10 Dynamics Khoom txuas nrog los ntawm txoj hlua hla lub pulley Atwood tshuab - Teeb Meem thiab Kev daws teeb meem
1. Thaiv A nrog qhov hnyav 5 kg, muab tso rau ntawm ib lub dav hlau kab rov tav. Thaiv B nrog qhov hnyav 3 kg dai ntawm ib kawg ntawm txoj hlua txuas nrog thaiv A hla lub pulley. Kev nrawm vim lub ntiajteb txawj nqus yog 10 m/s 2. Kev nrawm ntawm ob lub thaiv yog dab tsi ?
Paub:
Qhov hnyav ntawm thaiv A (mA) = 5 kg
Qhov hnyav ntawm thaiv B (mB ) = 3 kg
Kev nrawm vim lub ntiajteb txawj nqus (g) = 10 m/s 2
Qhov hnyav ntawm thaiv B (w B ) = m B g = (3)(10) = 30 Newtons
Xav tau: Kev ua kom nrawm ntawm ob lub blocks (a)
Tshuaj:
Lub dav hlau kab rov tav yog du yog li ntawd tsis muaj lub zog sib txhuam. Lub zog uas ua rau ob lub blocks nrawm dua yog qhov hnyav ntawm lub block B.
ΣF = ma
w B = (m A + m B ) a
30 = (5 + 3) ib
30 = 8 ib
ib = 30 / 8
a = 3.75 m/s 2
2.
Raws li daim duab saum toj no, 
(1) kev nrawm ntawm yam khoom = 0
(2) lub khoom txav mus rau qhov ceev tas li
(3) yam khoom tsis txav
(4) yam khoom txav mus los yog tias qhov hnyav ntawm yam khoom me dua lub zog uas rub yam khoom.
Tshuaj:
(1) Qhov kev nrawm ntawm yam khoom = 0.
Lub zog ntawm lub zog:
∑ F = ma –> kev nrawm (a) = 0
∑ F = 0
F 1 + F 2 – F 3 = 12 + 24 – 36 = 36 – 36 = 0 N
(2) Lub khoom txav mus rau qhov ceev tas li
Tsis muaj kev nrawm txhais tau tias yam khoom nyob twj ywm lossis txav mus los ntawm qhov ceev tas li.
(3) yam khoom tsis txav
Tsis muaj lub zog net txhais tau tias yam khoom nyob twj ywm.
(4) yam khoom txav mus los yog tias qhov hnyav ntawm yam khoom me dua lub zog uas rub yam khoom.
Qhov hnyav ua rau ntawm qhov kev taw qhia ntsug, thaum lub zog rub ua rau ntawm qhov kev taw qhia kab rov tav.
Cov khoom txav mus rau hauv qhov kev taw qhia kab rov tav yog li tsuas yog cov zog kab rov tav uas ua rau cov khoom
3. Yog tias tus coefficient ntawm kinetic friction ntawm lub block A thiab lub rooj nto yog 0.1. Acceleration vim gravity yog 10 m/s2, ces lub zog ua rau lub block A yog dab tsi kom lub system txav mus rau sab laug hauv 2 m/ s2.
Paub:
Qhov hnyav ntawm thaiv A (mA) = 30 kg
qhov hnyav ntawm thaiv A (w A ) = (30 kg)(10 m/s 2 ) = 300 kg m/s 2 lossis 300 Newtons
Qhov hnyav ntawm thaiv B (mB ) = 20 kg
qhov hnyav ntawm thaiv B (w B ) = (20 kg)(10 m/s 2 ) = 200 kg m/s 2 lossis 200 Newtons
Kev nrawm vim lub ntiajteb txawj nqus (g) = 10 m/s 2
Coefficient ntawm kinetic sib txhuam ( μk ) = 0.1
Kev nrawm ntawm lub kaw lus (a) = 2 m/s 2 (mus rau sab laug)
Lub zog ntawm kev sib txhuam kinetic (f k ) = μ k N = μ k w A = (0.1)(300) = 30 Newtons
Xav tau: Qhov loj ntawm lub zog F
Tshuaj:
Txoj cai thib ob ntawm Newton:
ΣF = ma
Tus khoom A txav mus rau sab laug:
F – fk – w B = (m A + m B ) a
F – 30 – 200 = (30 + 20)(2)
F – 230 = (50)(2)
F – 230 = 100
F = 230 + 100
F = 330 Newtons
4. Ob yam khoom, A = 2 kg thiab B = 6 kg, txuas rau ib kawg ntawm txoj hlua hla lub pulley, raws li pom hauv daim duab hauv qab no. Yog tias qhov kev nrawm vim lub ntiajteb txawj nqus yog 10 ms -2 ces qhov kev nrawm ntawm yam khoom B yog dab tsi.
