# Understanding Newton's 2nd Law of Motion

• tomtomtom1
In summary, the second law of motion, ##F=ma##, states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. It is a vector equation that takes into account the sum of all forces acting on an object, including the force of gravity, to determine its direction of acceleration. The force of gravity may be cancelled out by other forces, such as the normal force, in order to achieve a specific direction of acceleration.
tomtomtom1
Homework Statement
Understanding Newton's 2nd Law of Motion
Relevant Equations
NA
Hello all

I am trying to understanding Newton's 2md Law of Motion which states:-

Force = Mass * Acceleration

If I had a force of 10Newtons pushing an object along the ground (assume no friction) in a perfectly horizontal direction that has a Mass of 10kg then the objects acceleration would be 5m/s^2 in the horizontal direction.

My question why is gravity factored into this as shown in my sketch below:-

Gravity is acting on the mass while a force of 10N is being applied - so my question is shouldn't gravity be considered as another force acting downwards which would effect the acceleration and the direction of the Mass?

I hope this makes sense?

Just to clarify, as is always done, ##F=\frac{dp}{dt}## where ##p=mv##. If you don't know about calculus, you get the equation you have because mass is usually taken as a constant.
As to your question, yes it should be and is considered as such, but not in the way you're thinking of it, probably. The object in your picture is moving horizontally, and since we're neglecting air resistance and assuming no friction, there's nothing besides the ##10N## force to affect its horizontal motion. Gravity is making the object accelerate downwards, but has no effect on its horizontal motion (since the force of friction is ##F=[(\mu=0)\times N]=0##).

Last edited:
tomtomtom1 said:
Homework Statement: Understanding Newton's 2nd Law of Motion
Homework Equations: NA

Hello all

I am trying to understanding Newton's 2md Law of Motion which states:-

Force = Mass * Acceleration

If I had a force of 10Newtons pushing an object along the ground (assume no friction) in a perfectly horizontal direction that has a Mass of 10kg then the objects acceleration would be 5m/s^2 in the horizontal direction.

My question why is gravity factored into this as shown in my sketch below:-View attachment 251669

Gravity is acting on the mass while a force of 10N is being applied - so my question is shouldn't gravity be considered as another force acting downwards which would effect the acceleration and the direction of the Mass?

I hope this makes sense?

The force of gravity is there, but it is "cancelled" out by the normal force of the frictionless ground, because the object is not accelerating in the vertical direction.

You can verify this by drawing the free-body diagram and writing down the x and y components of the force equation.

BTW, once you start to include friction, the gravitational force WILL then be factor, because the frictional force depends on the normal force, and the normal force depends on gravitational force (and angle if it is inclined). So be careful what you are asking for, because you WILL start seeing gravitational force rears its ugly head soon enough.

Zz.

Delta2
tomtomtom1 said:
If I had a force of 10Newtons pushing an object along the ground (assume no friction) in a perfectly horizontal direction that has a Mass of 10kg then the objects acceleration would be 5m/s^2 in the horizontal direction.
5 m/s^2 is not what I get.

F=ma. Does 10 N equal 10 kg times 5 m/s2?

jbriggs444 said:
5 m/s^2 is not what I get.

F=ma. Does 10 N equal 10 kg times 5 m/s2?

should be 1 m/s2

Thank you.

jbriggs444
Other than the numbers, you also need to understand that the second law is not F = ma, but ##\vec F_{net}=m\vec a##. It is a vector equation in which ##\vec F_{net}## is the sum of all the forces added as vectors and ##\vec a## is the acceleration vector. Among other things it says that if you add all the forces that act on mass ##m##, the acceleration must be in the same direction as that sum. In the drawing you posted, you show a force to the right and the weight straight down. If that is all there is, when you add the two forces, you get a force pointing to the right and down in the "southeast" direction, yet you show the acceleration to the right. That cannot be correct. To resolve the discrepancy between the net force and the acceleration directions, you need to add a force that you missed; it is the normal force that points straight up and is provided by the surface that supports the mass. It is just large enough to cancel the weight so that now the sum of all the forces is to the right.

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learnandteach and Delta2
kuruman said:
It is a vector equation in which ##\vec F_{net}## is the sum of all the forces added as vectors and ##\vec a## is the acceleration vector.
Or the individual force vectors, ##\overrightarrow F_i##, and the associated individual acceleration vectors, ##\overrightarrow a_i## can be treated as ##\overrightarrow F_i = m \overrightarrow a_i##, and the force and acceleration vectors can be summed separately to get ##\overrightarrow F_{net} = m \overrightarrow a_{net}##.

Delta2

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

Newton's 2nd Law of Motion states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. This means that the greater the force applied to an object, the greater its acceleration will be, and the more mass an object has, the slower its acceleration will be.

## 2. How is Newton's 2nd Law of Motion related to the other laws of motion?

Newton's 2nd Law of Motion, also known as the Law of Acceleration, is closely related to the other two laws of motion. The first law, also known as the Law of Inertia, states that an object at rest will remain at rest and an object in motion will remain in motion at a constant velocity unless acted upon by an external force. The second law explains how the object's acceleration changes when it is acted upon by a force. The third law, also known as the Law of Action and Reaction, states that for every action, there is an equal and opposite reaction.

## 3. How do you calculate the acceleration of an object using Newton's 2nd Law of Motion?

To calculate the acceleration of an object, you can use the formula a = F/m, where a is the acceleration, F is the net force acting on the object, and m is the mass of the object. This means that to increase the acceleration of an object, you can either increase the force applied to the object or decrease its mass.

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

Mass and weight are often used interchangeably in everyday language, but they have different meanings in the context of Newton's 2nd Law of Motion. Mass is a measure of the amount of matter in an object, while weight is a measure of the force of gravity acting on an object. The mass of an object remains constant, while its weight can change depending on the force of gravity acting on it.

## 5. How does Newton's 2nd Law of Motion apply to real-life situations?

Newton's 2nd Law of Motion can be seen in many everyday situations, such as pushing a shopping cart, riding a bike, or throwing a ball. In all of these examples, the object's acceleration is directly proportional to the force applied and inversely proportional to its mass. This law also helps explain the motion of larger objects, such as cars or planes, and is essential in the development of technologies like rockets and satellites.

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