An object with a mass of #12# #kg# is on a surface with a kinetic friction coefficient of # 1 #. How much force is necessary to accelerate the object horizontally at #7 # #ms^-2#?

1 Answer
Feb 13, 2016

Answer:

The total force is composed of two pieces: the force required to accelerate the mass and the force required to overcome friction. #F=ma+mumg=12*7+1*12*9.8=201.6# #N#.

Explanation:

The total force is made up of two different forces.

If there were no friction, the force required to accelerate a mass of #12# #kg# at an acceleration of #7# #ms^-2# is given by Newton's Second Law :

#F=ma=12*7=84# #N#

The second part is the frictional force:

#F_f=muF_N# where #mu# is the frictional coefficient and #F_N# is the normal force, which in turn is #mg#, the mass times the acceleration due to gravity.

#F_f=mumg=1*12*9.8=117.6# #N#

To find the total force, just add these two forces:

#F=ma+mumg=12*7+1*12*9.8=201.6# #N#.