Kev sib npaug ntawm cov cev ntawm lub dav hlau inclined - kev siv Newton txoj cai thawj zaug cov teeb meem thiab kev daws teeb meem

1. Ib lub thaiv hnyav 2-kg pw rau ntawm ib lub dav hlau uas nkhaus ntawm lub kaum sab xis 37 ^o rau kab rov tav. Txheeb xyuas qhov loj ntawm lub zog sab nraud uas siv rau ntawm lub thaiv, kom lub thaiv tsis txhob swb rau hauv lub dav hlau. (sin 37 ^o = 0.6, cos 37 ^o = 0.8, g = 10 ms ^-2 , µk ₌ 0.2)

Paub:

Qhov hnyav (m) = 2 kg

Kev nrawm vim lub ntiajteb txawj nqus (g) = 10 m/s ²

Qhov hnyav ntawm lub thaiv (w) = mg = (2)(10) = 20 Newtons

Sin 37 ^o = 0.6

Cos 37 ^o = 0.8

Coefficient ntawm kinetic sib txhuam (µk ₎ = 0.2

Tus y-component ntawm qhov hnyav (w _y ) = w cos 37 ^o = (20)(0.8) = 16 Newtons

Tus x-component ntawm qhov hnyav (w _x ) = w sin θ = (20)(sin 37) = (20)(0.6) = 12 Newtons

lub zog ib txwm (N) = w _y = 16 Newtons

Xav tau : Lub zog sab nraud (F)

Kev daws teeb meem :

w_x = 12 Newtons

Lub zog ntawm kev sib txhuam kinetic (f _k ) = µ _k N = (0.1)(16) = 1.6 Newtons

Qhov loj ntawm lub zog sab nraud F uas siv rau ntawm lub thaiv :

F + fk _– wx ₌ 0

F = _wx – _fk

F = 12 – 1.6

F = 10.4 Newtons

Lub zog sab nraud F ntau dua 10.4 Newtons.

[irp]

2. Qhov hnyav ntawm ib lub thaiv = 2 kg, coefficient ntawm kev sib txhuam static µs ₌ 0.4 thiab θ = 45 ^o . Txheeb xyuas qhov loj ntawm lub zog F kom lub thaiv pib swb rau saum.

Paub:

Tus coefficient ntawm kev sib txhuam zoo li qub (µs ₎ = 0.4

Lub kaum sab xis (θ) = 45 ^o

Kev nrawm vim lub ntiajteb txawj nqus (g) = 10 m/s ²

Qhov hnyav ntawm lub thaiv (m) = 2 kilogram

Qhov hnyav ntawm lub thaiv (w) = mg = (2 kg) (10 m/s ² ) = 20 kg m/s ² = 20 Newtons

Tus x-component ntawm qhov hnyav (w _x ) = w sin θ = (20)(sin 45) = (20)(0.5√2) = 10√2 Newtons

Tus y-component ntawm qhov hnyav (w _y ) = w cos θ = (20)(cos 45) = (20)(0.5√2) = 10√2 Newtons

Xav tau : Qhov loj ntawm lub zog F

Tshuaj:

Lub thaiv pib swb rau saum, yog tias F ≥ w_x + f_s.

Tus x-feem ntawm qhov hnyav:

w _x = 10√2 Newtons

y-feem ntawm qhov hnyav :

w ₌ 10√2 Newton

Lub zog ib txwm :

N = wy ₌ 10√2 Newton

Lub zog ntawm kev sib txhuam static :

f _s = µs _N = (0,4)(10√2) = 4√2

Qhov loj ntawm lub zog F kom lub block pib swb mus rau saum :

F ≥ w _x + f _s

F ≥ 10√2 + 4 √2

F ≥ 14√2 Newtons

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