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 determine the maximum acceleration without the smaller block sliding off the top, we need to consider the forces acting on the system.
The force of friction between the two blocks is given by:
Ffriction = coefficient of static friction * normal force
The normal force is equal to the weight of the top block, which is given by:
Normal force = mass * gravitational acceleration
= 15 kg * 9.8 m/s^2
= 147 N
Substituting the values into the equation for frictional force:
Ffriction = 0.45 * 147 N
= 66.15 N
The maximum acceleration without the smaller block sliding off is equal to the net force acting on the system divided by the total mass:
Acceleration = (force applied - frictional force) / (mass of top block + mass of bottom block)
The force applied is equal to the weight of the entire system (both blocks) multiplied by the acceleration:
Force applied = (mass of top block + mass of bottom block) * gravitational acceleration
= (15 kg + 25 kg) * 9.8 m/s^2
= 392 N
Substituting the values into the equation for acceleration:
Acceleration = (392 N - 66.15 N) / (15 kg + 25 kg)
= 325.85 N / 40 kg
≈ 8.15 m/s^2
Therefore, the man can accelerate the blocks at a maximum rate of approximately 8.15 m/s^2 without having the smaller block slide off the top.