of the acceleration is 4.6 m/s2. What power have to the motor produce to reason this acceleration? m = 1100 kg vo = 0 m/s t = 5 s a = 4.6 m/s2 F = ma = (1100)(4.6) = 5060 N vf = vo + in ~ = (5) = 23 m/sThe average velocity is: 23/2 = 11.5 m/s ns = Fv = (5060)(11.5) = 5.82x104 W
32 ELASTIC pressure The pressure Fs used to a feather to stretch it or to compress it an lot x is directly proportional come x. Fs = - k x Units: Newtons (N) wherein k is a constant called the spring continuous and is a measure up of the stiffness that the details spring. The feather itself exerts a force in the contrary direction:
33 This pressure is sometimes called restoring force due to the fact that the spring exerts its pressure in the direction opposite come the displacement. This equation is known as the spring equation or Hooke’s Law.
37 The elastic potential power is offered by:PEs = ½ kx2 Units: Joules (J)
38 5.7 A dart of massive kg is pressed against the feather of a toy dart gun. The feather (k = 250 N/m) is compressed 6.0 cm and also released. If the dart detaches native the spring once the spring reaches its regular length, what speed does the dart acquire? m = 0.1 kg k = 250 N/m x = 0.06 m PEs = K ½ kx2 = ½ mv2 = 3 m/s