1. Ib lub pob, uas txuas rau qhov kawg ntawm txoj hlua kab rov tav, tig mus rau hauv ib lub voj voog uas muaj radius 20 cm. Lub pob tig ib ncig ntawm 360 o txhua ob. Txheeb xyuas qhov loj ntawm qhov kev nrawm ntawm centripetal!
Paub:
Qhov ceev ntawm lub kaum sab xis (ω ) = 360 o / vib nas this = 1 revolution/ vib nas this = 6.28 radians/ vib nas this
Lub vojvoog (r) = 20 cm = 0.2 m
Xav tau: Centripetal acceleration (a r )
Tshuaj:
ib r = v 2 / r —> v = r ω
a r = (r ω) 2 / r = r 2 ω 2 / r
ib r = r ω 2
a s = kev nrawm ntawm centripetal, v = linear velocity, r = radius, ω = angular velocity
Qhov loj ntawm centripetal acceleration :
a r = r ω 2 a r = (0,2 m)( 6.28 rad/s)
ib r = 1.256 m/ s2
[irp]
2. Lub log uas muaj 30 cm radius tig nrog lub zog 180 rpm. Txheeb xyuas qhov kev nrawm ntawm lub centripetal ntawm ib qho chaw ntawm ntug ntawm lub log!
Paub:
Lub vojvoog (r) = 30 cm = 0.3 m
Qhov ceev ntawm lub kaum sab xis ( ω ) = 180 lub voj voog / 60 vib nas this = 3 lub voj voog / vib nas this = (3) (6.28 radians) / vib nas this = 18.84 radians / vib nas this
Xav tau: kev nrawm ntawm centripetal ( a r ) ntawm r = 0.3 m
Tshuaj:
Qhov loj ntawm centripetal acceleration:
ib r = r ω 2
ib r = (0.3 m)(18.84 rad/s)
ib r = 5.65 m/ s2
3. Lub tsheb sib tw khiav ntawm txoj kev voj voog uas muaj vojvoog 50 meters. Yog tias lub tsheb khiav ceev 72 km/h, txiav txim siab qhov loj ntawm qhov kev nrawm ntawm lub centripetal!
Paub:
Lub vojvoog (r) = 50 meters
Ceev (v) = 72 km/h = (72)(1000 meters) / 3600 vib nas this = 20 meters/ vib nas this
Xav tau : qhov loj ntawm qhov kev nrawm ntawm centripetal (a r )
Tshuaj:
a r = v 2 / r = 20 2 / 50 = 400 / 50 = 8 m/s 2
[irp]
4. Lub tsheb muaj qhov siab tshaj plaws ntawm centripetal acceleration ntawm 10 m/s 2 , yog li lub tsheb tuaj yeem tig tau yam tsis plam tawm ntawm txoj kev nkhaus. Yog tias lub tsheb txav mus los ntawm qhov ceev tas li 108 km/h, qhov radius ntawm qhov nkhaus unbanked yog dab tsi?
Paub:
Kev nrawm ntawm lub zog centripetal (a r ) = 10 m/s 2
Lub tsheb ceev (v) = 108 km/ h = (108)(1000) / 3600 = 30 meters s /se c rau d
Xav tau: radius (r)
Tshuaj:
r = v 2 / a r
r = 30 2 / 10 = 900 / 10 = 90 meters s
[irp]
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