A hydraulic jack has an input piston that is 1.2 cm2 in area and an output piston that is 144 cm2 in area. How much input or effort force in newtons is needed to lift a car that weighs 25,000 newtons?
mechanical advantage = 144/1.2
so
25,000 (1.2 / 144) = 208 N
Well, well, well, looks like Mr. Hydraulic Jack has a lot of work to do! Let's do some calculations and put those muscles to work!
Now, we know that the input piston area is 1.2 cm², and the output piston area is 144 cm². So, we can calculate the force multiplication factor by dividing the output area by the input area. Mathematically, it's like asking "how many times bigger is the output area than the input area." Bear with me, here...
So, the force multiplication factor would be 144 cm² divided by 1.2 cm², which results in a factor of 120. Since we need to lift a car that weighs 25,000 Newtons, we just need to divide that weight by the force multiplication factor (120).
Grabbing my handy-dandy calculator, I'll do some more math magic...
25,000 Newtons divided by 120 gives us an input force of approximately 208.33 Newtons.
So, my dear friend, to lift that massive ride, you'll need an input force of approximately 208.33 Newtons!
Now, please, don't ask me to help you change a tire. I'm much better at cracking jokes than carrying cars!
To solve this problem, we can use the principle of Pascal's law, which states that the pressure exerted on a confined fluid is transmitted uniformly in all directions. The formula we can use is:
Effort force / Input force = Output area / Input area
Let's calculate the effort force needed to lift the car:
Given:
Input piston area = 1.2 cm^2
Output piston area = 144 cm^2
Weight of the car = 25,000 newtons
We can start by finding the input force:
Input force = input area × pressure
The pressure exerted on the fluid is the same throughout the hydraulic jack. So, we can calculate the input force using the formula:
Input force = input area × pressure
The pressure can be calculated by dividing the weight of the car by the output area:
Pressure = weight of the car / output area
Input force = input area × (weight of the car / output area)
Plugging in the values:
Input force = 1.2 cm^2 × (25,000 newtons / 144 cm^2)
Simplifying:
Input force = 1.2 cm^2 × (173.61 newtons/cm^2)
Input force = 208.33 newtons
Therefore, the input or effort force needed to lift the car is approximately 208.33 newtons.
To calculate the effort force required to lift the car using a hydraulic jack, we can use the principle known as Pascal's Law. According to Pascal's Law, pressure within an enclosed fluid is transmitted equally in all directions.
Here are the steps to calculate the effort force:
1. Determine the pressure exerted on the larger output piston:
Pressure = Force / Area
Since the area of the output piston is 144 cm² and the weight of the car is 25,000 N:
Pressure = 25,000 N / 144 cm²
2. Calculate the pressure exerted on the smaller input piston:
Since the pressure is transmitted equally in all directions, the pressure will be the same on both pistons.
Pressure (input piston) = Pressure (output piston)
3. Now we can find the effort force required to lift the car:
Effort Force = Pressure (input piston) x Area (input piston)
Since the area of the input piston is 1.2 cm²:
Effort Force = Pressure (input piston) x 1.2 cm²
To calculate the effort force in newtons, we need to convert the area and pressure to SI units (meters and pascals/meters²) since Newton is a unit in the SI system.
Let's perform the conversions and calculate the effort force required.