A friend asks you how much pressure is in your car tires. Unfortunately, you have misplaced your gauge but confident in your knowledge of physics you tell your friend “I can figure it out”. From the owner’s manual you find that the car’s mass is 1350 kg and that the tire manufacturer recommends 31 psi. Assuming that each tire supports one-fourth of the weight of the car, you use a ruler to find that the tires are 15 cm wide and the flattened segment of the tire in contact with the road is 13 cm long. What answer do you give your friend?
Express your answers in pounds per square inch (psi)
weight car=pressure*area*4tires
pressure=1350*9.8/(.15*.13*4)Pascals
now if you want to change from pascals to psi,
pressurePascals*0.000145 psi
To determine the pressure in the car tires, we can use the concept of pressure as force per unit area. Here are the steps to calculate it:
Step 1: Calculate the force exerted by each tire.
Given that each tire supports one-fourth of the car's weight, we need to determine the weight of the car.
Weight = mass × acceleration due to gravity
= 1350 kg × 9.8 m/s²
Step 2: Calculate the area of the flattened segment of the tire in contact with the road.
The flattened segment of the tire can be considered as a rectangle. The area is given by:
Area = length × width
= 13 cm × 15 cm
Step 3: Convert the area from square centimeters to square meters.
Since pressure is typically measured in Pascal (Pa), which is equal to N/m², we need to convert the area to square meters.
Area = (13 cm × 15 cm) / (100 cm/m)²
Step 4: Calculate the force exerted by each tire.
The force exerted by each tire is equal to the weight divided by the area.
Force = Weight / Area
Step 5: Convert the force from Newtons to pounds (since psi is commonly used for tire pressure).
1 Newton ≈ 0.2248 pounds
Force (in pounds) = Force × 0.2248
Step 6: Calculate the pressure in the tires.
Pressure = Force / Area
Step 7: Convert the pressure from Pascals to pounds per square inch.
1 Pa ≈ 0.00014503773773 psi
Pressure (in psi) = Pressure × 0.00014503773773
Now, by following these steps and using the given numbers, you can calculate the pressure in the car tires.
To find the pressure in the car tires, you can use the formula:
Pressure = Force / Area
First, let's calculate the force exerted on each tire by the weight of the car. Since each tire supports one-fourth of the weight, we can divide the car's mass by 4 and multiply it by the acceleration due to gravity (9.8 m/s^2) to find the force:
Force = (Mass / 4) * Acceleration due to gravity
Force = (1350 kg / 4) * 9.8 m/s^2
Next, let's calculate the area of contact between the tire and the road. We can approximate it as a rectangle, using the width and length measurements provided:
Area = Width * Length
Area = 15 cm * 13 cm
Now, we need to convert the units to meters for consistency. Since 1 meter is equal to 100 centimeters, we divide both width and length by 100:
Area = (15 cm / 100) * (13 cm / 100)
Now, we can substitute the values into the pressure formula:
Pressure = Force / Area
Pressure = [ (1350 kg / 4) * 9.8 m/s^2 ] / [ (15 cm / 100) * (13 cm / 100) ]
Since the given recommended pressure is in psi (pounds per square inch), we need to convert our answer from pascals to psi. We know that 1 pascal is equal to 0.000145038 psi:
Pressure (in psi) = Pressure (in pascals) * 0.000145038
Finally, substitute the numbers and solve for pressure:
Pressure (in psi) = [ (1350 kg / 4) * 9.8 m/s^2 ] / [ (15 cm / 100) * (13 cm / 100) ] * 0.000145038
Calculating this, you should get the answer to give your friend for the pressure in the car tires.