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A block of mass 200g rests on a rough horizontal table. A force of 0.6N pulls the block so that it moves with a constant acceleration of 1m/s². Calculate (i) the time it takes to travel a distance of 200m. (ii) the friction force between the block and the table.

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3 parts
c(i)

20 s\text{20 s}

c(ii)

0.4 N\text{0.4 N}

b(ii)

0.02 s\text{0.02 s}

Step-by-step solution

5 steps

Part c(i)· 1 step

Muda unaochukua kusafiri umbali wa 200 m200 \text{ m}.

Tunatumia mlinganyo wa kinematiki s=ut+12at2s = ut + \frac{1}{2}at^2.
Kwa kuwa block inaanza kutoka kupumzika, kasi ya awali u=0 m/su = 0 \text{ m/s}.
Tunapewa s=200 ms = 200 \text{ m} na a=1 m/s2a = 1 \text{ m/s}^2.

  1. Badilisha maadili kwenye fomula na utatue kwa tt.

    s=12at2s = \frac{1}{2}at^2 200 m=12(1 m/s2)t2200 \text{ m} = \frac{1}{2} (1 \text{ m/s}^2) t^2 400 m=(1 m/s2)t2400 \text{ m} = (1 \text{ m/s}^2) t^2 t2=400 s2t^2 = 400 \text{ s}^2 t=400 s2t = \sqrt{400 \text{ s}^2} 20 s\boxed{\text{20 s}}

Part c(ii)

0.4 N\text{0.4 N}

Nguvu ya msuguano kati ya block na meza.

Tunatumia Sheria ya Pili ya Newton: Fnet=maF_{net} = ma.
Nguvu halisi (FnetF_{net}) ni nguvu ya kuvuta (FpullF_{pull}) kutoa nguvu ya msuguano (FfrictionF_{friction}).
Hivyo, Fpull−Ffriction=maF_{pull} - F_{friction} = ma.
Tunapewa Fpull=0.6 NF_{pull} = 0.6 \text{ N}, m=200 g=0.2 kgm = 200 \text{ g} = 0.2 \text{ kg}, na a=1 m/s2a = 1 \text{ m/s}^2.

  1. Badilisha maadili kwenye mlinganyo na utatue kwa FfrictionF_{friction}.

    0.6 N−Ffriction=(0.2 kg)(1 m/s2)0.6 \text{ N} - F_{friction} = (0.2 \text{ kg}) (1 \text{ m/s}^2) 0.6 N−Ffriction=0.2 N0.6 \text{ N} - F_{friction} = 0.2 \text{ N} Ffriction=0.6 N−0.2 NF_{friction} = 0.6 \text{ N} - 0.2 \text{ N} 0.4 N\boxed{\text{0.4 N}}

    3. a) Fafanua frequency.

  2. Ufafanuzi wa frequency.

    Frequency ni idadi ya mizunguko kamili au mitetemo inayofanywa na kitu au wimbi kwa sekunde moja. Kitengo chake ni Hertz (Hz).

Part b(i)· 1 step

Kwenye grafu chora mstari unaoashiria amplitude ya wimbi.

Takwimu hapa chini inawakilisha grafu ya wimbi la uhamisho dhidi ya muda.

  1. Kuashiria amplitude.

    Amplitude ya wimbi ni umbali wa juu zaidi wa chembe kutoka kwenye nafasi yake ya usawa (mhimili wa muda). Kwenye grafu, unaweza kuchora mstari wima kutoka kwenye mhimili wa muda hadi kwenye kilele cha wimbi (pointi ya juu zaidi) au bonde la wimbi (pointi ya chini kabisa).

Part b(ii)

0.02 s\text{0.02 s}

Bainisha kipindi cha wimbi.

  1. Kuamua kipindi cha wimbi kutoka kwenye grafu.

    Kipindi (TT) ni muda unaochukuliwa kwa wimbi kukamilisha mzunguko mmoja kamili. Kutoka kwenye grafu, wimbi linakamilisha mzunguko mmoja kamili kwa 20 ms20 \text{ ms}.

    T=20 msT = 20 \text{ ms}

    Kubadilisha kwenda sekunde:

    T=20×10−3 sT = 20 \times 10^{-3} \text{ s} 0.02 s\boxed{\text{0.02 s}}
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