# Problem in inertial reference frame

• balest
In summary, the problem involves a truck and a pack on its back with a frictionless bed and a small block of wood stopping the pack. The pack has a certain size and mass, and the question is what is the minimum acceleration of the truck to turn over the pack. In the frame of the truck, the problem is easily solved, but it becomes more complicated in an inertial frame. The conversation delves into the concept of the normal force and its relation to the centre of gravity. The conclusion is that the normal force, when the pack begins to turn over, must pass through the centre of gravity due to the equivalence principle and the stability of the object.
balest
Well, in principle, this problem seems very easy but I don't know the exact explanation.Here we go. We have a truck and a pack in its back.The bed of the truck is frictionless and the pack is stopped by a small piece of wood of something like that. The size of the pack is whatever(for instance,base=2m^2, height=1,75m)and its mass is 2kg so the question is what is the minimum acceleration of the truck to turn over the pack. In the frame of the truck is easy for me to solve the problem but I don't know how to solve it in an inertial frame. What I want to know is why the normal force, in the exact moment when the pack begins to turn over, has to pass through the centre of gravity.Why? I'm mystified.

balest said:
Well, in principle, this problem seems very easy but I don't know the exact explanation.Here we go. We have a truck and a pack in its back.The bed of the truck is frictionless and the pack is stopped by a small piece of wood of something like that. The size of the pack is whatever(for instance,base=2m^2, height=1,75m)and its mass is 2kg so the question is what is the minimum acceleration of the truck to turn over the pack. In the frame of the truck is easy for me to solve the problem but I don't know how to solve it in an inertial frame. What I want to know is why the normal force, in the exact moment when the pack begins to turn over, has to pass through the centre of gravity.Why? I'm mystified.
Think of the pack as a point mass connected by a rigid rod to the fulcrum (the pack edge pressing against the block of wood). When the rod passes the vertical, the pack starts to turn over. At that point, where is the normal force? Where is the centre of gravity?

AM

In the exact situation when the pack begins to turn over I can see those forces

gravity applied in the center of gravity
horizontal normal force(x) applied in the corner near the piece of wood
vertical normal force(y) applied in the corner near the piece of wood too.

but the point is why the net normal force , that's to say, normal force(x)+normal force(y)=black arrow must go through cg(center of gravity). What is the rule,law or whatever in order to infer that?

In the situation you describe it's quite difficult for me to see the forces.I suppose that the normal force is near the fulcrum and vertical as well as the centre of gravity but I'm not sure.

Andrew Mason said:
Think of the pack as a point mass connected by a rigid rod to the fulcrum (the pack edge pressing against the block of wood). When the rod passes the vertical, the pack starts to turn over. At that point, where is the normal force? Where is the centre of gravity?

AM

Ok,now I know the answer.The point is incredibly the "equivalence principle" and the stability of an object. That seems crazy but just think of it. The horizontal aceleration of the truck(plus the gravity downward) is the same than a situation where the truck is inclined in such a way that the resulting force goes through the rear botton edge of the pack, that is to say the fulcrum(in this situation the pack is about to tip over) So that's why the resulting normal force is equivalent to a force going through the center of gravity, because of the equivalence principle,isn't it marvelous?

In this scenario, the pack is in a state of static equilibrium before the truck begins to accelerate. This means that the forces acting on the pack (gravity, normal force, and friction) are balanced and there is no net force acting on the pack. When the truck begins to accelerate, a net force is applied to the pack and it starts to rotate.

Now, in an inertial reference frame, the laws of physics hold true and the principle of inertia states that an object will remain at rest or in motion with constant velocity unless acted upon by an external force. In this case, the external force is the acceleration of the truck.

In order for the pack to rotate, the normal force must act at a distance from the center of gravity. This creates a moment (torque) that causes the pack to rotate. If the normal force were to act through the center of gravity, there would be no moment and the pack would not rotate.

So, in order for the pack to rotate, the normal force must act at a distance from the center of gravity. This is why the normal force must pass through the center of gravity at the exact moment when the pack begins to turn over. This is a result of the principles of inertia and rotational motion.

## What is an inertial reference frame?

An inertial reference frame is a coordinate system in which Newton's laws of motion hold true. This means that an object at rest will remain at rest and an object in motion will continue in a straight line at a constant velocity unless acted upon by an external force.

## What are some common problems in inertial reference frames?

Some common problems in inertial reference frames include the Coriolis effect, centrifugal force, and the acceleration of rotating reference frames.

## How do these problems affect scientific experiments?

These problems can affect scientific experiments by introducing errors or inaccuracies in measurements and calculations. For example, the Coriolis effect can cause objects to appear to deviate from their expected path, leading to incorrect data.

## How can scientists account for these problems?

Scientists can account for these problems by using correction factors or equations to adjust their data and calculations. They can also design experiments to minimize the effects of these problems, such as using larger scales to reduce the impact of the Coriolis effect.

## Are there any benefits to using inertial reference frames?

Yes, there are many benefits to using inertial reference frames in scientific research. They provide a consistent and predictable framework for studying motion and forces, and allow for accurate comparisons between experiments and observations. In addition, they are essential for developing theories and laws that govern the behavior of the physical world.

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