Question

Find the speed of the block when it covers a horizontal distance . It is given that the block never loses contact with the smooth horizontal surface, and the force always acts at an angle θ with the horizontal.

Answer 1

Answer:

Two blocks with masses m  

1

​  

 and m  

2

​  

 are stacked on a horizontal smooth surface. Coefficient of friction between the blocks is μ. A force F is applied at angle θ with the horizontal on block of mass m  

1

​  

. Find the maximum force F so that the blocks move together.

HARD

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ANSWER

N=(m  

1

​  

g+Fsinθ)

F  

f

​  

=uN

Fcosθ−F  

f

​  

=m  

1

​  

a

Fcosθ−u(m  

1

​  

g+Fsinθ)=m  

1

​  

    .......(1)

Fcosθ=(m  

1

​  

+m  

2

​  

)a             ..............(2)

From equation 1 and 2:

Fcosθ−u(m  

1

​  

g+Fsinθ)=  

m  

1

​  

+m  

2

​  

 

m  

1

​  

Fcosθ

​  

 

F=  

m  

2

​  

cosθ−u(m  

1

​  

+m  

2

​  

)sinθ

um  

1

​  

(m  

1

​  

+m  

2

​  

)g

​