Questions: A bicycle pump is sealed at one end and the piston pushed until the pressure of the trapped air increases to 4.00 x 10^3 Pa.
The area of the piston compressing the air is 5.00 x 10^-4 m^2.
The force that the trapped air exerts on the piston is
A 1.25 x 10^-9 N
B 8.00 x 10^-1 N
C 2.00 x 10^2 N
D 8.00 x 10^8 N
E 2.00 x 10^10 N.
Transcript text: 13. A bicycle pump is sealed at one end and the piston pushed until the pressure of the trapped air increases to $4.00 \times 10^{3} \mathrm{~Pa}$.
The area of the piston compressing the air is $5.00 \times 10^{-4} \mathrm{~m}^{2}$.
The force that the trapped air exerts on the piston is
A $\quad 1.25 \times 10^{-9} \mathrm{~N}$
B $\quad 8.00 \times 10^{-1} \mathrm{~N}$
C $\quad 2.00 \times 10^{2} \mathrm{~N}$
D $\quad 8.00 \times 10^{8} \mathrm{~N}$
E $\quad 2.00 \times 10^{10} \mathrm{~N}$.
Solution
Solution Steps
Step 1: Identify the Given Values
Pressure of trapped air, \( P = 4.00 \times 10^5 \) Pa
Area of the piston, \( A = 5.00 \times 10^{-4} \) m\(^2\)
Step 2: Use the Formula for Force
The force exerted by the trapped air on the piston can be calculated using the formula:
\[ F = P \times A \]
Step 3: Substitute the Given Values into the Formula