A man stacks a small block of wood on top of a larger block and then moves both by pushing the
bottom block. The large block has a mass of 25 kg, and the smaller block has a mass of 15 kg. The
coefficient of static friction between the two blocks is 0.45. How fast can the man accelerate the blocks
without having the smaller block slide off the top?
To find the maximum acceleration without the smaller block sliding off the top, we need to consider the net force acting on the smaller block.
The gravitational force acting on the smaller block can be calculated using the formula:
F_gravity = mass * acceleration_due_to_gravity
= 15 kg * 9.8 m/s^2
= 147 N
The maximum static frictional force can be calculated using the formula:
F_friction = coefficient_of_static_friction * normal_force
= 0.45 * F_normal
The normal force acting on the smaller block is equal to the force of gravity on the larger block:
F_normal = mass * acceleration_due_to_gravity
= 25 kg * 9.8 m/s^2
= 245 N
Therefore, the maximum static frictional force is:
F_friction = 0.45 * 245 N
= 110.25 N
The net force acting on the smaller block can be calculated by subtracting the frictional force from the gravitational force:
F_net = F_gravity - F_friction
= 147 N - 110.25 N
= 36.75 N
Now, we can use Newton's second law of motion to find the maximum acceleration:
F_net = mass * acceleration
36.75 N = 15 kg * acceleration
acceleration = 36.75 N / 15 kg
acceleration = 2.45 m/s²
Therefore, the man can accelerate the blocks at a maximum rate of 2.45 m/s² without having the smaller block slide off the top.