A force of 14.5 N pushes and pulls to blocks
as shown in the figure below. The vertical
contact surfaces between the two blocks are
frictionless. The contact between the blocks
and the horizontal surface has a coefficient of
friction of 0.12.
The acceleration of gravity is 9.8 m/s
2
.
What is the magnitude a of the acceleration
of the blocks?
Answer in units of m/s
2
.
To find the magnitude of the acceleration of the blocks, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's consider the horizontal forces acting on the blocks. The force of 14.5 N is being applied to both blocks. Therefore, the net horizontal force acting on both blocks is 14.5 N + 14.5 N = 29 N.
Now, let's consider the frictional force acting on the blocks. The coefficient of friction between the blocks and the horizontal surface is given as 0.12. The frictional force can be found by multiplying the coefficient of friction by the normal force. The normal force in this case can be found by multiplying the mass of the top block (m) by the acceleration due to gravity (g). Since the vertical contact surfaces between the blocks are frictionless, the normal force acting on the bottom block is equal to the weight of the bottom block only.
Let's denote the mass of the top block as m1 and the mass of the bottom block as m2. The normal force acting on the bottom block is equal to m2 * g, and the frictional force is equal to the coefficient of friction (0.12) multiplied by m2 * g. Therefore, the net horizontal force acting on the blocks can be calculated as 29 N - 0.12 * m2 * g.
We can now set up the equation using Newton's second law of motion:
m1 * a = 29 N - 0.12 * m2 * g
Now, we need to consider the vertical forces. The weight of each block can be calculated by multiplying their masses by the acceleration due to gravity:
Weight of top block (m1 * g) = m1 * 9.8 N
Weight of bottom block (m2 * g) = m2 * 9.8 N
Since the vertical contact surfaces between the blocks are frictionless, the normal force acting between the blocks is equal to the weight of the top block only, which is m1* g.
Applying Newton's second law of motion in the vertical direction, we get:
m2 * g - m1 * g = (m2 + m1) * a
Finally, we have a system of equations:
m1 * a = 29 N - 0.12 * m2 * g
m2 * g - m1 * g = (m2 + m1) * a
To solve for the acceleration (a), we need to know the values of the masses (m1 and m2). Once we have those values, we can substitute them into the equations and solve for the acceleration.