# [Irodov 1.65] Bar on top of a plank on a frictionless surface with a var. force.

• dharavsolanki
In summary, we are discussing the scenario of a plank with a bar placed on it on a smooth horizontal plane. A horizontal force, F = at (a is constant), is applied to the bar and we are trying to find the accelerations of the plank and the bar, w1 and w2, respectively, in relation to time t. The coefficient of friction between the plank and the bar is equal to k. At first, the bar will move along with the plank as a system until F = at reaches the maximum static friction between the two masses. After that, the plank will have a constant acceleration while the bar continues to accelerate. The graphs of these dependences will reveal more, particularly the jump when F = km2g
dharavsolanki
A plank of mass m1 with a bar of mass m2 placed on it lies on a smooth horizontal plane. A horizontal force growing with time t as F — at (a is constant) is applied to the bar. Find how the acceler-ations of the plank w1 and of the bar w2 depend on t, if the coefficient of friction between the plank and the bar is equal to k. Draw the approximate plots of these dependences.

I am discussing this question with a friend.

Initial Thoughts:

* The force is applied to the bar, the plank will experience the same force till a certain point.

* This point is actually when F = at becomes equal to the maximum static friction between the two masses.

* So, initially, till the static friction limit is reached, the bar will move along with the plank as a system, and after that, the plank will have a constant acceleration. While the bar will keep on accelerating.

The graphs will reveal something more. I am curious about the jump when F = km2g

## 1. What is the purpose of the bar on top of the plank in Irodov 1.65?

The bar on top of the plank serves as a point of contact for the variable force to act upon. It allows for the force to be applied at a specific location and direction.

## 2. Why is the surface in Irodov 1.65 described as frictionless?

The surface is described as frictionless because it eliminates the effects of friction, allowing for a more simplified analysis of the system. This assumption is often used in theoretical physics problems to focus on the main principles without the added complexity of friction.

## 3. How does the variable force affect the motion of the bar and plank in Irodov 1.65?

The variable force acts as an external force on the system, causing both the bar and plank to accelerate in the direction of the force. The magnitude and direction of the acceleration will depend on the strength and direction of the variable force.

## 4. What is the significance of using a plank instead of a solid object in Irodov 1.65?

The use of a plank allows for a more realistic scenario, as most objects in the real world are not perfectly rigid. The plank will experience some amount of deflection due to the applied force, which can affect the overall motion of the system.

## 5. How does the concept of energy conservation apply to the system in Irodov 1.65?

The concept of energy conservation applies to the system because the total energy of the system (kinetic and potential) remains constant as long as no external forces, such as friction, are present. This allows for the prediction of the final velocity of the bar and plank based on the initial conditions and the applied force.

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