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Q: Why can scieñtist disregard the electroms?
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Why does the mechanical (total) energy of the skater not change over time?

It certainly does; mechanical energy will be wasted due to friction. Otherwise, if you disregard friction, the fact that the total mechanical energy is conserved follows from conservation of energy.


If your driving 110 km along a straight road and you look to the side for 2 seconds how far do you travel during this inattentive period?

i am guessing you meant driving at the speed of 110 km/h if you meant something else then disregard this answer: i believe you traveled 30 meters


How much work is done on a 50-kg cargo that is lifted by a pulley 10 m from the ground?

How much work is done on a 50-kg cargo that is lifted by a pulley 10 m from the ground? (Disregard use of comma in writing digits.)


How is an object's mass related to the upward force needed to overcome the pull of gravity?

The upward force would have to overcome gravity, so the force should be F > -mg. Since the upward force and gravity work in opposite direction you can disregard the mass of the object (they cancel: F(gravity) = F(upward) => mg = -m(g+x)) . Consequently the object's mass is irrelevant.


The horizontal and vertical components of a projectile's velocity are independent of each other what does this statement mean?

That means the if you change one you do not necessarily change the other. In the case of the projectile the vertical component is dependent on time (if it is a projectile near a large mass like the earth) gravity acts on it accelerating the projectile in a downward direction. The horizontal component remains the same during the entire flight (if we disregard air resistance and such things).