如图4-1-16所示,质量m=2 kg的木块在倾角α=37°的斜面上由静止开始下

如图4-1-16所示,质量m=2 kg的木块在倾角α=37°的斜面上由静止开始下滑,木块与斜面间的动摩擦因数为0.5,已知:sin37°=0.6,cos37°=0.8,g取10 m/s2,求:

图4-1-16

(1)前2 s内重力做的功;

(2)前2 s内重力的平均功率;

(3)2 s末重力的瞬时功率.

答案

思路点拨:可先由W=Fssin37°来计算重力的功,再由P=W/t来计算重力的平均功率,由P=Fv求重力的瞬时功率.

解析:(1)木块所受的合外力为:

F=mgsinθ-μmgcosθ

=mg(sinθ-μcosθ)

=2×10×(0.6-0.5×0.8) N=4 N

物体的加速度为:a=F/m=4/2 m/s2=2 m/s2

前2 s内木块的位移:

s=at2=×2×22 m=4 m

所以,重力在前2 s内做的功为:

W=mgsinα·s=2×10×0.6×4 J=48 J.

(2)重力在前2 s内的平均功率为:

==24 W.

(3)木块在2 s末的速度:

v=at=2×2 m/s=4 m/s

重力在2 s末的瞬时功率

P=mgsinα·v=2×10×0.6×4 W=48 W.

答案:48 J  24 W  48 W

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