Does net force acting on a body always depends on the mass and acceleration of the body? Suppose only electrostatic force acts between two body then net force is equl to the electrostatic force, but there is no mass in electrostatic force formula.
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2 Answers
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In your electrostatic example using Coulomb's law, you would still set the coulomb force equal to the mass times the acceleration. Your net force does not need to depend on mass for Newton's second law.
answered Jan 5, 2018 at 2:14
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$\begingroup$ In a uniform circular motion centripetal force = mv^2/r = ma, thus a = v^2/r, ohkk now i got it since F= kq1q2/r^2 = ma, therefore a = (mkq1q2)/r^2, i just assumed that as both side mass cancelled in thg case of uniform circular motion the same must happen here, but there's no need to cancell m because acceleration depends on mass $\endgroup$– parshyaaJan 5, 2018 at 12:25
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$\begingroup$ Your comment is not entirely correct in reasoning.The electrostatic force is a fundamental force of the universe along with gravity, the strong force, and the weak force. It is its own thing. However, any force that causes an object to undergo circular motion can be called a centripetal force. mv^2/r = ma is true because under uniform circular motion the acceleration is v^2/r. This is not because of Newton's second law, but rather because this is always true in uniform circular motion. For the electrostatic force, you would say kq1q2/r^2 = ma due to Newton's second law. $\endgroup$ Jan 5, 2018 at 12:38
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$\begingroup$ I have read so many places that net force acting on a body is equal to force time acceleration(inertial frames), could you tell me how net force will not depend on mass $\endgroup$– parshyaaJan 5, 2018 at 14:26
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$\begingroup$ It is a question of what you mean by "depend". Physically, your net force does not have to depend on mass, like if there are only electrostatic forces present. In a physical sense, Newton's second law is more of a relationship between the net force on an object and the acceleration resulting from that net force. This acceleration will be proportional to the net force through the mass. So mathematically, you could say net force depends on mass I guess, but in the case of the electrostatic force, changing the mass of your charged object will change the acceleration and not the net force. $\endgroup$ Jan 5, 2018 at 14:31
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$\begingroup$ This is the difference between math and physics. In physics our equations have physical meaning. F = ma because a force produces an acceleration. You have to be aware of what the variables mean in relation to the physical set up. In general, you can't just change the mass and then expect the net force to change, because the net force could depend on other outside effects that do not depend on mass. It all depends on what is actually changing and what is constant. $\endgroup$ Jan 5, 2018 at 14:34
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According to Newtonian mechanics, your statement does hold true, but not always. I will explain a few cases here:
In the case of Electrostatic attraction or repulsion, the formula you've given for force is valid, but at the same time, this can be equated to the mass of any of the charges times the acceleration of that particular charge, under the influence of the Electrostatic force of attraction or repulsion.
In another case, suppose a balloon is being deflated and air moves out of it with a constant velocity. In this case the net instantaneous force on it will be equal to the product of the given velocity and the rate of change of mass, at that instant.
In the derivation of the expression of force using basic calculus, we get this formula:
F = (delta)(mv)
Since in most cases, the mass remains constant, we take it out of the bracket and write F = m(delta)(v)
Thus, f = ma is always valid, if the mass remains constant, as is your case of the attraction/repulsion of the two charges.
