题干

传送带以恒定速度v=4m/s顺时针运行,传送带与水平面的夹角θ=37°.现将质量m=2kg的小物品轻放在其底端(小物品可看成质点),平台上的人通过一根轻绳用恒力F=20N拉小物品,经过一段时间物品被拉到离地高为H=1.8m的平台上,如图所示.已知物品与传送带这间的动摩擦因数μ=0.5,设最大静摩擦力等于滑动摩擦力,g取10m/s2,已知sin37°=0.6,cos37°=0.8.求:

①物品从传送带底端运动到平台上所用的时间是多少?

②若在物品与传送带达到同速瞬间撤去恒力F,求物品还需多少时间离开皮带?

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答案(点此获取答案解析)

解:①物品在达到与传送带速度v=4m/s相等前,有:
F+μmgcos37°﹣mgsin37°=ma1
解得 a1=8m/s2

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