A 47.0 kg slab rests on a frictionless floor. A 18.0 kg block rests on top of the slab. The static coefficient of friction between the block and the slab is 0.50, while the kinetic coefficient of friction is 0.40. The top block is acted upon by a force of 120 N. What is the acceleration (in meters/second^2) of the bottom block?
The block on top can support a pull of 0.50*18*g = 88.2 N without slipping. Since the applied force is greater than that, it will slip and there will be a friction force of
Ff = 0.4*18*g = 70.56 N between the blocks. That will help pull the lower block forward.
The lower block will accelerate at a rate
a = Ff/47 = 70.56/47
= 1.50 m/s^2
To find the acceleration of the bottom block, we need to consider the forces acting on it.
First, let's analyze the forces acting on the top block:
- The force applied to the top block is 120 N.
- The force of friction between the top block and the slab opposes the applied force.
The force of friction can be calculated using the equation:
force of friction = coefficient of friction * normal force
The normal force acting on the top block is equal to its weight, which is given by:
normal force = mass * gravity
The frictional force acting on the top block can now be calculated:
force of friction (top block) = coefficient of friction * normal force (top block)
Next, let's consider the forces acting on the bottom block:
- The gravitational force acting on the bottom block is equal to its weight.
- The force of friction between the bottom block and the slab opposes the gravitational force.
The force of friction can be calculated using the same equation as before:
force of friction (bottom block) = coefficient of friction * normal force (bottom block)
The normal force acting on the bottom block is equal to the total weight of both blocks:
normal force (bottom block) = (mass of top block + mass of bottom block) * gravity
The net force acting on the bottom block is the difference between the gravitational force and the force of friction:
net force (bottom block) = (mass of top block + mass of bottom block) * gravity - force of friction (bottom block)
Finally, we can calculate the acceleration of the bottom block using Newton's second law:
net force (bottom block) = mass (bottom block) * acceleration
Rearranging the equation and substituting the known values, we can solve for acceleration (a):
acceleration (a) = net force (bottom block) / mass (bottom block)
By following this process and substituting the given values, you can find the acceleration of the bottom block.