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two blocks A and Bof masses 2kg and 3kg are connceted by a light string and placed on a horizontal surface if coefficient of friction for all surfaces os 0.1 and g=10 then the acceleration of the system is ? when the applied F=45

two blocks A and Bof masses 2kg and 3kg are connceted by a light string and placed on a horizontal surface if coefficient of friction for all surfaces os 0.1 and g=10 then the acceleration of the system is ? when the applied F=45
 

Grade:12

1 Answers

Kush
9 Points
5 years ago
m1 be the mass on the table, 
m2 be the hanging mass, 
g be the acceleration due to gravity, 
I be the moment of inertia of the pulley, 
w be the angular speed of the pulley. 

Equating initial PE of m2 to final KE of the whole system plus work done against friction: 
m2 gh = (m1 + m2)v^2 / 2 + Iw^2 / 2 + u m1 gh ...(1) 

v = rw 

Eliminating w from (1): 
2(m2 - u m1)gh = v^2[ m1 + m2 + I / r^2 ] 

I can't tell from the question which way round the masses are. Is som further explanation or a diagram missing? 

If m1 = 2kg and m2 = 3kg: 
v = sqrt{ 2(3.0 - 0.30 * 2.0)9.81 * 0.6 / [ 2.0 + 3.0 + 0.004 / 0.05^2 ] } 
= 2.07 m/s. 

If m1 = 3kg and m2 = 2kg: 
v = sqrt{ 2(2.0 - 0.30 * 3.0)9.81 * 0.6 / [ 3.0 + 2.0 + 0.004 / 0.05^2 ] 
= 1.40 m/s. 

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