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Three blocks m1=3kg,m2=2kg,m3=5kg lie on an inclined frictionless surface with inclination of 30 degree as shown in the figure.
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(a) what force(F) parallel to incline is needed to push the blocks up the plane with an acceleration a=2m/s2
(b) Find the contact force between m1 and m2 and between m2 and m3

Answer
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Hint: This question can be answered by using newton’s second law. According to Newton's second law for a particular system rate of change of momentum will be equal to the external force acting on the system. Here external force will be responsible for the resulting acceleration of the system
Formula used:
Fext=ma

Complete answer:
According to Newton's second law the unbalanced external force will be responsible for the acceleration of the system. By seeing the diagram below we can interpret important information.
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There will be weight of the blocks acting in the downward direction. If we resolve the weight of the blocks into components, we will get one component along the plane and another component perpendicular to the plane. We have the equation Fext=ma
Along the plane the weight component will be(m1+m2+m3)gsinθ
Where theta is the angle at which the plane is inclined with the horizontal which is 30 degrees here.
We need acceleration up the incline as 2ms2 and hence we have
F(m1+m2+m3)gsinθ=(m1+m2+m3)aF=(m1+m2+m3)gsinθ+(m1+m2+m3)aF=(3+2+5)×10×sin30+(3+2+5)2F=50N+20NF=70N
Let N12 be the normal reaction force between blocks 1 and 2 and N23 be the normal reaction force between blocks 2 and 3. Between 1 and 2 we have
N12(m2+m3)gsinθ=(m2+m3)aN12(2+5)gsin30=(2+5)×2N12=35N+14NN12=49N
Similarly between 2 and 3 we have
N23(m3)gsinθ=(m3)aN23(5)gsin30=(5)×2N23=25N+10NN23=35N
So we had the force required as 70 Newton and the normal reaction between first and second block as 49 Newton and between second and third block as 35 Newton.

Note:
In the given question there is no frictional force between the blocks and the inclined. If there is frictional force then the answer would be different because friction force will oppose the motion of the blocks. Since the blocks are intended to move upwards the incline, friction will be acting downwards the incline.
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