Newton 2nd law + frame of reference

In summary, the problem involves two blocks with friction between them. The top block is pulled with a force F and will move as long as F is less than or equal to the static friction. The free-body diagram of the top block has two forces in the horizontal direction: F and f_s. The correct frame of reference can be either the inertial frame of the ground or the accelerating frame of the bottom block, but the latter requires modification of Newton's laws to include an inertial force.
  • #1
fisico30
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hello forum,

i am struggling with the conceptual understanding of this problem:
Given two blocks, one on top of the other. There is friction between the two blocks.
The upper block is pulled with a force F. Thanks to friction, as long as F is smaller or equal to the static friction f_s(max) the objects will move, accelerate together, withouth having the top block slide over the lower block...

The free-body diagram of the top block involves only two forces in the horizontal direction: F and f_s. F=f_s for the top block not to slide while being pulled.

But that seems from the frame of reference of the lower block...

If we are observing the situation from the ground, the top (and bottom) block is accelerating, moving, so a net force need to be there...

The upper block is not moving relative to the lower block (relative velocity=0).

What is the correct frame of reference to use? I would say the one fixed with the ground (because inertial). But that would imply a net force on the top block, while we just have

F=f_s

thanks
fisico30
 
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  • #2
fisico30 said:
The free-body diagram of the top block involves only two forces in the horizontal direction: F and f_s.
That's true.
F=f_s for the top block not to slide while being pulled.
That's not true.

But that seems from the frame of reference of the lower block...

If we are observing the situation from the ground, the top (and bottom) block is accelerating, moving, so a net force need to be there...
Absolutely.

The upper block is not moving relative to the lower block (relative velocity=0).

What is the correct frame of reference to use? I would say the one fixed with the ground (because inertial). But that would imply a net force on the top block, while we just have

F=f_s
You can use either frame to analyze this problem. To use the inertial frame of the ground, just apply Newton's 2nd law as usual to both blocks.

But if you want to use the accelerating frame of the bottom block, then you'll have to modify Newton's laws to include an inertial force acting on the top block. The sum of all forces--including the inertial force--must add to zero. That's a bit different from saying F = f_s (which isn't true).
 
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1. What is Newton's second law of motion?

Newton's second law of motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In other words, the larger the force applied to an object, the greater its acceleration will be.

2. How does Newton's second law of motion apply to different frames of reference?

In order to apply Newton's second law of motion to different frames of reference, it is important to consider the concept of an inertial frame of reference. This is a frame of reference in which Newton's laws of motion are valid and the object is not experiencing any acceleration. The second law can be applied to both stationary and moving frames of reference, as long as the net force and mass are accurately measured within that specific frame.

3. Can an object have different accelerations in different frames of reference?

Yes, an object can have different accelerations in different frames of reference. This is because the acceleration of an object is dependent on the net force acting on it, and the net force can vary depending on the frame of reference. For example, an object may appear to be at rest in one frame of reference, but may be accelerating in another frame.

4. How is inertia related to Newton's second law of motion?

Inertia is the tendency of an object to resist changes in its state of motion. Newton's second law of motion explains that an object will only accelerate if there is a net force acting on it. The larger the mass of an object, the more inertia it has, and the more force is required to change its state of motion. This is why the second law is often stated as F=ma (force equals mass times acceleration).

5. Can Newton's second law be used to calculate the force on an object in a non-inertial frame of reference?

No, Newton's second law is only valid in an inertial frame of reference. In a non-inertial frame, there are additional forces at play, such as fictitious forces, that can affect the acceleration of an object. Therefore, the second law cannot be used to accurately calculate the force on an object in a non-inertial frame.

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