To measure indirectly the weight of a car by measuring the pressure in the tires and the surface area of the tires in contact with the road.
Background: Pressure is defined as force per unit area. If we know the force that is being exerted on an object and know the area over which that force acts, we can calculate the pressure by using the definition. For example, if a force of 100 lbs is exerted over an area of 10 square inches, then the pressure resulting from that force is
Pressure = Force/Area = 100 lbs/10 in2 = 10 lbs/in2.We can use the same relationship to determine the force if we know the pressure and the area. Simply rearranging the equation, we get
Force = Pressure x Area, or F = P A.
The rims of the wheels of a car are held off the ground primarily by the force of the air in the inflated tires. The tires theselves are elastic and often have steel belting which tend to support the car also, but most of the support results from the air pressure.
In this activity you will approximate the weight of your car by assuming the entire weight is supported by air pressure in the tires. The force of each tire on the ground is related to the pressure in the tires and the area of the tires in contact with the ground. The force of gravity pulls the car down and the road pushes up with the same strength. The force that the road pushes up on each tire is simply the pressure of that tire times the area of contact the tire makes with the ground.
The sum of the forces on the four tires of the car must be equal to the weight of the car (otherwise there would be a net force on the car).
Equipment and Supplies :
One car
Tire gauge
Four pieces of paper larger than the area of contact between your tires and the ground
Pencil & ruler.
Procedure:
Park your car on a clean dry level surface. Place four sheets of paper directly in front of all four tires (or directly behind). Gently roll the car onto the sheets of paper so that the tires are totally on the pieces of paper. Set the brakes and turn off the engine.
Using a pencil, outline on the sheets of paper the area of the tires in contact with the paper. You can trace around the side edges of the tires. To determine the line of contact in front and back of each tire, slip a piece of paper under the tire as far as it will go; then mark the line of contact with a pencil. You can complete the line after the paper is removed from under the tires. Be sure to label each piece of paper with the tire (e.g., front left, back right,…)
On each piece of paper under the tires, record the air pressure in the tire, which you should measure with a tire gauge. Most tire gauges read the pressure in pounds per inch squared (lbs/in2).
Move the car and retrieve the sheets of paper. Using a rulter, draw straight lines to approximate the area of the tires in contact with the ground. The shape should be roughly rectangular and the area can be determined by finding the product of the length and width of the rectangle.
Multiply the area of each tire by the corresponding pressure in that tire to get the force on that tire.
Add up the four forces. This is your estimate of the car’s weight. Compare the measured value with the value for the curb weight given in the owner’s manual (or look it up on the internet).
Worksheet
Tire Tire Pressure (lbs/in2) Tire Contact Area (in2) Force on Tire (lbs)
Front left
Front right
Rear left
Rear right
• List the actual curb weight of the car: Actual Weight = W= _ lbs
• Calculate the percent difference between your value of the car’s weight and the listed weight by using the formula
Percent Difference = x 100
• Comment on your values and any discrepancies. What do you think are the sources of error? (Note: if you are deviating significantly from this value, you should re-check your calculations.)
• Suppose one of your tires really needed more air (e.g., the pressure was found to be 15 psi instead of the recommended value of 35 psi). If you inflated this tire up to the recommended value, would that change the amount of weight supported by this tire? Would that change the surface area this tire makes with the ground? Explain your reasoning.
• Do your measurements show that the weight is equally distributed between the front and rear tires? How about between the left and right sides? Why might the weight not be distributed evenly?