Final answer:
The force on the student's head at sea level is calculated to be 6332.81 N using the metric area, and when converting to imperial units, the force is 1470.06 pounds-force. These values are obtained by multiplying the atmospheric pressure at sea level by the area of the top of the head in the respective units.
Step-by-step explanation:
To determine the force on the student's head at sea level, we can use the formula:
Force (F) = pressure (p) × area (A)
The atmospheric pressure at sea level is approximately 101,325 Pa (pascals). The area of the top of the student's head is given in centimeters and inches, so we will calculate for both units separately.
First, let's find the force in newtons:
The area in square meters for a 25 cm x 25 cm head top is:
A = 25 cm × 25 cm
A = 625 cm²
Since 10,000 cm² is equivalent to 1 m², we have:
A = 0.0625 m²
Now, the force in newtons is:
F = 101,325 Pa × 0.0625 m²
F = 6332.81 N
Next, let's convert the area into square inches to find the force in pounds:
A = 100 in²
Since 1 in² = 0.00064516 m², we have:
A = 100 in² × 0.00064516 m²/in²
A = 0.064516 m²
Now, the force in pounds can be found by converting newtons to pounds (1 N is approximately 0.224809 lb):
F = 101,325 Pa × 0.064516 m²
F = 6539.93 N × 0.224809 lb/N
F = 1470.06 pounds-force
The force in pounds is also a measure of weight, since force due to gravity is weight.