# Newton's 2nd Law: Conditions & Application

• semc
In summary, the conversation discusses the conditions for using Newton's second law and whether a varying mass is required for the equation. It is mentioned that F= d(mv)/dt is more general than F=ma and that if the mass is not constant, there are additional terms in the equation. The conversation also includes a physics problem involving a railroad car with a constant water leak and the effects of changing mass on its velocity.
semc
hmm...i was wondering is there any conditions for the use of Newton's second law?

What do you mean?

semc said:
hmm...i was wondering is there any conditions for the use of Newton's second law?

The 'conditions' which imply the usage of an equation are read from the equation itself.

i don't reali know how to put it in words but erm...we do not need a varying mass to use F=dmv/dt right?

Right. F= d(mv)/dt is more general than F=ma, which assumes a non-varying mass.

semc said:
i don't reali know how to put it in words but erm...we do not need a varying mass to use F=dmv/dt right?

Well, if the mass is not constant, then you have $$\vec{F}=\frac{d}{dt}(m\vec{v})=\frac{dm}{dt}\vec{v}+m\frac{d\vec{v}}{dt}$$.

Alright i just came across this dumb conditions and i wanted to verify that this is nonsense Thanks

Well, if the mass is not constant, then you have $$\vec{F}=\frac{d}{dt}(m\vec{v})=\frac{dm}{dt}\vec{v}+m\frac{d\vec{v}}{dt}$$.
An easy calculus problem, but a tricky physics problem. Suppose there is a railroad car coasting with speed V on a straight horizontal track without any rolling friction. The car is full of water and has initial mass Mo and velocity Vo. As the car rolls, the water in the tank leaks out of a hole in the bottom of the tank at a rate we can assume to be constant (maybe the hole gets a little bigger as the water level drops). So the mass M of the car is changing at a constant rate. The only forces acting on the car are gravity and the normal force, both of which are perpendicular to the motion. What happens to the velocity of the car?

## 1. What is Newton's 2nd Law?

Newton's 2nd Law, also known as the Law of Force and Acceleration, states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This can be mathematically represented as F=ma, where F is force, m is mass, and a is acceleration.

## 2. What are the conditions for Newton's 2nd Law to be applicable?

In order for Newton's 2nd Law to be applicable, the object must be experiencing a net force, meaning there is more than one force acting on it. The object must also have a non-zero mass and be in a state of acceleration, either speeding up or slowing down.

## 3. How is Newton's 2nd Law used in everyday life?

Newton's 2nd Law is used in a variety of everyday situations, such as driving a car, throwing a ball, or riding a bike. It helps us understand how different forces, such as friction and gravity, affect the motion of objects and how we can apply forces to achieve the desired acceleration.

## 4. What is the difference between mass and weight in relation to Newton's 2nd Law?

Mass is a measure of the amount of matter an object contains, while weight is a measure of the force of gravity acting on an object. In relation to Newton's 2nd Law, mass is constant and does not change, while weight can vary depending on the strength of the gravitational force.

## 5. Can Newton's 2nd Law be applied to objects in outer space?

Yes, Newton's 2nd Law can be applied to objects in outer space as long as there is a net force acting on the object. In the absence of air resistance and other external forces, an object's mass and the force acting on it will determine its acceleration. This is why astronauts experience weightlessness in space, as there is no gravitational force acting on them to cause acceleration.

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