Two blocks (one on top of the other), each of mass m = 2.4 kg, are pushed along the horizontal surface of a table by a horizontal force P of magnitude 6.8 N, directed to the right. The blocks move together to the right at constant velocity.
(a) Find the frictional force exerted on the lower block by the table.
(b) Find the coefficient of kinetic friction between the surface of the block and the table.
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To find the answers to these questions, we need to analyze the forces acting on the blocks.
(a) The frictional force exerted on the lower block by the table can be found using Newton's second law. Since the blocks are moving together at a constant velocity, we know that the net force acting on the system is zero. Therefore, the pushing force P must be balanced by the frictional force.
Using Newton's second law (F = ma), we can write the equation:
P - Frictional force = (m1 + m2) * a
Here, m1 and m2 represent the masses of the blocks, P is the pushing force, a is the acceleration, and the frictional force is what we want to find.
Since the blocks are moving together at a constant velocity, the acceleration is zero. Therefore, we can rearrange the equation to solve for the frictional force:
Frictional force = P
So, the frictional force exerted on the lower block by the table is 6.8 N.
(b) To find the coefficient of kinetic friction between the surface of the block and the table, we need to use the equation:
Frictional force = coefficient of kinetic friction * normal force
Here, the normal force is the force exerted by the table on the lower block, which is equal to the weight of the block (mg), where g is the acceleration due to gravity.
Since the blocks are moving together at a constant velocity, the upward normal force is equal to the downward gravitational force. So, we can write:
Normal force = (m1 + m2) * g
Therefore, the equation becomes:
Frictional force = coefficient of kinetic friction * (m1 + m2) * g
We already know the frictional force is 6.8 N, and we know the masses of the blocks (2.4 kg each). The acceleration due to gravity is approximately 9.8 m/s^2.
Plugging these values into the equation, we can solve for the coefficient of kinetic friction:
6.8 N = coefficient of kinetic friction * (2.4 kg + 2.4 kg) * 9.8 m/s^2
Simplifying the equation:
6.8 N = coefficient of kinetic friction * 4.8 kg * 9.8 m/s^2
Coefficient of kinetic friction = 6.8 N / (4.8 kg * 9.8 m/s^2)
Calculating the value gives us:
Coefficient of kinetic friction ≈ 0.142
Therefore, the coefficient of kinetic friction between the surface of the block and the table is approximately 0.142.