Dynamics ntawm cov khoom me me - teeb meem thiab kev daws teeb meem
1. Khoom A uas muaj qhov hnyav ntawm 6-kg thiab khoom B uas muaj qhov hnyav ntawm 4-kg txuas nrog los ntawm txoj hlua thiab rub los ntawm lub zog ntawm F = 60 N, raws li pom hauv daim duab hauv qab no. Tus coefficient ntawm kev sib txhuam kinetic ntawm hauv pem teb thiab ob qho khoom yog 0.5 (tan θ = ¾). Kev nrawm vim lub ntiajteb txawj nqus yog 10 m/s 2. Qhov loj ntawm lub zog nruj yog dab tsi?
Paub:
Qhov hnyav ntawm yam khoom A (mA) = 6 kg
Qhov hnyav ntawm yam khoom B (mB ) = 4 kg
Lub zog (F) = 60 Newton
Tus coefficient ntawm kinetic sib txhuam ntawm yam khoom thiab hauv pem teb (μ k ) = 0.5
Kev nrawm vim lub ntiajteb txawj nqus (g) = 10 m/s2
Tan θ = 3/4
Lub zog tensile (T)
Tshuaj:
Kab rov tav ntawm lub zog F:
F x = F cos θ
F x = (60)(4/5) = (4)(12) = 48 N
Cov khoom ntsug ntawm lub zog F:
F y = F sin θ
Fy = (60)(3/5) = (3)(12) = 36 N
Lub zog ib txwm muaj rau ntawm yam khoom A:
NA = w A = m A g = (6)(10) = 60 N
Lub zog ib txwm muaj rau ntawm yam khoom B:
N B + F y – w B = 0
N B + F y = w B
N B = w B – F y = m B g – F y = (4)(10) – 36 = 40 – 36 = 4 N
Lub zog ntawm kev sib txhuam kinetic ntawm yam khoom A thiab hauv pem teb:
f kA = μ k N A = (0.5)(60) = 30 N
Lub zog ntawm kev sib txhuam kinetic ntawm yam khoom B thiab hauv pem teb:
f kB = μ k N B = (0.5)(4) = 2 N
Xam qhov kev nrawm ntawm ob yam khoom:
ΣF = ma
F x – T + T – f kB – f kA = (m A + m B ) a
F x – f kB – f kA = (m A + m B ) a
48 – 2 – 30 = (6 + 4) ib
16 = 10 ib
ib = 16/10
a = 1.6 m/s 2
Xam lub zog ntawm lub zog:
Khoom A:
ΣF = ma
TA – f kA = m A a
TA – 30 = (6)(1.6)
TA – 30 = 9.6
TA = 9.6 + 30 = 39.6 N
Khoom B:
ΣF = ma
F x – f kB – TB = m B a
48 – 2 – TB = (4)(1.6)
46 – TB = 6.4
46 – 6.4 = TB
T₂ = 39.6 N
2. Yog tias tus coefficient ntawm kinetic friction ntawm ob lub blocks thiab hauv pem teb yog 0.2, qhov acceleration ntawm ob yam khoom yog dab tsi? (cos 37 o = 0,8, sin 37 o = 0,6)
Paub:
Qhov hnyav ntawm yam khoom A (mA) = 4 kg
Qhov hnyav ntawm yam khoom B (mB ) = 2 kg
Lub zog (F) = 30 Newton
Tus coefficient ntawm kinetic sib txhuam ntawm yam khoom thiab hauv pem teb (μ k ) = 0.2
Kev nrawm vim lub ntiajteb txawj nqus (g) = 10 m/s2
cos 37 o = 0.8
sin 37 o = 0.6
Xav tau: Kev nrawm ntawm ob yam khoom
Tshuaj:
Lub zog ntawm lub zog F:
F x = F cos θ
F x = (30)(0.8) = 24 N
Lub zog ntsug ntawm lub zog F:
F y = F sin θ
Fy = (30)(0.6) = 18 N
Lub zog ib txwm muaj rau ntawm yam khoom A:
NA = w A = m A g = (4)(10) = 40 N
