1. Ib lub thawv hnyav 2-kg qeeb qeeb ntawm 10 m/s mus so. Tus coefficient ntawm kev sib txhuam kinetic yog 0.2. Kev nrawm vim lub ntiajteb txawj nqus yog 10 m/s 2. Qhov loj ntawm kev hloov chaw yog dab tsi?
Paub lawm;
Qhov hnyav (m) = 2 kg
Qhov ceev pib ( v₂o ) = 10 m/s
Qhov ceev kawg (v t ) = 0 m/s
Tus coefficient ntawm kinetic friction ( μk ) = 0.2
Qhov hnyav (w) = mg = (1 kg)(10 m/s2 ) = 10 kg m/s2 = 10 N
Xav tau: Qhov loj ntawm kev hloov chaw (d)
Tshuaj:
Lub hauv paus ntsiab lus ntawm lub zog ua haujlwm-mechanical :
W nc = ΔEM
W nc = ΔEK + ΔEP
W nc = ½ m (v t 2 – vo o 2 ) + mgh
W nc = txoj haujlwm ua los ntawm lub zog tsis ruaj khov uas ua rau ntawm qhov khoom
ΔEK = qhov kev hloov pauv ntawm lub zog kinetic
ΔEP = kev hloov pauv ntawm lub zog muaj peev xwm
m = pawg
v = qhov ceev
g = kev nrawm vim yog lub ntiajteb txawj nqus
h = qhov kev hloov pauv ntawm qhov siab
Qhov kev hloov pauv ntawm qhov siab h = 0 yog li ΔEP = 0
W nc = ΔEK
Ua haujlwm los ntawm lub zog tsis ruaj khov:
W nc = -F c d = – μ k N d = – μ k wd = – μ k mgd
W nc = -(0.2)(2)(10)(s)
W nc = – (4)(2)
Lub cim rho tawm qhia tias qhov kev taw qhia ntawm lub zog sib txhuam kinetic yog qhov sib txawv rau qhov kev taw qhia ntawm kev hloov chaw.
Kev hloov pauv ntawm lub zog kinetic:
ΔEK = ½ m (v t 2 – v o 2 ) = ½ (2) (0 – 10 2 ) = 0 – 100 = -100
Qhov loj ntawm kev hloov chaw:
W nc = ΔEK
– 4 vib nas this = – 100
s = -100/-4
s = 25 m
[irp]
2. Ib lub thaiv swb rau ntawm ib lub dav hlau inclined. Tus coefficient ntawm kinetic friction yog 0.4. Acceleration vim lub gravity yog g = 10 ms -2 . Txheeb xyuas qhov ceev kawg thaum lub thaiv ntaus hauv av.
Paub:
Qhov siab pib (h₂o ) = 6 m
Qhov siab kawg (ht ) = 0 m
Qhov ceev pib (v o ) = 0
Tus coefficient ntawm kinetic friction ( μk ) = 0.4
Kev nrawm vim yog lub ntiajteb txawj nqus (g) = 10 ms -2
cosθ = 8/10
Qhov feem ntsug ntawm qhov hnyav = w y = w cos θ = mg cos θ = m (10) (8/10) = m (10)(4/5) = m (40/5) = 8 m
Lub zog ib txwm = N = wy = 8 m
Lub zog ntawm kev sib txhuam kinetic = f k = μ k N = μ k w y = (0.4)(8 m) = 3.2 m
Xav tau: Qhov ceev kawg (v t )
Tshuaj:
Lub hauv paus ntsiab lus ntawm lub zog ua haujlwm-mechanical:
W nc = Δ EM
W nc = Δ EK + Δ EP
Kev hloov pauv ntawm lub zog kinetic:
ΔEK = 1/2 m (vt2 -vo2) = 1/2 m (v)t2 - 0) = 1/2 mvt2
Kev hloov pauv ntawm lub zog muaj peev xwm:
Δ EP = mg (ht – h o ) = m (10)(0-6) = m (10)(-6) = – 60 m
Kev ua haujlwm ua los ntawm lub zog ntawm kev sib txhuam kinetic:
W nc = – f k s = – ( 3.2 m)(10) = – 32 m
Lub cim rho tawm qhia tias qhov kev taw qhia ntawm lub zog ntawm kev sib txhuam kinetic yog qhov sib txawv rau qhov kev taw qhia ntawm kev hloov chaw.