Paub:
Qhov hnyav ntawm yam khoom A (mA) = 2 kg, mB = 6 kg, g = 10 m/s2
qhov hnyav ntawm yam khoom A (w A ) = (m A )(g) = (2)(10) = 20 N
qhov hnyav ntawm yam khoom B (w B ) = (m B )(g) = (6)(10) = 60 N
Xav tau: Kev ua kom nrawm ntawm yam khoom b (kev ua kom nrawm ntawm lub kaw lus).
Tshuaj:
w B > w A kom yam khoom B txav mus rau hauv qab, yam khoom A txav mus rau sab saud
ΣF = ma
w B – w A = (m A + m B ) a
60 – 20 = (2 + 6) ib
40 = (8) ib
a = 5 m/s 2
5. Ob yam khoom txuas nrog ib txoj hlua hla lub pulley du, raws li pom hauv daim duab hauv qab no. Yog tias m 1 = 1 kg, m 2 = 2 kg, thiab kev nrawm vim lub ntiajteb txawj nqus yog 10 ms -2 , ces lub zog nruj T yog dab tsi.
Paub:
Qhov hnyav ntawm yam khoom 1 (m1) = 1 kg
Qhov hnyav ntawm yam khoom 2 (m2 ) = 2 kg
Kev nrawm vim lub ntiajteb txawj nqus (g) = 10 m/s 2
qhov hnyav ntawm yam khoom 1 (w 1 ) = m 1 g = (1 kg)(10 m/s 2 ) = 10 kg m/s 2 lossis 10 Newtons
qhov hnyav ntawm yam khoom 2 (w 2 ) = m 2 g = (2 kg)(10 m/s 2 ) = 20 kg m/s 2 lossis 20 Newtons
Xav tau: Lub zog nruj (T)?
Tshuaj:
w 2 > w 1 yog li m 2 txav mus rau hauv qab , m 1 txav mus rau sab saud.
Txoj Cai Thib Ob ntawm Newton ntawm Kev Txav Mus Los :
ΣF = ma
w 2 – w 1 = (m 1 + m 2 ) a
20 – 10 = (1 + 2) ib
10 = (3) ib
a = 3.3 m/s 2
Kev nrawm ntawm lub cev = 3.3 m/s 2.
m2 txav mus rau hauv qab:
w 2 – T 2 = m 2 a
20 – T 2 = (2)(3.33)
20 – T 2 = 6.66
T 2 = 20 – 6.66
T 2 = 13.3 Newtons
m 1 txav mus rau sab saud:
T 1 – w 1 = m 1 a
T 1 – 10 = (1)(3.3)
T 1 – 10 = 3.33
T 1 = 10 + 3.33
T 1 = 13.3 Newtons
Lub zog nruj (T) = 13.3 Newtons.
6. Qhov hnyav ntawm m1 = 6 kg thiab qhov hnyav ntawm m2 = 4 kg. Qhov chaw kab rov tav yog du. Kev nrawm vim lub ntiajteb txawj nqus yog 10 m/s2 . Qhov kev nrawm ntawm lub cev yog dab tsi.
Paub:
Qhov hnyav ntawm m1 = 6 kg
qhov hnyav ntawm m2 = 4 kg
kev nrawm vim lub ntiajteb txawj nqus (g) = 10 m/s 2
qhov hnyav ntawm w 1 = m 1 g = (6 kg)(10 m/s 2 ) = 60 kg m/s 2 lossis 60 Newtons
qhov hnyav ntawm w2 = m2 g = (4 kg)(10 m/s2 ) = 40 kg m/s2 lossis 40 Newtons
Xav tau: Kev nrawm ntawm lub kaw lus (a)
Tshuaj:
m 1 ntawm ib lub dav hlau kab rov tav du tsis muaj kev sib txhuam kom lub kaw lus raug nrawm los ntawm qhov hnyav ntawm lub thaiv 2.
Siv txoj cai thib ob ntawm Newton:
∑ F = ma
w 2 = (m 1 + m 2 ) a
40 N = (6 kg + 4 kg) ib
40 N = (10 kg) ib
a = 40 N / 10 kg
a = 4 m/s 2
7. Ob lub blocks, txhua lub block muaj qhov hnyav ntawm 2 kg, txuas nrog los ntawm ib txoj hlua hla lub pulley, raws li pom hauv daim duab hauv qab no. Lub dav hlau kab rov tav thiab lub pulley yog du. Yog tias lub block B raug rub los ntawm lub zog kab rov tav ntawm 40 Newtons, ces qhov kev nrawm ntawm lub block yog dab tsi. Kev nrawm vim lub ntiajteb txawj nqus yog 10 m / s 2.
