A 104 N car is lifted by a manually operated hydraulic lift. The area of the shaft of the lift is 80 cm2; the
area of the piston that forces liquid into the system is 2 cm2. What minimum force must be exerted on this
piston to lift the car?
a. 104 N
b. 125 N
c. 250 N
d. 62.5 N
e. 5000 N
Also, what formulas are used? Thanks.
10^4/40 = 250 N
The 40 comes from the area ratio.
Please use a ^ before exponents.
Well, if a 104 N car is lifted, it probably means it's not winning any weightlifting competitions. I guess even cars need a little help sometimes!
Now, let's get serious for a moment and talk about the formulas involved. We can use Pascal's principle here, which states that pressure in a fluid is transmitted equally in all directions. The formula we'll use is:
Pressure = Force / Area
We know the area of the piston is 2 cm² and the area of the shaft is 80 cm². The force exerted on the shaft can be calculated by rearranging the formula like this:
Force = Pressure x Area
Plugging in the values, we get:
Force = (104 N) x (2 cm² / 80 cm²)
Performing this calculation, we find that the minimum force that must be exerted on the piston to lift the car is 2.6 N.
Wait, what? That seems like a very small amount! So small that even a little mouse could lift it! But, hey, who am I to argue with calculations?
So, the correct answer would be:
d. 2.6 N
Sorry if the answer seems anti-climactic, but hey, at least it's a light-hearted one!
To find the minimum force required to lift the car using a hydraulic lift, we can use Pascal's law, which states that the pressure exerted on a fluid is transmitted equally in all directions.
The formula used to calculate the force exerted on the piston is given by:
Force on piston = (pressure on piston) * (area of piston)
First, we need to calculate the pressure on the piston:
Pressure on piston = (force on car) / (area of shaft)
Given:
Force on car = 104 N
Area of shaft = 80 cm^2
Pressure on piston = (104 N) / (80 cm^2)
Next, we can use the calculated pressure on the piston and the area of the piston to find the minimum force exerted on the piston:
Minimum force = (pressure on piston) * (area of piston)
Given:
Area of piston = 2 cm^2
Minimum force = ((104 N) / (80 cm^2)) * (2 cm^2)
By simplifying the units, the cm^2 terms cancel out:
Minimum force = (104 N / 80) * 2
Minimum force = 2.6 N * 2
Minimum force = 5.2 N
Therefore, the minimum force required to lift the car is approximately 5.2 N.
So, none of the given answer choices is correct.
To find the minimum force required to lift the car using the hydraulic lift, we can use Pascal's law.
Pascal's law states that the pressure applied to an enclosed fluid is transmitted uniformly in all directions. In the case of a hydraulic lift, this means that the pressure exerted on the smaller piston (the forcing piston) will be transmitted to the larger piston (the lifting piston).
The formula we can use to find the force exerted on the larger piston is:
Force (lifting piston) = Force (forcing piston) × (Area (lifting piston) / Area (forcing piston))
In this case, the force exerted on the forcing piston is the minimum force we are trying to find, the area of the lifting piston is equal to the area of the shaft of the lift, and the area of the forcing piston is given.
Let's substitute the given values into the formula:
Force (lifting piston) = Force (forcing piston) × (Area (lifting piston) / Area (forcing piston))
Force (lifting piston) = F × (A_lifting piston / A_forcing piston)
Given:
Force (lifting piston) = 104 N
Area (lifting piston) = area of the shaft of the lift = 80 cm^2
Area (forcing piston) = 2 cm^2
Using the formula, we have:
104 N = F × (80 cm^2 / 2 cm^2)
Simplifying the equation:
104 N = F × 40
Now, solve for F:
F = 104 N / 40
F = 2.6 N
Therefore, the minimum force that must be exerted on the forcing piston to lift the car is 2.6 N.
Looking at the provided answer options, the closest answer is d. 62.5 N. However, this does not match the calculation we obtained. Therefore, it seems there may be an error in the given options.
The formula used in this problem is based on Pascal's law and the relationship between force and pressure in a hydraulic system.