A block is held against the vertical front wall of a cart. The coefficient of static friction between the block and the wall is 0.4 . What is the minimum horizontal acceleration with which the cart must move forward so that the block does not slide down the wall? (Take g = 10 m s ⁻² )

Step-by-step solution

Let the mass of the block be m and the acceleration of the cart be a . In the reference frame of the accelerating cart, a pseudo force ma acts on the block, pressing it against the vertical wall. This provides the normal force: N = ma The maximum static friction force available to prevent the block from falling is: f_ s, max = _s N = _s ma For the block not to slide down, this upward frictional force must balance the downward gravitational force: _s ma mg a g _s Substituting the given values _s = 0.4 and g = 10 m s