A 1.4-kg block slides across a rough surface such that it slows down with an accerleration of 1.2 m/s2. What is the coefficient of kinetic friction between the block and the surface?
Wb = mg = 1.4 kg * 9.8 N./kg = 13.72 N.
= Weight of block.
Fb = 13.72 N. @ 0 Deg.
Fp = 13.72*sin(0) = 0 = Force parallel to surface.
Fv = 13.72*cos(0) = 13.72 = Force perpendicular to surface.
Fn = Fp-Fk = ma,
0-u*13.72 = 1.4*(-1.2 = -1.68,
-13.72u = -1.68,
u = 0.1224.
To find the coefficient of kinetic friction between the block and the surface, we can use the following equation:
Net force = mass x acceleration
The net force acting on the block is the force of kinetic friction. It can be expressed as:
Force of kinetic friction = coefficient of kinetic friction x normal force
The normal force acting on the block is equal to the weight of the block, which can be calculated as:
Normal force = mass x gravity
Substituting the expressions for normal force and force of kinetic friction into the equation of net force, we get:
mass x acceleration = (coefficient of kinetic friction) x (mass x gravity)
Canceling out the mass on both sides of the equation, we have:
acceleration = coefficient of kinetic friction x gravity
Now, we can rearrange the equation to solve for the coefficient of kinetic friction:
coefficient of kinetic friction = acceleration / gravity
Given that the acceleration is 1.2 m/s² and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the coefficient of kinetic friction:
coefficient of kinetic friction = 1.2 m/s² / 9.8 m/s² ≈ 0.122
Therefore, the coefficient of kinetic friction between the block and the surface is approximately 0.122.