An object with a mass of #2 kg# is on a surface with a kinetic friction coefficient of # 9 #. How much force is necessary to accelerate the object horizontally at #3 ms^-2#?
There are two components of the required force: one to overcome the frictional force and one to accelerate the object. The total force is
To accelerate a mass on a frictionless surface, it is just necessary to apply the force described by Newton's Second Law:
In this case, an additional force is required to overcome the frictional force, which is defined this way:
The normal force in this case is just the weight force of the object:
Pulling it all together to find the total force, we get:
Substituting in the values from the question:
(I remarked on another similar question, but it bears repeating here: 9 is not a reasonable or sensible value for a coefficient of friction. The fault is with the teacher or book asking the question in the first place, not the student asking it here. Friction coefficients are typically between 0 and 1, sometimes slightly above 1, in some extreme cases approaching 2, but 9 is just way off the scale. 0.9 would be a much more sensible number.)