truck tire pressure / load on road

pescador

hi to all

problem:
a truck with a total weight of 5000kN and with 4 wheels will be placed on 4 glass cups each under one wheel. if each tire has a internal air pressure of 2MPa. what will be the load on each cup? and if the truck was standing on the road with out the cups under wheels what will be the load on the road.

Andrew Mason

So what are your thoughts on how tire pressure affects the downward force of the truck?

AM

pescador

if the tires were solid then i can exactly say that the load per tire transfering down to road is 5000/4 = 1250 kN
but the tires are like pneumatic pillows. so some of the load should be carried by the tire surface.

pescador

the load effecting to road should be the surface of the interface between the tire and road * tire internal pressure.

Andrew Mason

So if we, say, let out half the tire air (and, therefore, reduced pressure by half), the load on the road would reduce by half?

AM

pescador

no because if we let the half of air out. then the touching surface area to the road of the tire will increase and the load will remain the same.

Andrew Mason

So what effect does tire pressure have on the force exerted on the ground by the truck?

AM

pescador

sees like nothing if i dunt make a wrong model

pescador

if we say that it has no effect on the load why we have so mch pressure on the tires?

Andrew Mason

The pressure inside the tires is balanced by the forces holding the tire to the wheel. It contributes no net force to the road.

AM

pescador

got it

so if i have a truck of total weight is a N on 4 tires with a tire pressure of p Pa then the surface area touching the road per tire should be

[tex] N/(4*p) [/tex]

so there force to the road will be pressure times the surface area so N again.

pescador

do u have a source that tells theory about the pressurized systems with flexible layer?

pescador

ok lets change the subject.

i got a basketball it stands still on the road. then i come and start pressing on the ball with my one foot. the ball will be deformed from the point that i press. and also the area of the ball touching the road will be deformed and increase.

i think that because of the volume decrease in the ball the pressure will increase and then this pressure will transfer my weight to the road with it's increased area touching the road. so there reaction force from the road will increase.

true?

Andrew Mason

You are making it too complicated. The tire pressure does not affect the load on the road. At best, it changes the distribution of the load so changing air pressure may change the pressure on the road somewhat. But that is all. The pressure in the tires has no bearing on the total force on the road.

AM

pescador

:) ok.

last one. what will happen if i increase the load (add more things to truck) there must be a limit for that if i put more weight and suppose that the tire surface is strong enough. the air will go upwards and the truck will touch the bottom. but if i put more pressure on it will lift the truck again.
so there must be a connection, hmm dunno may be alittle mixed up

Andrew Mason

If you have a deflated tire and pump it up, the truck will rise as the air pressure builds up inside the tire. The air in the tire does work as it expands. This work raises, slightly, the centre of mass of the truck and increases its gravitational potential energy. But (when the truck stops moving up) the force exerted on the road is exactly the same as it was with the deflated tire.

Draw a diagram showing the forces on the truck and on each wheel. Since the truck is not accelerating in the vertical direction, the vertical forces sum to 0. Those forces are the weight of the truck (down) and the normal force of the road on the tires (up). The air in the tire is exerting a force in both directions but is balanced by the mechanical forces holding the tire onto the truck. It would be exactly the same if the truck was sitting on four vertical springs.

AM

pescador

so can we clearly say that the weight of truck is transfered to pressured tire by [tex] surface area 1*pressure [/tex] and it transfers the same load to the road by [tex] surface area 2*pressure[/tex]

surface area 1 : area of the rigid part touching to the tire
surface area 2 : area of the tire touching to road