# Newton's third law not evident when pushing a light object?

If i push an object with a small mass/inertia with as much force as i can exert, such as a physics textbook, is this object exerting an equal and opposite force on me? Because unlike when i push a heavier object like a table, i do not get pushed back or feel the equal or opposite force.

• You are more massive than the book, your resulting acceleration from the books force on you is much smaller – Triatticus Apr 10 '19 at 22:50

Newton's Law still holds here. The reason that you do not feel much force from the object is that you are not exerting much force on it in the first place.

Your hand and arm have mass, and your muscles have a maximum output. You can only accelerate your hand so fast, even when it's completely empty.

Light objects take very little force to create large accelerations. For something light like a feather or a grain of rice, the force required to accelerate as fast as your empty hand is tiny. The coupled force back onto your hand is also tiny and possibly below the threshold of detection.

Let's be optimistic and consider you might be able to accelerate your hand at a huge rate like $$10g$$. That then means the accelerating force (and also the force back onto your hand) from any object is about 10 times greater than its weight. A single feather would push back with the weight of 10 feathers. Still such a small amount that you would have trouble noticing.

To really notice, you might need to accelerate it at more like $$100$$ or $$1000g$$, and that's just not something your muscles can do to your hand.

When you push a book, it starts to move with the application of a relatively smaller force (the action). You feel the smaller force (the reaction). You don't get a chance to push harder. On the other hand, you need to push harder (the action) to the set the table moving, and the table pushes back on you harder (the reaction). Had you pushed the table with a smaller force, it would have applied a smaller force. But it won't move.

• Does this mean that only the force that I exert on the book to overcome its inertia is exerted back on me? – Ubaid Hassan Apr 11 '19 at 7:30
• @UbaidHassan You start by pushing slightly. Let the book doesn't move at this point. But applies an equal force on you hand. You slightly increase the applied force, the book starts to apply an increased force on your hand. Now, when the book starts moving, that's the maximum force you can apply, and that's the maximum reaction that you can get from it. At each step, the force you apply on the book is equal to the force that the book applies on you. – SRS Apr 11 '19 at 7:56
• So once the object is moving, I cannot exert more force in the direction it’s moving? , then why does it accelerate if it is pushed in the same direction while it’s already moving? Or do you mean to say it will no longer apply a reaction force on my hand when it accelerates in the direction my hand is? – Ubaid Hassan Apr 11 '19 at 8:24
• @UbaidHassan "So once the object is moving, I cannot exert more force in the direction it’s moving?" Yes. – SRS Apr 11 '19 at 9:01
• So it’s impossible for an object to accelerate in the direction it is already moving? – Ubaid Hassan Apr 11 '19 at 10:17