Question

The following data are obtained for a car: The tire pressure is measured as 28.0 psi, and the width and length of the contact surface of each tire are 7.50 in and 8.75 in, respectively. What is the approximate weight of the car?

Short answer

Question: Determine the approximate weight of the car, given that the tire pressure is 28.0 psi, the width of the contact surface of a single tire is 7.50 in, and the length of the contact surface is 8.75 in. Answer: First, calculate the contact area of a single tire (A_tire) as follows: A_tire = width × length A_tire = 7.50 in × 8.75 in A_tire = 65.625 in² Next, convert the tire pressure from psi to pascals: 28.0 psi × 6894.76 Pa/psi = 193054.28 Pa Now, find the force exerted by a single tire (Force_tire) using the pressure and contact area: Force_tire = Pressure × A_tire Force_tire = 193054.28 Pa × 65.625 in² Remember to convert in² to m²: 1 in² = 0.00064516 m² 65.625 in² × 0.00064516 m²/in² = 0.042337 m² Now we can calculate the force on a single tire: Force_tire = 193054.28 Pa × 0.042337 m² Force_tire = 8171.3 N Calculate the total force on all four tires: Force_total = 4 × Force_tire Force_total = 4 × 8171.3 N Force_total = 32685.2 N Finally, find the weight of the car: Weight_car = Force_total Weight_car = 32685.2 N The approximate weight of the car is 32,685.2 Newtons.

Step-by-step solution

Calculate the contact area of a single tire

To calculate the contact area of a single tire, we will multiply its width and length. Given the width of the tire as 7.50 in and the length as 8.75 in, the contact area (A_tire) can be calculated as: A_tire = width × length

Convert tire pressure to force on a single tire

Next, we need to convert the tire pressure (28.0 psi) into the force exerted by a single tire. We can use the formula: Force_tire = Pressure × A_tire Remembering that 1 psi = 6894.76 Pa (pascals), we will first convert the tire pressure to pascals.

Calculate the total force on all four tires

Now that we have calculated the force on a single tire, we need to find the total force on all four tires. Since there are four tires supporting the car, the total force can be calculated as: Force_total = 4 × Force_tire

Determine the weight of the car

Finally, we will use the total force exerted by all four tires to find the weight of the car. In this case, we will assume that the force exerted by the tires equals the weight of the car. Therefore, the weight of the car can be found by simply equating the total force to the weight: Weight_car = Force_total Now let's do the calculations to find the weight of the car.