Moving cart that rotates when acclerating

[travisr34]

Homework Statement

There are 5 forces R1 and R2 which are the vertical reaction forces on the rear and front wheels respectively. F1 and F2 are the friction forces on the wheels. And finally Mg which acts at the center of gravity which is closer to R2 then R1. Only known value is R1 which will be 0 when tipping occurs, because of this the cart will rotate about R2. The rear wheels are powered by gears while the front ones are just stuck to an axel. I would like to know the linear acceleration that the cart must undergo in order for tipping to occur. I don't really want to plug in numbers just solve it leaving the variable terms

Homework Equations

Summ of the forces in the x,y and moments.

The Attempt at a Solution

forces in x =-f1-f2=ma.
forces in y=R1+R2-mg=0
moments about R1 where clockwise is positive=mg(d1)-R2(d2)=I*alpha(angular acceleration)

 

[Nate810]

d1 is the distance from R2 to cg and d2 is the distance from R1 to cg. I is the moment of inertia about the cg. I know R1=0 so I can get a value for R2 but that doesn't seem to help. I'm not sure how to solve the equation since I don't have a value for F1, F2 or Mg.

 

[ogb p]

I would approach this problem by first identifying all the relevant forces and their directions. In this case, there are five forces acting on the cart: R1, R2, F1, F2, and Mg. R1 and R2 are vertical reaction forces, F1 and F2 are friction forces, and Mg is the force of gravity acting at the center of gravity.

Next, I would use the equations of motion to analyze the forces in the x and y directions and the moments about R1. In the x direction, the sum of the forces is equal to the mass of the cart times its acceleration. In the y direction, the sum of the forces is equal to zero since the cart is not accelerating in the vertical direction. For the moments, I would use the equation that takes into account the distance between the forces and the center of rotation, as well as the moment of inertia and the angular acceleration.

Since the only known value is R1, which will be zero when tipping occurs, I would leave all other variables as unknowns and solve the equations to find the linear acceleration that would cause tipping to occur. This would give a general solution that can be applied to any situation, as opposed to plugging in specific numbers.

In addition, I would also consider other factors that could affect the tipping of the cart, such as the mass and distribution of the load on the cart, the coefficient of friction between the wheels and the ground, and the strength and stability of the cart's structure. These variables could also be included in the equations to provide a more accurate and comprehensive solution.

Overall, as a scientist, I would approach this problem by using the fundamental principles of physics and considering all relevant factors to determine the linear acceleration required for tipping to occur.