Please help me finding a radius of the wheels to overcome the obstacle?

[joonsunkingka]

Hi to all.
Please help me to clarify this situation:

There is a 4-wheel cart powered by friction drive using the dc motor. The cart will carry heavy stuffs on the top. what radius of wheels will be able to overcome a 1 cm high and 0.7 cm wide and 14 cm long speed bump(it is like a thin stick)?

For ex. here are some data based on the picture attached.
r1 = 0.0475 inch
w1 = 490 rad/s
w2= don't know.
r2= (not 1.75 inch in picture)I don't know, r2 is what i am trying to calculate.
mg= (5kg) (9.8)


Which formulas must I use to determine appropriate radius of wheel to overcome the speed bump easily?

Thank you all for help!

 

[Navin A S]

To determine the appropriate radius of the wheel to overcome the speed bump, you need to consider the forces that are involved. The force of gravity (mg) will act downwards on the cart and its weight, while the force of friction between the wheel and the ground will act opposingly. You also need to consider the centripetal force that is generated by the cart’s inertia when it is turning. The centripetal force can be calculated using the formula F = mv2/r, where m is the mass of the cart, v is the speed of the cart and r is the radius of the wheel. The force of friction between the wheel and the ground can be determined using the formula F = μmg, where μ is the coefficient of friction and mg is the weight of the cart. You can then calculate the minimum radius of the wheel that is required to overcome the speed bump by solving the equations for the forces mentioned above. This will give you an estimate of the appropriate radius of the wheel that is required to overcome the speed bump.