You push a 33-kg table across a 6.2-m-wide room. In the process, 1.5 kJ of mechanical energy gets converted to internal energy of the table/floor system. What’s the coefficient of kinetic friction between table and floor?
μ * m * g * 6.2 = 1.5 kJ
To find the coefficient of kinetic friction between the table and the floor, we can use the concept of work-energy theorem. The work done against friction can be calculated using the equation:
Work done against friction = change in mechanical energy
In this case, the change in mechanical energy is given as 1.5 kJ (kilojoules). However, mechanical energy is defined as the sum of kinetic energy (KE) and potential energy (PE). But we are only concerned with kinetic energy here.
Since the table is pushed across a distance of 6.2 m, we know that the only external force acting on the table is the force of kinetic friction (f). The work done against friction is given by the equation:
Work done against friction = force of friction x distance
Using the equation for work done against friction, we can derive:
f x d = change in mechanical energy
f x 6.2 = 1.5 kJ
To find the force of friction (f), we need to use Newton's second law:
Force of friction = mass x acceleration
However, in this case, we can use another form of Newton's second law that relates force of friction to the normal force (N) and the coefficient of kinetic friction (μ).
Force of friction = coefficient of kinetic friction x normal force
The normal force is equal to the weight of the table (mg), where m is the mass of the table and g is the acceleration due to gravity.
Substituting the values, we have:
coefficient of kinetic friction x mg = f
Now, we can substitute the value of f in the previous equation:
coefficient of kinetic friction x mg x 6.2 = 1.5 kJ
Solving for the coefficient of kinetic friction, we have:
coefficient of kinetic friction = (1.5 kJ) / (mg x 6.2)
Plug in the value of the mass of the table (33 kg), the acceleration due to gravity (9.8 m/s²), and solve for the coefficient of kinetic friction.