【題目】(5分)在半徑R=5 000 km的某星球表面,宇航員做了如下實(shí)驗(yàn),實(shí)驗(yàn)裝置如圖甲所示,豎直平面內(nèi)的光滑軌道由軌道AB和圓弧軌道BC組成,將質(zhì)量m=0.2 kg的小球從軌道AB上高H處的某點(diǎn)靜止滑下,用力傳感器測出小球經(jīng)過C點(diǎn)時(shí)對軌道的壓力F,改變H的大小,可測出相應(yīng)F的大小,F(xiàn)隨H的變化如圖乙所示。求:

(1)圓軌道的半徑。

(2)該星球的第一宇宙速度。

【答案】(1)r=0.2 m (2)

【解析】(1)小球過C點(diǎn)時(shí)有:(1分)

對小球從出發(fā)到C點(diǎn),由動(dòng)能定理得:

聯(lián)立①②得:(1分)

由圖可知:當(dāng)H1=0.5 m時(shí),F(xiàn)1=0 N,解得:r=0.2 m

當(dāng)H2=1.0 m時(shí),F(xiàn)1=5 N,解得:g=5 m/s2(1分)

(2)對該行星表面的附近的衛(wèi)星有:(1分)

解得:(1分)

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