To determine the maximum acceleration without the smaller block sliding off the top, we need to calculate the maximum force of static friction between the two blocks.
The formula for static friction is:
Frictional force = coefficient of static friction * Normal force
The normal force is equal to the weight of the smaller block, which is its mass multiplied by the acceleration due to gravity (9.8 m/s²).
Normal force = mass of smaller block * acceleration due to gravity
Normal force = 15 kg * 9.8 m/s²
Normal force = 147 N
The maximum force of static friction can be calculated as:
Maximum frictional force = coefficient of static friction * Normal force
Maximum frictional force = 0.45 * 147 N
Maximum frictional force = 66.15 N
Since the maximum frictional force between the blocks is equal to the force applied to accelerate the blocks, we can use Newton's second law to calculate the maximum acceleration.
Force = mass * acceleration
66.15 N = (25 kg + 15 kg) * acceleration
66.15 N = 40 kg * acceleration
Acceleration = 66.15 N / 40 kg
Acceleration = 1.65375 m/s²
Therefore, the man can accelerate the blocks at a maximum rate of 1.65375 m/s² without having the smaller block slide off the top.