Allegra's favorite ride at the Barrel-O-Fun Amusement Park is the Flying Umbrella, which is lifted by a hydraulic jack. The operator activates the ride by applying a forcce of 72 N to a 3.0-cm-wide cylindrical piston, which holds the 20000. N ride off the ground. What is the diameter of the piston that holds the ride?
HERE IS THE CORRECT WORK:
pressure1 = pressure2
force1/area1 = force2/area2
72/3 = 20,000/x
24x = 20,000
x(area) = 833.3333333333
we have the area, but the question asks for the diameter.
area = PI * r^2
833.3 = PI * r^2
r = 16.29 cm
diameter = 2r
16.29 * 2 = __32.58176 cm__
Is it 32.57 cm?
When I solve this problem, I get 32.58.
I am pretty sure you got the answer correct - not BOBPURSELY.
Well, if the operator is applying a force of 72 N to a 3.0 cm-wide piston, we need to find the diameter of the piston that holds the 20000 N ride off the ground.
Let me do some quick math here. *calculating noises*
Okay, just like how I calculate the best punchline, I've got the answer. The formula we can use here is:
Force1/Force2 = Area1/Area2
Now, let's plug in the numbers. We know that the force applied by the operator is 72 N, and the force holding the ride is 20000 N. The formula becomes:
72 N/20000 N = π(r1)²/π(r2)²
We can simplify this further:
72 N/20000 N = (r1)²/(r2)²
Since we're given the width of the piston, which is 3.0 cm, we can find the radius (r1) by dividing it by 2.
Therefore, r1 = 1.5 cm = 0.015 m.
Now, let's plug in the values we know:
72 N/20000 N = (0.015 m)²/(r2)²
Time for the grand finale! Solving for (r2)²... *drumroll*
(r2)² = [(0.015 m)² * 20000 N]/72 N
(r2)² = 0.00625 m²
And taking the square root of both sides:
r2 = 0.079 m
Now, the diameter of the piston that holds the ride is twice the radius, so:
diameter = 2 * r2 = 2 * 0.079 m = 0.158 m
So, the diameter of the piston that holds the ride is approximately 0.158 meters.
Now, who's up for some umbrella flying at the Barrel-O-Fun Amusement Park? Just watch out for clowns like me hovering around!
To find the diameter of the piston that holds the ride, we can use the following formula:
Force = Pressure x Area
First, let's calculate the pressure applied by the operator on the piston.
The area of a cylinder is given by the formula:
Area = π * radius^2
Given that the width of the piston is 3.0 cm, we can find the radius by dividing it by 2:
Radius = Width / 2 = 3.0 cm / 2 = 1.5 cm = 0.015 m
Now we can calculate the area using the formula:
Area = π * (0.015 m)^2
Given that the force applied by the operator is 72 N, we can rearrange the formula to find the pressure:
Pressure = Force / Area
Substituting the values into the formula, we get:
Pressure = 72 N / (π * (0.015 m)^2)
Next, we can calculate the pressure exerted by the operator on the piston.
Now let's find out how much force is acting on the piston to hold the ride.
Given that the ride weighs 20000. N, this force is acting downward and the piston is balancing it. Therefore, the force exerted by the ride is also 20000. N.
Now we can rearrange the formula to find the area of the piston:
Area = Force / Pressure
Substituting the values, we get:
Area = 20000. N / Pressure
Since we already have the pressure calculated, we can substitute that value into the formula:
Area = 20000. N / (72 N / (π * (0.015 m)^2))
Simplifying further, we get:
Area = 20000. N * (1 / (72 N / (π * (0.015 m)^2)))
Dividing the N terms gives:
Area = 20000. N * π * (0.015 m)^2 / 72 N
Now, we can calculate the area of the piston.
Finally, we can find the diameter of the piston by using the formula:
Diameter = 2 * radius
Given that the radius is 0.015 m, we can calculate the diameter by substituting the value into the formula:
Diameter = 2 * 0.015 m
Simplifying further, we get:
Diameter = 0.03 m
Therefore, the diameter of the piston that holds the ride is 0.03 meters.
pressure1=pressure2
force1/area1=force2/area2
force1/diam1^2=force2/diam2^2
diameter2= sqrt(force2/force1) * diameter1
= sqrt (20,000/72)* 3cm
= a little over 60cm