A passenger is pulling on the strap of a 15.0-kg suitcase with a force of 60.0 N. The strap makes an angle of 32.5° above the horizontal. A 37.8-N friction force opposes the motion (horizontal) of the suitcase. Determine the acceleration of the suitcase.

Question

anonymous · Answer

The acceleration is in the horizontal direction, therefore you need to find the force in that direction.  First find the force due to the passenger pulling the case in the x-dir.  Do
$$F_x = Fcos(\theta)$$
Where F is the 60N force the dude is pulling with.  Now you also know that friction is opposing this motion.  So you need to subtract that from the result above.  Since F_x and the force due to friction are in the same direction, you can just subtract them "like" scalars.  Now just use Newton to find the acceleration.  ie
$$a = F_{net}/m $$
where F_net is the net force in the horizontal direction and m is the mass of the suitcase.