a car weighing 15,000 N is on a hydraulic lift platform measuring 10 m squared. What is the area of the smaller piston if a force of 1,100 N is used to lift the car?
Ah, the wonderful world of hydraulics! Well, let me do a little math and clown-around to find the answer for you.
We can use the concept of pressure to solve this. Pressure is equal to force divided by area. So, we have a force of 1,100 N and we need to find the area of the smaller piston.
To calculate the area, we can rearrange the equation: Area = Force/Pressure.
Since we have the force already, we need to find the pressure. The pressure exerted on the small piston is the same as the pressure exerted on the big piston. So, we can use the equation: Pressure = Force/Area.
The force on the big piston is 15,000 N, and its area is 10 m². Using the pressure equation, we can find the pressure: Pressure = 15,000 N / 10 m² = 1,500 N/m².
Now, we can substitute the pressure back into our first equation: Area = 1,100 N / 1,500 N/m².
Drumroll please... After canceling out the units, we get the area of the smaller piston equal to 0.733 m². Voila!
So, the area of the smaller piston would be approximately 0.733 square meters. I hope that helps, and remember, always clown around with math!
To determine the area of the smaller piston, we can use the hydraulic lift equation:
Force on the larger piston / Area of the larger piston = Force on the smaller piston / Area of the smaller piston
Given:
Force on the larger piston (F1) = 1,100 N
Area of the larger piston (A1) = 10 m²
Force on the smaller piston (F2) = 15,000 N
Area of the smaller piston (A2) = ?
Let's plug in the values into the formula and solve for A2:
1,100 N / 10 m² = 15,000 N / A2
To find A2, we need to cross multiply:
1,100 N * A2 = 10 m² * 15,000 N
Now we can solve for A2:
A2 = (10 m² * 15,000 N) / 1,100 N
A2 = 150,000 m²⋅N / 1,100 N
A2 = 136.36 m² (rounded to two decimal places)
Therefore, the area of the smaller piston is approximately 136.36 m².
To find the area of the smaller piston, we can use the principle of Pascal's law, which states that pressure applied to an enclosed fluid is transmitted equally in all directions. In this scenario, the pressure exerted on the smaller piston will be equal to the pressure exerted on the car.
First, let's find the pressure applied to the car:
Pressure = Force / Area
The force applied to the car is given as 15,000 N, and the area of the lift platform is 10 m^2. Substituting these values into the equation:
Pressure on the car = 15,000 N / 10 m^2
Next, we equate the pressure applied to the smaller piston to the pressure on the car:
Pressure on the smaller piston = Pressure on the car
The force applied to the smaller piston is given as 1,100 N. Let's denote the area of the smaller piston as 'A'. Substituting these values into the equation:
Pressure on the smaller piston = 1,100 N / A
Now we can set up an equation by equating the two pressures:
Pressure on the smaller piston = Pressure on the car
1,100 N / A = 15,000 N / 10 m^2
To find the area of the smaller piston (A), we can solve for it:
A = (1,100 N * 10 m^2) / 15,000 N
A = 1,1000,000 N m^2 / 15,000 N
A = 73.33 m^2
Therefore, the area of the smaller piston is approximately 73.33 m^2.