Net Force Homework: Direction of Net Force

[edanzig]

Homework Statement

I don't have a picture of this situation so I will do my best to describe it in words. If we have a box that's "swinging" in a circular motion at the end of a string, but at the same time the box is experiencing a frictional force due to it's brushing against another object. The picture in my book shows a box on a tabletop that's being moved in a centripetal motion due to the actions of a string while at the same time it's experiencing a frictional force from the table. The question wants to know the direction of the net force at a certain point.

Homework Equations

F(net) = sum of all forces

The Attempt at a Solution

I assumed that at any given point on the "circle of motion" the net force should be pointing inward towards the center of the circle, after all that's the direction of the acceleration. The correct answer given is that the net force is a combination of the frictional vector and centripetal vector. This makes absolutely no sense to me. If the net force wasn't going inwards towards the center of the circle then the object wouldn't move the way it is. Thanks for any help.

 

[HallsofIvy]

I don't see why you say it "makes absolutely no sense" because they are saying just what you say. Yes, the net force is a "combination of the frictional vector and centripetal vector" And, yes, the net force is "going inwards toward the center of the circle" though not directly toward the center. The net force is the sum of the large centripetal force vector, toward the center of the vector, and the much smaller frictional force vector, tangent to the circle, giving a vector that points slightly off the center.

 

[Doc Al]

I assumed that at any given point on the "circle of motion" the net force should be pointing inward towards the center of the circle, after all that's the direction of the acceleration.

That would be the case for uniform (constant speed) circular motion, where there is no tangential acceleration. In such a case the net force is towards the center and the acceleration is purely centripetal. But in this problem there is also a tangential component of acceleration due to the friction.

 

[BvU]

The nice thing about strings is that they can only exercise a force along the string. If you want to maintain a circular motion for the box, you can't keep your hand (if that's what is holding the string) still, but you have to pull and make a small circle with that hand. String direction is more or less tangential to that small circle: you are doing work ! Namely to offset the energy loss from friction.
How nice.

 

[HalfLostAndSearching]

I can understand your confusion and frustration with this question. However, it is important to remember that the net force is the sum of all forces acting on an object, and it can point in any direction. In this case, the net force is a combination of the centripetal force, which is directed towards the center of the circle, and the frictional force, which is directed opposite to the motion of the box.

The reason for this is that the centripetal force is responsible for keeping the box moving in a circular motion, while the frictional force is acting against it, trying to slow it down. The net force will ultimately determine the direction and speed of the box's motion.

It is also important to note that the direction of the net force can change at different points along the circular path, as the magnitude and direction of the frictional force may vary. So while the net force may be pointing towards the center of the circle at one point, it may be pointing in a different direction at another point.

I hope this explanation helps to clarify the concept of net force and its direction in this scenario. Keep in mind that physics can be complex and counterintuitive at times, but with practice and understanding, you will be able to solve these types of problems confidently.