Question

Find mass m of the hanging blocm which will prevent the smaller block from slipping over the triangular block. All the surfaces are fructionless and the pulley is ideal.​

Answer 1

Answer:

PHYSICS

Find the mass of M of the hanging block in figure which will prevent the smaller block from slipping over the triangular block.All the surfaces are frictionless and the strings and the pulleys are tight.

question

December 27, 2019avatar

Pavani Raikwar

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ANSWER

Smaller block tends to slip down under the force that

is the component of its weight along the plane = mg.sin. In

order to prevent the block from slipping, this block along

with the triangular block needs to be accelerated by the system so that

the component of pseudo force on the block balances the component of weight

which is trying to move the block. Let the required acceleration of the

triangular block be 'a'. In order to apply Newton's Laws of Motion with respect

to the non-inertial frame of the triangular block, we add a pseudo force 'ma' on

the smaller block opposite to the direction of 'a'. Component of this force

along the plane is 'ma.cos'. See the diagram below. (Normal force on the block

has zero component along the plane hence not shown in the diagram)

So in order to prevent the smaller block from slipping,

ma.cos = mg.sin

a = g.tan ............................... (A)

Let the tension in the string be T. Downward force on the hanging block M is 'Mg-T' and its acceleration is 'a'. It gives,

Mg-T=Ma T = Mg-Ma. .......... (B)

Consider the forces on the triangular block along the acceleration 'a'. The only horizontal force is T which is causing the movement of both blocks having mass M' and m. It gives,

T = (M'+m)a ................................(C)

Equating (B) and (C).

Mg-Ma = (M'+m)a

M = (M'+m)a/(g-a)

{Put the value of 'a' from (A)}

M = (M'+m)g.tan/(g-g.tan)

M = (M'+m)tan/(1-tan)

(Divide numerator and denominator by tan)

M = (M'+m)/(cot-1) It is the required mass of the hanging block to prevent the smaller block from slipping over the triangular block.

Explanation:

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