Understanding Newton's Laws of Motion

[Solidmozza]

Hi,
This is more of a problem with concept rather than an actual mathematical problem, so forgive me if I don't use the template provided.

I'm just having an issue with Newtons laws of motion. If I were to pull a box across a floor to the right with my hand, assuming that the mass of the box is 40 kg and the force I use is 20 N, I know mathematically the acceleration is 0.5m/s^2 to the right. However, what happens to the equal and opposite forces? I mean, the box is exerting a force on your hand/body that is equal to 20 N but in opposite direction, but its inertial mass is less than that of my body so the box should still accelerate in my direction, right? But shouldn't the acceleration be less than simply 0.5m/s^2 to the right, because let's say my mass was 80 kg, the acceleration to the left = 0.25m/s^2 and the acceleration to the right is 0.5m/s^2, leaving me with a net acceleration of 0.25m/s^2 to the right? Is it just the frictional force that is combating the force of the box on me that prevents this from happening, and if so, is it just the case that the box doesn't have enough friction to oppose the force of my hand?
Additionally, if this above situation was conducted in a vacuum (me and the box just somewhere in a vacuum, no floor) would the acceleration to the right be 0.25m/s^2?

I know this is probably old hat and is simple stuff, but I appreciate the help!
Thanks

 

[Doc Al]

To understand how an object will accelerate you must know the net force on it. By stipulation, the 20 N force that you exert on the box is the only force acting on the box, so it's the net force on the box. True, the box exerts a 20 N force on your hand. But is that the only force acting on your hand? No.

 

[m2003]

for reaching out and asking about Newton's Laws of Motion. I can understand how these concepts can be confusing and it's great that you're seeking clarification. Let's break down your questions and discuss them one by one.

Firstly, you are correct in your understanding that the box exerts an equal and opposite force on your hand/body. This is known as Newton's Third Law of Motion. In this case, the box is pushing on your hand with a force of 20 N to the left, while your hand is pushing on the box with a force of 20 N to the right.

Now, let's talk about the acceleration of the box. Newton's Second Law of Motion tells us that the acceleration of an object is directly proportional to the net force exerted on it and inversely proportional to its mass. In your example, the net force on the box is 20 N to the right (force applied by your hand) and its mass is 40 kg. Therefore, the acceleration of the box is indeed 0.5 m/s^2 to the right.

Next, you bring up the concept of inertia. Inertia is the tendency of an object to resist changes in its motion. It is directly related to an object's mass. In your example, the box has a mass of 40 kg, while your body has a mass of 80 kg. This means that your body has more inertia than the box, and therefore, it will resist changes in its motion more than the box. This is why your body will not accelerate as much as the box, even though the forces acting on both are equal and opposite.

Now, let's address your question about friction. Friction is indeed a force that can oppose the motion of an object. However, in this case, the frictional force between the box and the floor is not significant enough to have a significant impact on the acceleration of the box. It is the net force (the force applied by your hand minus the frictional force) that determines the acceleration of the box.

Finally, in a vacuum where there is no friction, the acceleration of the box would still be 0.5 m/s^2 to the right. This is because the net force on the box (20 N to the right) is still greater than the force of inertia (0 N) acting on it.

I hope this helps clarify your understanding of Newton's Laws of Motion. They are fundamental principles that explain how objects