A hand-driven tire pump has a 2.50 cm diameter piston and a maximum stroke of 31.0 cm.
(a) How much work do you do in one stroke if the average gauge pressure is 2.40 multiplied by 105 N/m2 (about 35 psi)? (You may consider this an isothermal process.)
(b) What average force do you exert on the piston, neglecting friction and gravity?
force on piston: pressure*area=force
work done: PV=work
I don't know which are the "area" and "V". Can you show me the steps. Thanks.
To determine the work done in one stroke and the average force exerted on the piston, we can use the following equations:
(a) Work (W) = Force (F) x Distance (d)
(b) Average force (F_avg) = Pressure (P) x Area (A)
First, let's calculate the work done in one stroke:
(a) Work (W) = Force (F) x Distance (d)
The force can be calculated using the formula for pressure:
Pressure (P) = Force (F) / Area (A)
Rearranging the formula, we have:
Force (F) = Pressure (P) x Area (A)
The area of the piston can be calculated using the formula for the area of a circle:
Area (A) = π x radius^2
Given:
Pressure (P) = 2.40 x 10^5 N/m^2 (Is in Pascal or Pa)
Diameter (diameter) = 2.50 cm = 0.025 m (Convert from cm to m)
Radius (r) = diameter / 2 = 0.025 m / 2 = 0.0125 m
Substituting the values into the formulas:
Area (A) = π x radius^2
Area (A) = π x (0.0125 m)^2
Area (A) = 3.14 x (0.0125 m)^2
Area (A) ≈ 0.000490875 m^2
Now we can calculate the force:
Force (F) = Pressure (P) x Area (A)
Force (F) = 2.40 x 10^5 N/m^2 x 0.000490875 m^2
Force (F) ≈ 117.81 N (Round off to two decimal places)
The work done in one stroke can be calculated as:
Work (W) = Force (F) x Distance (d)
Work (W) = 117.81 N x 0.31 m
Work (W) ≈ 36.53 J (Round off to two decimal places)
Therefore, the work done in one stroke is approximately 36.53 Joules.
Now let's calculate the average force exerted on the piston:
(b) Average force (F_avg) = Pressure (P) x Area (A)
Using the value of the area we calculated earlier:
Average force (F_avg) = 2.40 x 10^5 N/m^2 x 0.000490875 m^2
Average force (F_avg) ≈ 117.81 N (Round off to two decimal places)
Therefore, the average force exerted on the piston is approximately 117.81 Newtons, neglecting friction and gravity.