Block A, with a mass of 10 kg, rests on a 35 incline. The coefficient of static friction is 0.40. An attached string is parallel to the incline and passes over a massless, frictionless pulley at the top. What is the largest mass MB, attached to the dangling end, for which A remains at rest?

Mass of object B is 9 kg for which block A remains at rest.

Explanation:

Given:

Mass of the block A, = 10 kg

Co-efficient of friction, = 0.4

Angle of inclination, = 35°

Mass of block B is unknown.

Have a look to the FBD of the inclined surface along with the two masses and the friction forces and the component of downward weight W (i.e mg).

Let the mass of the block B is .

Forces acting on .

⇒ Net horizontal force,   ...(i)

⇒ Net vertical force,                        ...(ii)

  Plugging value of N from equation (ii) to (i).

  T (the force on the string) can be written as.

⇒

⇒      ...equation (iii)

Net forces acting on .

⇒        

⇒                              ...equation (iv)

Equating (iv) and (iii) as both are string forces on the same pulley.

⇒

⇒

⇒ Plugging the values.

⇒

⇒ kg

And   kg

So,

The largest mass of  , attached to the dangling end, for which remains at rest is of 9 kg.

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