**Sticking of
a Block with Accelerated Cart**

Acceleration of an object is defined as its rate of change of velocity at that instant. It is denoted as “a” and the units are\(m/{{\sec }^{2}}\). Any object experiencing an unbalanced force, constant or variable show acceleration (or) Any object undergoing a change in its velocity either magnitude or direction or both is said to be accelerated.

When a cart moves with some acceleration toward right then a pseudo force acts on block toward left. This force is action force by a block on cart.

A Pseudo force also called as fictitious force, inertial force. It is an apparent force that acts on all masses whose motion is described using a non-inertial frame of reference frame, such as rotating reference frame. Pseudo force comes in effect when the frame of reference has started acceleration compared to a non-accelerating frame.

Now block will remain static with respect to cart. If friction force \(\mu R\ge mg\)

\(\Rightarrow \mu mg\ge mg\) \(\left[ As\,\,R=ma \right]\)

\(\Rightarrow a\ge \frac{g}{\mu }\) \(\therefore \,\,\,\,{{a}_{\min }}=\frac{g}{\mu }\)This is the minimum acceleration of the cart so that block doesn’t fall and the minimum force to hold the block together.

\(Minimum\,\,Force\left( {{F}_{\min }} \right)=\left( M+m \right){{a}_{\min }}\) \(\Rightarrow Minimum\,Force\left( {{F}_{\min }} \right)=\left( M+m \right)\frac{g}{\mu }.\)