A block of mass m is placed against the vertical front surface of a cart. The cart is accelerating horizontally forward. If the coefficient of static friction between the block and the vertical surface is 0.25 , what is the minimum acceleration of the cart required to prevent the block from falling down? (Take g = 10 m/s ^2 )

Step-by-step solution

Let the acceleration of the cart be a . In the reference frame of the cart, a pseudo force ma acts on the block in the backward direction, pressing it against the vertical surface. Thus, the normal reaction is N = ma . The frictional force acting upwards to prevent the block from falling is f = _s N = _s ma . For the block to not fall, the frictional force must balance its weight: f mg _s ma mg a g _s Substitute the given values: a_ min = 10 0.25 = 40 m/s ^2 . Answer: 40 m/s ^2