A hand-driven tire pump has a piston with a 2.50 cm diameter and a maximum stroke of 30 cm. how much work do you do in one stroke if the average gauge pressure is 2.40×105 N.m – 2?
Select one:
a. 141 J
b. 4.5×107 J
c. 35.3 J
d. 1.41 ×108 J
force*distance=pressure*area*distance=
2.40E5Pa*PI( .0125)^2*.3 = ?
35.3J
To find the work done by the hand-driven tire pump, we can use the formula for work:
Work = Force × Distance
First, let's find the force exerted by the piston. The force can be calculated using the equation for pressure:
Force = Pressure × Area
The area of the piston can be calculated using the formula for the area of a circle:
Area = π × radius^2
Given that the diameter of the piston is 2.50 cm, the radius is 2.50 cm / 2 = 1.25 cm = 0.0125 m.
Now we can calculate the area:
Area = π × (0.0125 m)^2
Next, we can substitute the given gauge pressure into the formula for force:
Force = 2.40 × 10^5 N/m^2 × Area
Now we know the force exerted by the piston. To find the work done in one stroke, we need to multiply the force by the distance traveled by the piston.
The distance traveled by the piston is given as 30 cm, which is equal to 0.30 m.
Finally, we can calculate the work:
Work = Force × Distance
Now, let's plug in the values:
Work = (2.40 × 10^5 N/m^2 × Area) × 0.30 m
Simplifying this equation will give us the answer:
Work = (2.40 × 10^5 N/m^2 × π × (0.0125 m)^2) × 0.30 m
Calculating this will result in the answer for the work done in one stroke.