Simple vector component question

[CanElec]

Hi I am solving a problem at work right now and in order to do so I had to dust off my old physics book. But I've come across something which once made sense but I don't understand it now.

If you have a force, say 100lbs, acting at an angle, say 45 degrees, and break it up into its components why don't the components add up to 100 lbs? Both horizontal and vertical components end up around 70lbs.

So the sum of the forces acting upon the object being pushed against is approximately 140 lbs? Where does the extra force come from? Shouldn't the sum of the components equal the initial force?

 

[mathman]

If you resolve the two 70 lb components onto a pair of axes, along the 45 deg angle you started with and a line perpendicular to it, you will find that the components along the 45 deg line add up to 100 lbs, while the components along the perpendicular are equal in magnitude and opposite in direction, so they cancel.

 

[ImAnEngineer]

If there is a mass which is in rest, the gravitational force F that acts on it equals the mass m times the gravitational acceleration g (F=mg). This force points towards the center of the earth. In order to prevent the mass from accelerating through the floor or whatever it is resting on, a force of equal magnitude but opposite direction must act on it (the normal force). If there is a force that acts on the object at an angle (i.e. not in the opposite direction of gravity), it still has to have a parallel component which is equal in magnitude and opposite to the force of gravity. Since it also has a horizontal force (which does not help preventing the object sink through the floor) the resultant force of the two must be bigger than the normal force alone.