Lub zog ib txwm muaj rau ntawm yam khoom B:
N B + F y – w B = 0
N B + F y = w B
N B = w B – F y = m B g – F y = (2)(10) – 18 = 20 – 18 = 2 N
Lub zog ntawm kev sib txhuam kinetic ntawm yam khoom A thiab hauv pem teb:
f kA = μ k N A = (0.2)(40) = 8 N
Lub zog ntawm kev sib txhuam kinetic ntawm yam khoom B thiab hauv pem teb:
f kB = μ k N B = (0.2)(2) = 0.4 N
Kev nrawm ntawm ob yam khoom:
ΣF = ma
F x – f kB – f kA = (m A + m B ) a
24 – 0.4 – 8 = (4 + 2) ib
15.6 = 6 ib
ib = 15.6 / 6
a = 2.6 m/s 2
3. Ob yam khoom txuas nrog ib txoj hlua hla lub pulley raws li pom hauv daim duab hauv qab no. Qhov hnyav ntawm yam khoom A = m A , qhov hnyav f yam khoom B = m B thiab qhov kev nrawm ntawm thaiv B yog a. Kev nrawm vim yog lub ntiajteb txawj nqus yog g. Lub zog nruj ntawm thaiv B yog dab tsi.
Tshuaj:
Qhov chaw kab rov tav yog du yog li ntawd tsis muaj kev sib txhuam. Lub zog tsuas yog uas ua rau lub kaw lus nrawm dua yog qhov hnyav ntawm lub thaiv B.
Kev ua kom nrawm ntawm lub system:
Lub zog nruj (T):
Hloov m A hauv kab zauv 1 nrog m A hauv kab zauv 2.
- Qhov txawv ntawm statics thiab dynamics hauv cov ntsiab lus ntawm cov khoom me me yog dab tsi?
- teb: Kev kawm txog statics yog kawm txog cov zog ntawm cov khoom me me uas nyob hauv qhov sib npaug, qhov twg txhua lub zog sib npaug, thiab tsis muaj kev nrawm. Dynamics, ntawm qhov tod tes, kawm txog cov zog thiab kev txav mus los ntawm cov khoom me me thaum cov zog tsis sib npaug, ua rau muaj kev nrawm.
- Txoj Cai Thib Ob ntawm Newton siv rau kev txav ntawm ib qho khoom me me li cas?
- teb: Txoj Cai Thib Ob ntawm Newton hais tias lub zog ua rau ib qho khoom me me yog sib npaug rau qhov loj ntawm cov khoom me me npaug nws qhov kev nrawm: Txoj cai no piav qhia txog yuav ua li cas lub zog yuav cuam tshuam rau kev txav ntawm ib qho khoom me me, nyob ntawm nws qhov hnyav thiab qhov kev nrawm uas lub zog tsim tawm.
- Lub hauv paus ntsiab lus ntawm kev txuag ntawm linear momentum yog dab tsi, thiab nws siv li cas rau cov khoom me me?
- teb: Lub hauv paus ntsiab lus ntawm kev txuag lub zog linear hais tias tag nrho lub zog linear ntawm lub kaw lus kaw ntawm cov khoom me me tseem nyob ruaj khov yog tias tsis muaj lub zog sab nraud ua rau lub kaw lus. Qhov no txhais tau tias tag nrho lub zog ua ntej thiab tom qab kev sib cuam tshuam ntawm cov khoom me me hauv lub kaw lus yuav zoo ib yam.
- Lub tswv yim ntawm kev ua haujlwm ua rau ib qho khoom me me muaj feem cuam tshuam li cas rau lub zog siv thiab kev hloov chaw ntawm cov khoom me me?
