Question

you inflate the tires of your car to a gauge pressure of 43.0 lb/in2. if your car has a mass of 1600 kg and is supported equally by its four tires, determine the following. (a) contact area between each tire and the road m2 (b) will the contact area increase, decrease, or stay the same when the gauge pressure is decreased? increase decrease stay the same (c) gauge pressure required to give each tire a contact area of 105 cm2 lb/in2

Answer 1

To calculate the contact area between each tire and the road, divide the weight of the car by the pressure. When the gauge pressure is decreased, the contact area between the tire and the road will increase. To determine the gauge pressure required for a specific contact area, divide the weight of the car by the contact area and multiply by 4.

Step-by-step explanation:

To calculate the contact area between each tire and the road, we can use the formula:

Contact area = Total weight of the car / Pressure

Since the car is supported equally by all four tires, the weight on each tire is 1/4 of the total weight. So, the contact area between each tire and the road is:

Contact area = (1/4) * Weight of the car / Pressure

Regarding part (b) of the question, when the gauge pressure is decreased, the contact area will increase. This is because a decrease in pressure leads to a larger area of distribution, increasing the contact area between the tire and the road.

For part (c), to determine the gauge pressure required to give each tire a contact area of 105 cm², we can rearrange the previous formula:

Gauge pressure = (Weight of the car / Contact area) * 4

Substituting the values, we get:

Gauge pressure = (Weight of the car / 105 cm²) * 4

Make sure to convert the weight of the car and the desired contact area to the appropriate units before performing the calculation.

Answer 2

The contact area of a car tire can be calculated by dividing the weight supported by each tire by the gauge pressure. If the gauge pressure decreases, the contact area increases. To achieve a specific contact area, one can solve the Pressure = Force / Area equation with the desired area value.

Step-by-step explanation:

Calculating Tire Contact Area and Gauge Pressure

To calculate the contact area between each tire and the road, we start with the car’s total weight, which is supported by the four tires at the given gauge pressure. Using the formula Pressure = Force / Area, we can determine the area with the following steps:

1. Convert the car’s mass to weight in Newtons (N) using Weight = Mass × Gravity, with gravity approximated as 9.8 m/s².
2. Divide the weight by four to get the weight supported by each tire.
3. Convert the gauge pressure from lb/in² to N/m².
4. Solve for the contact area, Area = Force / Pressure.

The contact area would be equal to the force exerted by the car through each tire divided by the gauge pressure.

If the gauge pressure is decreased, the contact area will increase because there is now less force per unit area exerted on the road. Conversely, if the gauge pressure were to be increased, the contact area would decrease.

To find the gauge pressure required to give each tire a contact area of 105 cm², we reverse the process. Convert 105 cm² to m², use the weight supported by each tire, and solve Pressure = Force / Area. This will give us the new gauge pressure in N/m² which can then be converted back to lb/in² for the final answer.