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a man of mass 50kg standing on one end of a stationary wooden plank resting on a frictionless surface the mass of the plank is 100kg and its length is 75m and the coefficient of friction between the man and plank is 0.2 find the least possible time in which the man reach the other end starting from rest and stopping at the other end

a man of mass 50kg standing on one end of a stationary wooden plank resting on a frictionless surface the mass of the plank is 100kg and its length is 75m and the coefficient of friction between the man and plank is 0.2 find the least possible time in which the man reach the other end starting from rest and stopping at the other end

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2 Answers

Arun
25750 Points
4 years ago
Dear student
 
a = 0.2 *10 + (50*0.2*10/10) = 2 + 10 = 12
 
Vmax = √(2*12*150) = 60
 
Hence
 
60 *(t/2) = 300
t/2 = 5
t = 10 sec
 
Hope it helps
 
Vikas TU
14149 Points
4 years ago
Dear student 
a1=μmg/m=2m/s^2
a2=(μmg)M=1m/s^2
Plank as frame of reference Plank comes to rest
tanα=3=h/t
h=3t
for minimum time, man will acceleration and retard with a1/2 for equal time interval t Area of v vs t graph = displacement
1/2(2t)(3t)=75
t=5
minimum time =2t=10sec

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