Final answer:
The maximum horizontal force that can be applied to a 3 kg block on a 2 kg block without sliding off, given a static friction coefficient of 0.4, is 12 N.
Step-by-step explanation:
The question asks for the maximum horizontal force that can be applied to a 3 kg block resting on a 2 kg block without causing the 3 kg block to slide off. The coefficient of static friction between the blocks is given as 0.4. To find this force, we can use the formula for static friction, which is Fmax = μs × N, where Fmax is the maximum static frictional force, μs is the coefficient of static friction, and N is the normal force.
The normal force here is the weight of the 3 kg block, which is m × g (where m is the mass and g is the acceleration due to gravity, 9.8 m/s² for Earth). So, N = 3 kg × 9.8 m/s² = 29.4 N.
The maximum static frictional force is thus Fmax = 0.4 × 29.4 N = 11.76 N. Rounding up to the nearest whole number gives us 12 N, so the maximum horizontal force without causing the block to slide off is 12 N.