Newton's second law and D'Alembert's principle

[jrm2002]

Newton's second law!

According to Newton's second law if the resultant force acting on a body is non zero the body moves with an acceleration proportional to the mass of the body, right?Then,
1. Can anyone explain this in an intuitive sense?
2. In solving problems we say that the resultant force is equivalent to the product "ma"(mass times acceleration).How?
3. Can anyone explain the D'Alembert's principle?
_________________
Jrm

 

[HallsofIvy]

You have given Newton's second law incorrectly- though it may be just a typo.

If an object is acted upon by a constant force then its acceleration is inversely proportional to the mass of the object: a= k/m.

If an object of constant mass is acted on by a force then its acceleration is proportional to the force: a= pF.

Those can be reconciled by taking k= F and p= 1/m so that a= F/m or F= ma.

 

[Harmony]

1. The greater force you exert upon an object, the greater the acceleration is. For example, the harder you swing your bat, the higher the acceleration of the ball.

2. Let say you exert force of 3N to the right upon a troly, which has weight of 3kg. Ignoring friction, the total resultant force will be 3N to the right. So, the acceleration of the troly, is equals to F/m, that is 1ms-2.

Hope this will help you. Regarding the third question, I have no idea at all.

 

[jrm2002]

Thanks for the replies.
However, I shall be grateful if you could explain the meaning of acceleration in an intuitive sense.
I know we define acceleration as rate of change of velocity.Can anyone bring about an intuitive understanding.

 

[arildno]

What do you mean by "intuitive understanding"?

You know how to find average velocities given positions and time, right?

To find the average acceleration, just use a similar procedure.

 

[dicerandom]

However, I shall be grateful if you could explain the meaning of acceleration in an intuitive sense.
I know we define acceleration as rate of change of velocity.Can anyone bring about an intuitive understanding.

You can feel the difference between acceleration and velocity. Get in your car and find a smooth road (hard to do here in California... but this is a thought experiment anyway). Travel down that road at a constant speed, that's velocity. Mash down the gas pedal, that's acceleration. Stomp on the brake, that's acceleration.

If you're traveling at one speed one instant and another speed at another instant, there was an acceleration which caused your speed to change. Your experience with the car should also show you how acceleration and force are inheriantly linked.

 

[row]

well,you must know that we are being pulled down by gravity which produces acceleration g, you don't move at all but thanks to reaction of ground you feel it.And force of gravity is (g)x(your mass) that is your weight.Also while your standing net force on you is zero and you don't move.Hope this is intutive enough

 

[jrm2002]

That means to have an acceleration we need a force?Right?
I also have another fundamental doubt:
1.What is mass?
2. What is difference between mass andweight?

 

[Joel]

1. A fundamental property of matter that (among other things) determine how the matter reacts to a force.
2. Weight is the force on a mass due to gravity.

 

[Harmony]

2. Weight may change due to difference of gravitation, mass don't. An object's mass on Earth is same as it's mass on moon.

 

[row]

well take it this way, mass is the amount of a substance and weight is the force produced due to various reasons.

 

[dfx]

1.What is mass?

"Mass is the property of an object which resists changes in motion."

While we're on the topic, I never quite understood this definition. Will someone please explain?

 

[Joel]

"Mass is the property of an object which resists changes in motion." While we're on the topic, I never quite understood this definition. Will someone please explain?

Well, I probably don't know any more about it than you, but I understand it simply as a result from all the experiments that confirm Newton's second law. Acceleration is per definition change in motion and a bigger mass will clearly "resist a change in motion" and result in less acceleration (a = F/m) if the force is constant.