Question about net force/acceleration/constant velocity

[phosgenic]

I read in my textbook that an object can have constant velocity when net force and acceleration are equal to 0. For an example like a puck on frictionless ice that continues to move after it has had a force applied to it that is all good and fine, I understand that inertia keeps the puck moving.

I am wondering how in an example similar to the above, the object can have constant velocity and net force can be equal to 0, with horizontally applied forces that are NOT equal to 0. For example, a puck being pushed by a hockey stick on some snowy ice, or me pushing a book across a table. Doesn't the applied force from the hockey stick or the force from my hand have to be greater than the force of friction from the ice or the table for the puck or book to move? if this is true, then net force is not equal to 0, yet the puck/book still has constant velocity and now all of Newton's principles make no sense to me. I'm hoping someone can clarify this/these concept(s).

Thanks!

EDIT: I'll add one more question here, how would you calculate (not specifically, just conceptually) the acceleration of an object that has constant speed but changing direction only?

 

[cepheid]

Welcome to PF,

I read in my textbook that an object can have constant velocity when net force and acceleration are equal to 0. For an example like a puck on frictionless ice that continues to move after it has had a force applied to it that is all good and fine, I understand that inertia keeps the puck moving.

I am wondering how in an example similar to the above, the object can have constant velocity and net force can be equal to 0, with horizontally applied forces that are NOT equal to 0. For example, a puck being pushed by a hockey stick on some snowy ice, or me pushing a book across a table. Doesn't the applied force from the hockey stick or the force from my hand have to be greater than the force of friction from the ice or the table for the puck or book to move? if this is true, then net force is not equal to 0, yet the puck/book still has constant velocity and now all of Newton's principles make no sense to me. I'm hoping someone can clarify this/these concept(s).

Thanks!

EDIT: I'll add one more question here, how would you calculate (not specifically, just conceptually) the acceleration of an object that has constant speed but changing direction only?

It seems like your question is of the form, "if I deliberately envision a scenario where Newton's laws are violated, then I find that Newton's laws aren't obeyed. What's going on?" I'm not being facetious here. I just think that contradiction is there because you put it there.

If the puck has a non-zero net force acting on it, then it will have a non-zero acceleration. That's all there is to it.

 

[rcgldr]

For example, a puck being pushed by a hockey stick on some snowy ice, or me pushing a book across a table. Doesn't the applied force from the hockey stick or the force from my hand have to be greater than the force of friction from the ice or the table for the puck or book to move?

Static friction has to be overcome to get the puck to initially move, and then kinetic (sliding) friction is involved. The puck will accelerate until the force is reduced to match kinetic friction.

I'll add one more question here, how would you calculate (not specifically, just conceptually) the acceleration of an object that has constant speed but changing direction only?

The math can be complex, but one example where this is commonly done is a car making maneuvers (turns) while at constant speed. The path can be just about any shape (spiral, parabola, hypebola, ellipse, circle, sine wave, ...) that doesn't have sharp inflection points (corners with a radius of 0).

 

[phosgenic]

Static friction has to be overcome to get the puck to initially move, and then kinetic (sliding) friction is involved. The puck will accelerate until the force is reduced to match kinetic friction.

The math can be complex, but one example where this is commonly done is a car making maneuvers (turns) while at constant speed. The path can be just about any shape (spiral, parabola, hypebola, ellipse, circle, sine wave, ...) that doesn't have sharp inflection points (corners with a radius of 0).

Good answer, thanks. And no, I wasn't trying to envision a scenario to violate Newton's laws. In the situation I presented they aren't violated, I just couldn't understand how they were operating in that context, as the examples that are given in my textbook/lectures are similar to the first example I gave.

 

[Nickie]

First off, it is important to understand that the concept of net force and acceleration are closely related. Net force is the sum of all the forces acting on an object, and acceleration is the rate of change of an object's velocity. When net force is equal to 0, it means that the forces acting on the object are balanced and there is no acceleration. This can result in the object having constant velocity, as seen in the example of the puck on frictionless ice.

In the case of the puck being pushed by a hockey stick or a book being pushed across a table, there are indeed forces acting on the object. However, the key factor here is the direction of these forces. In the case of the puck, the force from the hockey stick is in the same direction as the motion of the puck, while the force of friction from the ice is in the opposite direction. These forces cancel each other out, resulting in a net force of 0 and constant velocity.

This concept can be applied to your second question as well. When an object has constant speed but changing direction only, it means that the net force acting on the object is always perpendicular to its motion. This is known as centripetal force, and it is responsible for keeping the object moving in a circular path. The magnitude of this force can be calculated using the formula F=ma, where F is the centripetal force, m is the mass of the object, and a is the centripetal acceleration.

In summary, constant velocity is possible when net force is equal to 0, as the forces acting on the object are balanced. This can occur even when there are applied forces that are not equal to 0, as long as they are in opposite directions or perpendicular to the object's motion. I hope this helps clarify these concepts for you.