a 40 kg student is riding a bicycle to school. the bicycle has a mass of 12 kg. the area that each tire makes contact with the road can be approximated by a rectangle of dimensions 6 cm x 4 cm. what is the pressure that each tire exerts on the road? give your answer in kPa to the nearest tens place.
To find the pressure that each tire exerts on the road, we can use the formula:
Pressure = Force / Area
First, let's calculate the force exerted by the student. We know that force is equal to mass multiplied by acceleration. However, since the problem does not provide the acceleration, we can assume that the bike is moving at a constant speed, which means there is no acceleration. Therefore, the force exerted by the student is equal to the weight of the student, which can be calculated as mass multiplied by the acceleration due to gravity (9.8 m/s²):
Force_student = 40 kg * 9.8 m/s²
Force_student = 392 N
Next, let's calculate the force exerted by the bicycle. Following the same logic, the force exerted by the bicycle is equal to the weight of the bicycle:
Force_bicycle = 12 kg * 9.8 m/s²
Force_bicycle = 117.6 N
Now, we can calculate the total force exerted by both the student and the bicycle:
Total_force = Force_student + Force_bicycle
Total_force = 392 N + 117.6 N
Total_force = 509.6 N
Next, let's calculate the area of each tire. Since each tire is approximated by a rectangle, we can use the formula:
Area = Length * Width
Area = 6 cm * 4 cm
Area = 24 cm²
To convert this to square meters, we divide by 10,000 (since 1 m² = 10,000 cm²):
Area = 24 cm² / 10,000
Area = 0.0024 m²
Now, we can calculate the pressure exerted by each tire:
Pressure = Total_force / Area
Pressure = 509.6 N / 0.0024 m²
Pressure ≈ 212333.3 Pa
Finally, let's convert the pressure from Pascals (Pa) to kilopascals (kPa):
Pressure ≈ 212333.3 Pa / 1000
Pressure ≈ 212.3 kPa
Therefore, each tire exerts approximately 212.3 kPa of pressure on the road.