- teb: Kev ua haujlwm ua rau ib qho khoom me me yog qhov khoom ntawm lub zog siv rau qhov khoom me me, qhov kev hloov chaw ntawm qhov khoom me me, thiab cosine ntawm lub kaum sab xis ntawm lub zog thiab cov vectors hloov chaw: .
- Qhov txawv ntawm lub zog kinetic thiab lub zog muaj peev xwm hauv cov ntsiab lus ntawm ib qho khoom me me yog dab tsi?
- teb: Lub zog Kinetic yog lub zog ntawm ib qho khoom me me vim nws txoj kev txav mus los thiab yog muab los ntawm 1/2 , qhov twg yog lub mass thiab yog qhov ceev. Lub zog muaj peev xwm yog lub zog khaws cia rau hauv ib qho khoom me me vim nws qhov chaw nyob hauv lub zog (xws li lub zog gravitational lossis hluav taws xob). Qhov kev qhia tshwj xeeb rau lub zog muaj peev xwm nyob ntawm lub zog ua rau ntawm qhov khoom me me.
- Lub zog ntawm ib lub khoom me me muaj feem cuam tshuam li cas rau qhov kev hloov pauv ntawm nws lub zog?
- teb: Lub zog uas lub zog ntawd siv rau ib yam khoom me me yog qhov sib npaug ntawm lub zog uas lub zog ntawd siv rau yam khoom me me thiab lub sijhawm uas lub zog ntawd siv rau. Nws yog sib npaug rau qhov kev hloov pauv ntawm lub zog ntawm yam khoom me me: .
- Lub ntsiab lus ntawm "free particle," yog dab tsi thiab nws ua li cas?
- teb: Ib qho khoom me me uas tsis muaj zog yog ib qho uas tsis raug kev quab yuam. Raws li Newton Txoj Cai Thawj Zaug, ib qho khoom me me uas tsis muaj zog yuav nyob twj ywm yog tias thaum xub thawj nws nyob twj ywm lossis txav mus nrog qhov ceev tas li yog tias thaum xub thawj nws txav mus los.
- Kev sib txhuam ua lub luag haujlwm dab tsi hauv cov dynamics ntawm cov khoom me me?
- teb: Kev sib txhuam yog ib lub zog uas tawm tsam qhov kev txav mus los ntawm cov chaw sib chwv. Hauv cov ntsiab lus ntawm cov khoom me me, kev sib txhuam tuaj yeem ua rau qeeb lossis nres qhov kev txav mus los ntawm cov khoom me me, nyob ntawm qhov kev coj thiab qhov loj ntawm lub zog sib txhuam.
- Lub zog hauv nruab nrab cuam tshuam li cas rau txoj kev ntawm ib qho khoom me me?
- teb: Lub zog hauv nruab nrab yog lub zog uas ua raws txoj kab txuas lub khoom me me mus rau ib qho chaw ruaj khov, hu ua qhov chaw nruab nrab. Cov zog no feem ntau tshwm sim hauv kev sib cuam tshuam ntawm lub ntiajteb txawj nqus thiab hluav taws xob thiab yuav ua rau lub khoom me me txav mus rau hauv txoj kev uas tswj tau lub zog ntawm lub kaum sab xis tshwj xeeb nyob ib puag ncig qhov chaw nruab nrab, feem ntau ua rau muaj kev ncig elliptical lossis voj voog.
- Qhov kev sib raug zoo ntawm lub zog sab nraud uas ua rau lub kaw lus ntawm cov khoom me me thiab qhov nrawm ntawm kev hloov pauv ntawm tag nrho cov zog linear ntawm lub kaw lus yog dab tsi?
- teb: Raws li Newton Txoj Cai Thib Ob uas siv rau ib lub kaw lus ntawm cov khoom me me, lub zog sab nraud uas ua rau lub kaw lus yog sib npaug rau qhov kev hloov pauv ntawm tag nrho cov zog linear ntawm lub kaw lus: , qhov twg yog tag nrho cov zog linear.
