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Fyrsta skilyrði fyrir jafnvægi

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Presentation on theme: "Fyrsta skilyrði fyrir jafnvægi"— Presentation transcript:

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2 Fyrsta skilyrði fyrir jafnvægi
Annað skilyrði fyrir jafnvægi

3 Skilgreining massamiðju!

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5 Yfirlitstafla, glæra 1 K Yrðing Hvenær Dæmi Mótdæmi 3
v = v0 + a t o.s.frv. Jöfn hröðun Fall, skáborð, trissa Fall í vökva arad = v2/R atan = d Iv I/dt Hlutur á ferð Hringhreyfing 4 Fnet = m a Newton 2 Daglegt líf (Einstein) FA on B = - FB on A Newton 3 Vagnhestur Engin 5 fs < msn Stöðunúningur Velta fk = mkn Hreyfinúningur Hlutur rennur Velta, straumefni 6 W =  F.ds Alltaf Allir kraftar W = F.s F = fasti F = m g F = k/r2 W =  Fx dx F = Fx Einvíð hreyfing Þrívíð hreyfing Wtot = DK Allt

6 Yfirlitstafla, glæra 2 K Yrðing Hvenær Dæmi Mótdæmi 6 P = F.v (afl)
Alltaf Bíll Engin 7 WAB(1) = WAB(2) Kraftur geyminn F = m g F = - l v $U: DU = -W E = K + U DE = 0 F = - grad U Ef allir kraftar geymnir U = m g y U = ½ k x2 U = -GmM/r Sama 8 p = m v Alltaf, skilgreining Fext = dP/dt Newton Daglegt líf (Einstein) P = fasti Fext = 0 Árekstrar K = fasti Fjaðrandi árekstur Billjarðkúlur, öreindir

7 Yfirlitstafla, glæra 3 K Yrðing Hvenær Dæmi Mótdæmi 8 J =  F dt = DP
Alltaf, skilgr. Árekstrar Engin rCM = S mi ri/M Skilgr. Agnakerfi (Einstein) P = S pi = MvCM Afleiðing Sama Fext=dP/dt =MaCM Newton P = MvCM = fasti Fext = 0 10 K = KCM + Krot Alltaf Velta KCM = ½ MvCM2 Hliðrun og snúningur

8 Yfirlitstafla, glæra 4 K Yrðing Hvenær Dæmi Mótdæmi 9 K = ½ Iw 2
Stjarfhlutur Trissuhjól 10 Lz = Izw Miðað við snúningsás Nemandi á palli Annar ás text = dL/dt Alltaf Kraftapar á gjörð Engin t = Ia Um fastan ás Ás á hreyfingu L = fasti text = 0 Nemandi með lóð Iiwi =Ifwf I að breytast Diskar

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10 Example 11.1, síðu 408 Univ.Phys.

11 A 1-kg rock is suspended by a massless string from one end of a 1-m measuring stick. What is the mass of the measuring stick if it is balanced by a support force at the 0.25-m mark?                                                             kg kg 3. 1 kg 4. 2 kg 5. impossible to determine

12 A 1-kg rock is suspended by a massless string from one end of a 1-m measuring stick. What is the mass of the measuring stick if it is balanced by a support force at the 0.25-m mark?                                                             kg kg 3. 1 kg 4. 2 kg 5. impossible to determine

13 You decide to make yourself a desk, by attaching a wide shelf to the top of two legs. (A side view is shown.)                                                             When you put a book down on the end of the shelf, the force exerted ON the shelf at the attachment point labeled "A" is approximately 1. Upwards 2. Downwards 3. Rightwards 4. Leftwards 5. Zero

14 You decide to make yourself a desk, by attaching a wide shelf to the top of two legs. (A side view is shown.)                                                             When you put a book down on the end of the shelf, the force exerted ON the shelf at the attachment point labeled "A" is approximately 1. Upwards 2. Downwards 3. Rightwards 4. Leftwards 5. Zero Ef hillunni væri ekki haldið niðri í þennan enda snerist hún!

15 You decide to make yourself a desk, by attaching a wide shelf to the top of two legs. (A side view is shown.)                                                             When you put a book down on the end of the shelf, the force exerted ON the shelf at the attachment point labeled “B" is approximately 1. Upwards 2. Downwards 3. Rightwards 4. Leftwards 5. Zero

16 You decide to make yourself a desk, by attaching a wide shelf to the top of two legs. (A side view is shown.)                                                             When you put a book down on the end of the shelf, the force exerted ON the shelf at the attachment point labeled “B" is approximately 1. Upwards 2. Downwards 3. Rightwards 4. Leftwards 5. Zero Hvað héldi hillunni annars uppi? (Þyngd bókarinnar virkar niður, í “A” er líka kraftur sem virkar niður.)

17 Example 11.3, síðu 411 Univ.Phys.

18 Spenna/Bjögun = Fjaðurstuðull

19 Togspenna Togbjögun

20 Þjöppunarspenna Þjöppunarbjögun

21 I-bjálki ! (léttur en sterkur)
Þjöppunarspenna Togspenna I-bjálki ! (léttur en sterkur)

22 Rýmisspenna Rýmisbjögun

23 Rýmisspenna/Rýmisbjögun
Rýmisfjaðurstuðull

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25 Skúfspenna/Skúfbjögun = Skúfstuðull

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28 1. Setup A is more likely to fail. 2. Setup B is more likely to fail.
A rock climber wants to set up a belay anchor to hang on. Compare the following two setups:                                                         (The top points are solid attachments to the rock, the loop at the bottom of the small slings is what the climber will hang off of. The slings are getting old, and could break if the tension in them is too large.) 1. Setup A is more likely to fail. 2. Setup B is more likely to fail. 3. The two setups are equivalent.

29 1. Setup A is more likely to fail. 2. Setup B is more likely to fail.
A rock climber wants to set up a belay anchor to hang on. Compare the following two setups:                                                         (The top points are solid attachments to the rock, the loop at the bottom of the small slings is what the climber will hang off of. The slings are getting old, and could break if the tension in them is too large.) 1. Setup A is more likely to fail. 2. Setup B is more likely to fail. 3. The two setups are equivalent. Togið er miklu meira!

30 A door is pushed on by two forces, a smaller (tilted) force at the door knob and a larger force nearer the hinge as shown. The door does not move. The force exerted on the door by the hinge.... 1. is zero 2. points ­ (along +y) 3. points ¯ (along -y) 4. points (lower right, in diagram) 5. points in some other direction

31 A door is pushed on by two forces, a smaller (tilted) force at the door knob and a larger force nearer the hinge as shown. The door does not move. The force exerted on the door by the hinge.... 1. is zero 2. points ­ (along +y) 3. points ¯ (along -y) 4. points (lower right, in diagram) 5. points in some other direction


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