Final answer:
During one stroke of the tire pump, 35.34 Joules of work is done, achieved by exerting an average force of 117.81 Newtons on the piston.
Step-by-step explanation:
A hand-driven tire pump with a 2.50-cm diameter piston and a maximum stroke of 30.0 cm is used to inflate a tire. To determine the work done and the average force exerted on the piston during one stroke, we'll perform the following calculations:
First, we calculate the area of the piston using the formula πr², where r is the radius in meters.
Next, we use the given average gauge pressure to find the average force exerted by the pump using the formula Force = Pressure × Area.
Finally, we calculate the work done using the formula Work = Force × distance (stroke depth).
Performing these calculations:
Radius(r) = diameter / 2 = 2.50 cm / 2 = 1.25 cm = 0.0125 m
Area(A) = πr² = π × (0.0125 m)² = 4.9087 × 10⁻´ m²
Average force(F) = Pressure(P) × Area(A) = 2.40 × 10⁵ N/m² × 4.9087 × 10⁻´ m² = 117.81 N
Work(W) = Force(F) × distance(d) = 117.81 N × 0.30 m = 35.34 J
Thus, in one stroke, you do 35.34 Joules of work, and the average force you exert on the piston is 117.81 Newtons.