Paub:
qhov hnyav ntawm thaiv A (mA) = qhov hnyav ntawm thaiv B (mB) = 2 kg
Kev nrawm vim lub ntiajteb txawj nqus (g) = 10 m/s 2
Lub zog ntawm F = 40 N
qhov hnyav ntawm yam khoom A (w A ) = mg = (2)(10) = 20 N
Xav tau: Kev ua kom nrawm ntawm lub kaw lus (a)?
Tshuaj:
Siv txoj cai thib ob ntawm Newton:
∑ F = ma
F – w A = (m A + m B ) a
40 – 20 = (2 + 2) ib
20 = (4) ib
ib = 20 / 4
a = 5 m/s 2
8. Qhov hnyav ntawm lub thaiv A = 2 kg thiab qhov hnyav ntawm lub thaiv B = 1 kg. Lub thaiv B pib thaum so, tom qab ntawd nws nrawm mus rau hauv av kom txog thaum nws ntaus hauv av. Qhov nrawm vim yog lub ntiajteb txawj nqus yog 10 m/s 2. Lub zog nruj yog dab tsi.
Paub:
Qhov hnyav ntawm thaiv A (mA) = 2 kg
Qhov hnyav ntawm thaiv B (mB ) = 1 kg
Kev nrawm vim lub ntiajteb txawj nqus (g) = 10 m/s 2
Qhov hnyav ntawm thaiv B (w B ) = m B g = (1)(10) = 10 Newtons
Xav tau: Qhov loj ntawm lub zog nruj (T)
Tshuaj:
Tsis quav ntsej lub zog sib txhuam.
Kev nrawm ntawm lub kaw lus (a)
∑ F = ma
w B = (m A + m B ) a
10 = (2 + 1) ib
10 = 3 ib
ib = 10/3
Lub zog nruj (T)
Lub zog nruj ntawm lub thaiv A:
∑ F = ma
T = m A a = (2)(10/3) = 20/3 = 6.7 Newtons
Lub zog nruj ntawm lub thaiv B:
∑ F = ma
w B – T = m B a
10 – T = (1)(10/3)
10 – T = 3.3
T = 10 – 3.3 = 6.7 Newtons
Lub zog nruj (T) = 6.7 Newtons
9. Qhov hnyav ntawm lub thaiv A = 2 kg thiab qhov hnyav ntawm lub thaiv B = 1 kg. Lub zog sib txhuam ntawm yam khoom A thiab lub dav hlau kab rov tav = 2.5 Newtons. Tsis txhob xav txog kev sib txhuam ntawm lub pulley thiab txoj hlua. Qhov kev nrawm ntawm ob lub thaiv yog dab tsi.
Paub:
Qhov hnyav ntawm thaiv A (mA) = 2 kg
Qhov hnyav ntawm thaiv B (mB ) = 1 kg
Lub zog sib txhuam ntawm lub xauv a thiab lub dav hlau kab rov tav (f kA ) = 2.5 Newtons
Kev nrawm vim lub ntiajteb txawj nqus (g) = 10 m/s 2
Qhov hnyav ntawm lub thaiv (w B ) = m B g = (1)(10) = 10 Newtons
Xav tau: Kev ua kom nrawm ntawm ob lub blocks (a)
Tshuaj:
Siv txoj cai thib ob ntawm Newton:
∑ F = ma
w B – fk = (m A + m B ) a
10 – 2.5 = (2 + 1) ib
7.5 = 3 ib
ib = 7.5 / 3
a = 2.5 m/s 2
10. Qhov hnyav ntawm lub thaiv a = 30 kg, so ntawm ib lub dav hlau kab rov tav txuas nrog lub thaiv B nrog qhov hnyav ntawm 10 kg hla lub pulley. Qhov kev nrawm ntawm lub kaw lus yog dab tsi. Kev nrawm vim lub ntiajteb txawj nqus yog 10 ms -2.
Paub:
Qhov hnyav ntawm thaiv A (mA) = 30 kg
Qhov hnyav ntawm thaiv B (mB ) = 10 kg
Kev nrawm vim lub ntiajteb txawj nqus (g) = 10 m/s 2
qhov hnyav ntawm thaiv B (w B ) = m B g = (10)(10) = 100 Newtons
Xav tau: Kev nrawm ntawm lub kaw lus (a)
Tshuaj:
∑ F = ma
w B = (m A + m B ) a
100 = (30 + 10) ib
100 = 40 ib
ib = 100 / 40
a = 2.5 m/s 2
