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a child wants to pump up a bicycle tire so that its pressure is 1.2 × 10⁵ pa above that of atmospheric pressure. if the child uses a pump with a circular piston 0.035 m in diameter, what force must the child exert? the area of a circle is (π/4) d²
76 n
240 n
89 n
54 n
120 n

Explanation:

Step1: Recall Pressure Formula

Pressure \( P \) is force \( F \) per unit area \( A \), so \( P=\frac{F}{A} \), which rearranges to \( F = P \times A \).

Step2: Calculate Piston Area

The piston is circular with diameter \( D = 0.035 \, \text{m} \). The area of a circle is \( A=\frac{\pi}{4}D^{2} \). Substituting \( D = 0.035 \, \text{m} \):
\( A=\frac{\pi}{4}(0.035)^{2}\approx\frac{3.1416}{4}(0.001225)\approx0.000962 \, \text{m}^2 \).

Step3: Calculate Force

Pressure \( P = 1.2\times 10^{5} \, \text{Pa} \). Using \( F = P \times A \):
\( F=(1.2\times 10^{5})\times0.000962\approx115.44 \, \text{N} \), which is closest to \( 120 \, \text{N} \) (considering rounding during steps).

Answer:

120 N (corresponding to the option with "120 N")