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.

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 $\quad 2.00 \times 10^{10} \mathrm{~N}$.
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Solution

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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

\[ F = (4.00 \times 10^5 \, \text{Pa}) \times (5.00 \times 10^{-4} \, \text{m}^2) \]

Step 4: Perform the Multiplication

\[ F = 4.00 \times 5.00 \times 10^5 \times 10^{-4} \] \[ F = 20.00 \times 10^1 \] \[ F = 2.00 \times 10^2 \, \text{N} \]

Final Answer

The force that the trapped air exerts on the piston is \( 2.00 \times 10^2 \, \text{N} \). The correct option is C.

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