Question

a body of 60kg is pushed up with just enough force to start it moving on a rough horizontal surface with /ls=0.5 and /lk=0.4 and force continues to acts forward. what is the acceleration of the body?​

Answer 1

Answer :-

Acceleration of the body is 0.98 m/s²

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Here is the Required Explanation:-

As the mass of the block is 60kg . It is just tends to move on rough surface .

So, forces acting on body will be the Limititing friction(fₗ) and Kinetic friction fₖ(rough surface).

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So, The equation will be the

fₗ - fₖ= ma

As we know that ,

Limititing Friction(fₗ) = μₛN

Kinetic friction (fₖ) = μₖN

So,

fₗ - fₖ = ma

μₛN - μₖN = ma

As we know that N (normal reaction is mg)

So,

μₛmg - μₖmg = ma

Taking common mg

(μₛ - μₖ)mg = ma

Cancelling "m" on both sides

(μₛ - μₖ)g = a

Substituting the values,

(0.5)-(0.4)g = a

Here as we know that "g" is Acceleration due to gravity

We take g = 9.8 m/s²

(0.1) 9.8 = a

a = 0.98 m/s²

So, acceleration of the body is 0.98 m/s²

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Note :- Its value slightly varies if g = 10 m/s²

Then acceleration will be 1 m/s² .

For fre.e body diagram refer attachment. ${}$