问题 问答题

如图,用一劲度系数k=100N/m的轻质弹簧秤水平拉着质量m=1kg的物体向右做匀速直线运动,此时弹簧秤示数F=2N.

(1)画出此时的受力分析图,并求弹簧秤的形变量x1和物体与地面间的动摩擦系数μ.

(2)如果弹簧秤突然变为竖直向上拉物体,使物体继续维持原来的匀速直线运动,则此时的弹簧秤形变量x2为多少?物体与地面间的动摩擦系数又为多少?

答案

(1)物体在竖直方向受重力和支持力作用,大小均为G=mg=1kg×10N/kg=10N,水平方向受到的拉力F和摩擦力f是平衡力,大小相等,方向相反如图所示:

根据胡克定律得:

F=kx1

解得:x1=

2
100
=0.02m,

f=F=μmg

解得:μ=

2
10
=0.2

(2)如果弹簧秤突然变为竖直向上拉物体,使物体继续维持原来的匀速直线运动,则竖直方向弹力等于重力,水平方向不受力,即:

F2=mg=10N

则有:x2=

F2
k
=
10
100
=0.1m

物体与地面间的动摩擦系数不变,仍为0.2.

答:(1)受力分析图如图所示,弹簧秤的形变量x1为0.02m,物体与地面间的动摩擦系数μ为0.2.

(2)此时的弹簧秤形变量x2为0.1m,物体与地面间的动摩擦系数为0.2.

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