Why do we take k=1 in the derivation of F=k*ma?

[Dale]

Oh dear, it's necroposting season again

How prescient of you!

 

[Physics guy]

So is F=ma valid? What if a=0, as when a body is moving at constant velocity? Then is F=0? I don't think so. If I am struck by a car moving at constant velocity, I guarantee you that I will feel a force. Perhaps there's something I'm missing here.

Interesting question that even I took a long to get an answer. Fortunately now I have an answer. This can be understood by accepting Newtons laws of motion to be true (even though no one can prove them to be true). Second law of motion say that force is directly proportional to the rate of change of momentum, which gave is the famous equation that F = ma. So this equation tells us that a net force can only act if there is a change in momentum of a body ie, the body undergoes acceleration. During collision what we can expect is the same when a car moving with constant velocity hits a person, during the collision there is a reduction in the velocity of the car for a small instant, this causes a change in momentum and thus a force is applied to the person (may god save him). This is especially so in the case of vehicles having larger mass in which the change in momentum will be larger

 

[pbuk]

So is F=ma valid? What if a=0, as when a body is moving at constant velocity? Then is F=0? I don't think so. If I am struck by a car moving at constant velocity, I guarantee you that I will feel a force. Perhaps there's something I'm missing here.

Interesting question that even I took a long to get an answer. Fortunately now I have an answer.

Unfortunately you have missed the same thing as @Edeff missed: the force you feel is the product of your mass and your acceleration. Any (negative) acceleration of the car is only relevant to the car and its occupants.

@Edeff is assuming that the mass of the car is infinite and therefore it does not lose any momentum in the collision; again this is only relevant to the occupants of the car (who will not feel anything). In the limit as the mass of the car tends to infinity the change in velocity of the person that is hit tends to instantaneous and so they suffer the effect of a force tending to infinity.

 

[Physics guy]

Unfortunately you have missed the same thing as @Edeff missed: the force you feel is the product of your mass and your acceleration. Any (negative) acceleration of the car is only relevant to the car and its occupants.

@Edeff is assuming that the mass of the car is infinite and therefore it does not lose any momentum in the collision; again this is only relevant to the occupants of the car (who will not feel anything). In the limit as the mass of the car tends to infinity the change in velocity of the person that is hit tends to instantaneous and so they suffer the effect of a force tending to infinity.

Well replied

 

[jbriggs444]

@Edeff is assuming that the mass of the car is infinite and therefore it does not lose any momentum in the collision;

Be careful. A correct conclusion is that the lost vehicle velocity is zero (or infinitesimal). The lost momentum is non-zero.

 

[pbuk]

Be careful. A correct conclusion is that the lost vehicle velocity is zero (or infinitesimal). The lost momentum is non-zero.

I agree that considering momentum is problematic here, that's why I avoided it.

In the limit as the mass of the car tends to infinity the change in velocity of the person that is hit tends to instantaneous and so they suffer the effect of a force tending to infinity.

 

[berkeman]

The OP's question has been answered, and after some member requests and a Mentor discussion, this thread is now closed. Thank you everyone.