Qhov ceev kawg (v t ):
W nc = Δ EK + Δ EP
– 32 m = 1/2 mv t 2 – 60 m
– 32 m = m (1/2 v t 2 – 60)
– 32 = 1/2 v t 2 – 60
– 32 + 60 = 1/2 v t 2
28 = 1/2 v t 2
2 (28) = v t 2
56 = vt 2
vt = √4.14
v t = 2 √14 ms -1
[irp]
3. Ib lub thaiv swb rau ntawm ib lub dav hlau uas nkhaus. Qhov ceev pib yog 0 m/s thiab qhov ceev kawg yog 10 ms -1 . Yog tias lub zog ntawm kev sib txhuam kinetic yog 2 N thiab kev nrawm vim lub ntiajteb txawj nqus g = 10 ms -2 , qhov siab (h) yog dab tsi?
Paub:
Qhov hnyav (m) = 1 kg
Qhov ceev pib (v o ) = 0 (qhov chaw so ntawm lub thaiv)
Qhov ceev kawg (v t ) = 10 ms -1
Qhov siab pib (h₂o ) = h
Qhov siab kawg (ht ) = 0
Lub zog ntawm kev sib txhuam kinetic (f k ) = 2 N
Kev nrawm vim yog lub ntiajteb txawj nqus (g) = 10 ms -2
Xav tau: Qhov siab (h)
Tshuaj:
Kev ua haujlwm ua los ntawm lub zog ntawm kev sib txhuam kinetic:
W nc = – f k s = – (2 )(15) = – 30
Lub cim rho tawm qhia tias qhov kev taw qhia ntawm lub zog ntawm kev sib txhuam kinetic yog qhov sib txawv rau qhov kev taw qhia ntawm kev hloov chaw.
Kev hloov pauv ntawm lub zog kinetic:
ΔEK = 1/2 m (vt2 -vo2) = 1/2 (1)(102 - 0) = 1/2 (102) = 1/2 (100= 50 TZS
Kev hloov pauv ntawm lub zog muaj peev xwm:
Δ EP = mg (ht – h₂o ) = (1)(10)(0-h) = (10)(-h) = -10 h
Lub hauv paus ntsiab lus ntawm lub zog ua haujlwm-mechanical:
W nc = Δ EK + Δ EP
– 30 = 50 – 10 teev
10 teev = 50 + 30
10 teev = 80
h = 80/10
siab = 8 m
4Yog tias ib lub thaiv txav mus rau hauv ib lub dav hlau uas nkhaus, ces….
A. Txoj haujlwm ua los ntawm lub zog gravity ntawm lub block loj dua qhov kev hloov pauv ntawm lub zog muaj peev xwm ntawm lub block
B. Lub zog kho tshuab nce ntxiv
C. Lub zog kinetic thiab nws lub zog muaj peev xwm raug txo qis
D. Txoj haujlwm ua tiav los ntawm lub zog sib txhuam sib npaug rau qhov kev hloov pauv ntawm lub zog kinetic ntawm lub block
tshuaj
A tsis yog lawm
Txoj haujlwm ua los ntawm lub zog ntawm lub ntiajteb txawj nqus rau ntawm lub block yog sib npaug rau qhov kev hloov pauv ntawm lub zog gravitational ntawm lub block.
B tsis yog lawm
Yog tias lub dav hlau uas muaj kab hauv c du ces lub zog tshuab ntawm lub thaiv yuav ruaj khov. Thaum nyob saum lub dav hlau uas nkhaus thiab tseem tsis tau txav mus los, lub zog tshuab ntawm lub thaiv yuav sib npaug rau lub zog gravitational potential. Lub thaiv tseem so kom nws lub zog kinetic yog xoom. Thaum txav mus rau hauv lub dav hlau uas nkhaus, qhov siab ntawm lub thaiv yuav txo kom lub zog gravitational potential kuj txo qis. Lub zog gravitational potential yuav txo qis vim nws hloov mus rau lub zog kinetic. Txawm hais tias lub zog gravitational potential hloov mus rau hauv lub zog kinetic, lub zog tshuab yog ruaj khov.
