A body starts slipping down an incline and moves half meter in half second. How long will it take it to move the next half meter?Concept of Physics - 1 , HC VERMA , Chapter 6:Friction "
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Solution :
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Suppose a body is accelerating downward with an acceleration A:
From the free body diagram :
R-mg Cosθ=0
R=mg Cos θ
and
-ma +mg sin θ-μR=0
a= mg (sinθ-μCosθ)/m
= g(sinθ-μCosθ)
For the first half meter : u=0 m/s
S= 5m
t=0.5 sec
So V=u+at
=0+0.5x4
=2m/s
From S=ut +1/2at2
0.5=0+1/2 ax(0.5)2
a= 4m/s2
For the next half meter,u=2m/s
a= 4m/s 2
S=0.5
0.5= 2t+(1/2 ) 4t²
2t²+2t -0.5=0
4t²+4t -1=0
t=-4±√16 +16/0.2 x4
t= 1.6556/8
=0.2027 sec
Time taken to cover next half meter is 0.21sec.
*************************************
Suppose a body is accelerating downward with an acceleration A:
From the free body diagram :
R-mg Cosθ=0
R=mg Cos θ
and
-ma +mg sin θ-μR=0
a= mg (sinθ-μCosθ)/m
= g(sinθ-μCosθ)
For the first half meter : u=0 m/s
S= 5m
t=0.5 sec
So V=u+at
=0+0.5x4
=2m/s
From S=ut +1/2at2
0.5=0+1/2 ax(0.5)2
a= 4m/s2
For the next half meter,u=2m/s
a= 4m/s 2
S=0.5
0.5= 2t+(1/2 ) 4t²
2t²+2t -0.5=0
4t²+4t -1=0
t=-4±√16 +16/0.2 x4
t= 1.6556/8
=0.2027 sec
Time taken to cover next half meter is 0.21sec.
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