问题 问答题

如图所示,半径为R=0.8m的四分之一圆弧形光滑轨道竖直放置,圆弧最低点B与长为L=1m的水平桌面相切于B点,BC离地面高为h=0.45m,质量为m=1.0kg的小滑块从圆弧顶点D由静止释放,已知滑块与水平桌面间的动摩擦因数μ=0.6,取g=10m/s2.求:

(1)小滑块刚到达圆弧面的B点时对圆弧的压力大小;

(2)小滑块落地点与C点的水平距离.

答案

(1)滑块由D到B过程中,由动能定理得

      mgR=

1
2
mvB2         

在B点,由牛顿第二定律得:F-mg=m

v2B
R

故解得vB=4m/s,F=30N                       

由牛顿第三定律知对圆弧的压力大小为30N,方向竖直向下.

(2)由B到C过程,由动能定理得:-μmgL=

1
2
m
v2C
-
1
2
m
v2B

代入解得vc=2m/s

滑块由C点开始做平抛运动,由h=

1
2
gt2得,t=
2h
g

落地点与C点水平距离为s=vCt=vC

2h
g
=0.6m

答:

(1)小滑块刚到达圆弧面的B点时对圆弧的压力大小为30N;

(2)小滑块落地点与C点的水平距离是0.6m.

阅读理解

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