Yog tias lub dav hlau nkhaus ces lub zog tshuab ntawm lub thaiv yuav txo qis vim yog txoj haujlwm tsis zoo uas lub zog sib txhuam ua. Lub zog sib txhuam yog lub zog tsis txuag. Txoj haujlwm uas lub zog tsis txuag ua rau ntawm ib yam khoom ua rau lub zog tshuab ntawm yam khoom txo qis.
C yog lawm
Lub dav hlau uas nkhaus yog qhov ntxhib yog li muaj lub zog sib txhuam uas tawm tsam kev txav ntawm lub thaiv. Lub zog sib txhuam yog lub zog tsis txuag. Theorem ua haujlwm-lub zog kho tshuab hais tias kev ua haujlwm ua los ntawm lub zog tsis txuag (piv txwv li lub zog sib txhuam) yog sib npaug rau qhov kev hloov pauv ntawm lub zog kho tshuab. Hauv qhov kev nrhiav no, lub zog kho tshuab tab tom txo qis.
Lub zog tshuab ntawm lub block = lub zog gravitational potential + lub zog kinetic.
D tsis yog lawm.
Cov haujlwm ua los ntawm lub zog sib txhuam ntawm lub thaiv yog sib npaug rau qhov kev hloov pauv ntawm lub zog tshuab ntawm lub thaiv, tsis yog qhov kev hloov pauv ntawm lub zog kinetic ntawm lub thaiv. Muaj tseeb tias lub zog sib txhuam sib tw rau kev txav ntawm lub thaiv yog li nws txo qhov ceev ntawm lub thaiv thiab txo lub zog kinetic ntawm lub thaiv. Tab sis paub tias lub zog kinetic ntawm lub thaiv los ntawm lub zog gravitational. Yog li nws yog qhov tseeb hais tias cov haujlwm ua los ntawm lub zog sib txhuam sib npaug rau qhov kev hloov pauv ntawm lub zog tshuab (lub zog tshuab txo qis).
Cov lus teb yog C.
5. Ib yam khoom uas nyob rau hauv pem teb ntxhib raug ntaus kom nws txav mus rau 3 vib nas this ces nres. Yog tias qhov hnyav ntawm yam khoom paub yog 10 grams, lub zog sib txhuam ntawm yam khoom thiab hauv pem teb yog 2 kilodyne. Txheeb xyuas seb lub zog sib txhuam ua haujlwm li cas.
A. 0.18 J
B. -0.18 J
C. 0.36 J
D. -0.36 J
Paub:
Lub sijhawm luv (t) = 3 vib nas this
Qhov ceev kawg (v t ) = 0 m/s (khoom so)
Qhov hnyav ntawm yam khoom (m) = 10 grams = 10/1000 kg = 1/100 kg = 0.01 kg
Kev sib txhuam quab yuam (F) = 2 kilodynes = 2 x 10 3 dynes
Xav tau: Ua haujlwm (W) ua los ntawm lub zog sib txhuam
Tshuaj:
Kev hloov pauv ntawm cov units ntawm lub zog:
1 Newton = 1 x 10 5 dyne
1 dyne = 1 / 10 5 Newtons = 1 x 10 -5 Newtons = 10 -5 Newtons
Lub zog sib txhuam (F) = 2 x 10 3 dyne = 2 x 10 3 x 10 -5 Newton = 2 x 10 -2 Newton = 2/100 Newton = 0.02 Newton
Lub zog ua haujlwm-mechanical theorem hais tias kev ua haujlwm yog ua los ntawm lub zog tsis-conservative ntawm ib yam khoom sib npaug rau qhov kev hloov pauv ntawm lub zog mechanical ntawm yam khoom.
Yog tias ib yam khoom txav mus rau ntawm lub dav hlau inclined ces lub zog mechanical (ME) = lub zog gravitational potential (PE) + lub zog kinetic (KE). Tab sis yog tias yam khoom txav mus rau ntawm lub dav hlau kab rov tav xwb yog li tsis muaj kev hloov pauv ntawm qhov siab ces lub zog mechanical = lub zog kinetic. Ntawm lub dav hlau kab rov tav, lub zog gravitational potential yog xoom vim tsis muaj kev hloov pauv ntawm qhov siab.
