Question

Imagine a situation in which the given arrangement is placed inside an elevator that can move only in the vertical direction and compare the situation with the case when it is placed on the ground if the elevator accelerates downward with $a_o$(< g)

• A. the limiting friction force between the block M and the surface decreases
• B. the system can accelerate with respect to the elevator even when m <
• C. the system does not accelerate with respect to the elevator unless m >
• D. the tension in the string decreases

Answer 1

The correct option is C

the system does not accelerate with respect to the elevator unless m >

Draw the Free body diagram in the lifts frame

(M$a_o$ is the pseudo force)

$\therefore \sum F_y=0$

$\therefore$ N = (Mg - M$a_o$) (given $a_o$< g)

= M(g - $a_o$)

We can see that the normal force reduces from Mg to M(g - $a_o$)

$\therefore$ limiting friction will reduce

$\therefore N=(Mg-M{a}_o)(given{a}_o<g)$

$\therefore$ = M(g-$a_o$)

We can see that the normal force reduces from Mg to M(g-$a_o$)

$\therefore$ Limiting friction will reduce

Let us assume, the system is accelerated.

Then, T-f =Ma ($\sum F_x$)

Mg - m$a_o$ -T = ma ($\sum F_y$)

m(g - $a_o$) - f = (m+M)a

If they are accelerating,then f=f${}_{max}$ = $\mu N$=$\mu$ M(g-$a_o$)

$\therefore$ m(g-$a_o$) - $\mu$ M(g-$a_o$)= (m+M)a

$\Rightarrow$a = $\frac{g-a_o}{m+M}$(m - $\mu$M)

$\therefore$For acceleration to occur,

m>$\mu M$ as a constant be negative.