Balance of Torque forces (scrambler machine)

[Edvin]

Hi,

I'm trying to understand the physics on a Scrambler; and am having difficulty with balance of torques equation.
In below image a vehicle is moving to the right while breaks are applied.

The balance of torque is defined as:
h * F₁ + h * F₂ + b * N₁ = (B-b) * N₂

I understand the normal forces; and the direction of friction force; but, having difficulty with balance of forces.
Please let me know if my interpretation of diagram is correct; and if I am missing anything.

1) Force direction
When we apply the break, the torque force is to the right. So, am I right to say that we are going to use the friction force magnitude that is pointing to the left; but, the real torque direction is still clockwise against an imaginary vertical wheel arm.

2) Expression: h * F1 + h * F2 + b * N1 = (B-b) * N2
Am I correct to say that we are assuming a rigid arm of height "h" in this problem; thereby, ignoring the fact that we have an axis in the center of the wheel?

3) Expression: h * F1 + h * F2 + b * N1 = (B-b) * N2
I understand the location of horizontal center of mass; but, are we ignoring the vertical center of mass for this problem? I know friction force is k * N, which considers the mass; but, I can't help think that the center of mass is not considered along height h (vertically).

4) Expression: h * F1 + h * F2 + b * N1 = (B-b) * N2
Why are we adding these forces? Are we to visualize one giant torque system (regardless of distance between the wheels)?

5) Equation: h * F1 + h * F2 + b * N1 = (B-b) * N2
Why is (b * N1) added to the left side of the equation. I guess we add this torque because the rotational direction is clockwise (same as when breaking is applied); and since the downward direction force is same as normal force, we add it to the left side of our equation.

6) Expression: h * F1 + h * F2 + b * N1 = (B-b) * N2
Am I correct to state that this expression goes to the right side of the equation because it is opposite direction of all other forces.

7) Am I correct to say that the equation would remain the same, even if we lower the horizontal axle and center of the mass such that it is the bellow the wheel axis. I guess only torque to the center wheel changes; but, the equation remains the same.

Thanks in advance.

-Edvin

 

[eljose79]

Dear Edvin,

Thank you for reaching out for clarification on the physics of a Scrambler. Let me try to address your questions and provide some insight into the balance of torques equation.

1) Force direction:
You are correct in saying that when the brakes are applied, the torque force is to the right. This is due to the friction force acting on the wheel in the opposite direction of the vehicle's motion. The friction force is what allows the vehicle to slow down and eventually come to a stop.

2) Expression: h * F1 + h * F2 + b * N1 = (B-b) * N2:
In this equation, we are assuming a rigid arm of height "h" for simplicity. This means that we are not considering the axis in the center of the wheel, as it would not have a significant effect on the balance of torques in this scenario. However, if we were to consider the axis, it would have a small contribution to the overall torque equation.

3) Expression: h * F1 + h * F2 + b * N1 = (B-b) * N2:
The vertical center of mass is not considered in this problem because it does not have a significant effect on the balance of torques. The friction force, which is proportional to the normal force, takes into account the mass of the object. Therefore, the vertical center of mass does not need to be considered separately.

4) Expression: h * F1 + h * F2 + b * N1 = (B-b) * N2:
We are adding these forces because they all contribute to the overall torque of the system. By adding them together, we can find the net torque acting on the system and determine if it is balanced or not.

5) Equation: h * F1 + h * F2 + b * N1 = (B-b) * N2:
The reason why we add (b * N1) to the left side of the equation is because it is a torque acting in the same direction as the other torques on the left side. This is due to the clockwise rotation caused by the friction force.

6) Expression: h * F1 + h * F2 + b * N1 = (B-b) * N2:
You are correct in saying that this expression goes to the right side of the equation because it is in the opposite direction of all the other torques on the left