Lub zog sib txhuam yog lub zog tsis txuag. Lub zog sib txhuam feem ntau ua rau qhov ceev ntawm yam khoom thiab lub zog kinetic ntawm yam khoom txo qis. Yuav xaus lus tias txoj haujlwm ua los ntawm lub zog sib txhuam ntawm yam khoom sib npaug rau qhov txo qis ntawm lub zog mechanical.
Raws li lej:
Ua Haujlwm (W) = Qhov kev hloov pauv ntawm lub zog kho tshuab (ΔEM)
Fs = ΔEP + ΔEK
Fs = mg Δh + ½ m ( vt2 – vo2 )
Fs = mg (0) + ½ m (0 2 – vo o 2 )
Fs = 0 + ½ m (– ( vo2 ) )
Fs = – ½ mv o 2 ———— Kab zauv 1
Kev Piav Qhia: F = lub zog sib txhuam, d = kev hloov chaw, m = pawg neeg, v = qhov ceev pib
Qhov kev hloov chaw (d) thiab qhov ceev pib (v o ) tseem tsis tau paub vim tias ua ntej xam v o lossis d. Txoj haujlwm ua los ntawm lub zog sib txhuam xam siv ib qho ntawm cov qauv tom qab paub v o lossis d.
Tus qauv ntawm kev hloov chaw (d) ntawm kev txav mus los tsis sib xws:
vt2 = vo2 + 2 (-a ) s
Qhov ceev kawg (vt ) = 0 thiab qhov kev nrawm (a) yog kos npe tsis zoo vim tias qhov khoom raug qeeb (qhov ceev ntawm qhov khoom raug txo qis).
0 = vo2 – 2 kev tshaj tawm
vo2 = 2 kev tshaj tawm
d = vo o 2 / 2 a ———— Kab zauv 2
Hloov d hauv kab zauv 2 nrog d hauv kab zauv 1:
F d = – ½ mv o 2
F (v2 / 2a ) = – ½ mv2
(F/2a) v o 2 = – ½ mv o 2
F/2a = – ½ m
F = (2)(a)(-1/2)(m)
F = – (a)(m)
ib = - (F / m)
a = – 0.02 Newtons / 0.01 kilograms
a = - 2 Newton/kilogram
ib = – 2 m/s 2
Tus qauv los xam qhov ceev pib (v o ) hauv kev txav mus los tsis sib xws:
v t = vo o + at —–> Qhov ceev kawg (v t ) = 0, Kev nrawm (a) = 2 m/s 2 , lub sijhawm luv (t) = 3 vib nas this
0 = v0 + (-2)(3)
0 = v0 – 6
v0 = 6 meters/ sijhawm
Lub zog sib txhuam ua haujlwm (W):
W = – ½ mv o 2 = -1/2 (0.01)(6 2 ) = -1/2 (0.01)(36)
W = -1/2 (0.36)
W = – 0.18 Joule
Txoj haujlwm ua los ntawm lub zog sib txhuam yog kos npe tsis zoo uas txhais tau tias txoj haujlwm txo qis lub zog tshuab ntawm yam khoom.
Yog paub d ces txoj haujlwm yuav raug suav los ntawm kev siv cov qauv ntawm W = F d.
Cov lus teb yog B.
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- Cov teeb meem thiab kev daws teeb meem ntawm lub zog ua haujlwm
- Cov teeb meem thiab kev daws teeb meem ntawm lub zog ua haujlwm-kinetic
- Cov teeb meem thiab kev daws teeb meem ntawm lub hauv paus ntsiab lus ntawm lub zog ua haujlwm-mechanical
- Cov teeb meem thiab kev daws teeb meem ntawm lub zog gravitational
- Lub zog muaj peev xwm ntawm cov teeb meem caij nplooj ntoos hlav elastic thiab kev daws teeb meem
- Teeb meem fais fab thiab kev daws teeb meem
- Kev siv ntawm kev txuag lub zog mechanical rau kev txav mus los dawb
- Kev siv ntawm kev txuag lub zog kho tshuab rau kev txav mus rau saum thiab nqis hauv kev txav mus los dawb
- Kev siv ntawm kev txuag lub zog kho tshuab rau kev txav mus los ntawm qhov chaw nkhaus
- Kev siv ntawm kev txuag lub zog kho tshuab rau kev txav mus los ntawm lub dav hlau inclined
- Kev siv ntawm kev txuag lub zog kho tshuab rau kev txav mus los ntawm projectile
