For the car lift shown in the figure below, the pistons on the left and right have areas 25 cm2
and 750 cm2
respectively. The car and the right piston have a total weight of 15,000 N.
(a) What force must be applied on the left piston (if it has negligible weight)?
I know the pressure on both pistons must be the same, but I am finding it a bit challenging to find the weight of the car and the right piston separately.
total piston area = 775 cm^2
so
775 P = 15000
P = 15000 / 775
so
left force = 25 P = 15000 (25/775) Newtons
To find the force that must be applied on the left piston, we can use Pascal's law, which states that the pressure exerted on a fluid is transmitted equally in all directions.
The formula we can use is:
Pressure = Force / Area
First, let's calculate the pressure exerted on the right piston:
Pressure_right = Force_right / Area_right
Given that the area of the right piston is 750 cm², which is equivalent to 0.075 m², and the total weight on the right piston is 15,000 N, we can calculate the force:
Force_right = Pressure_right * Area_right
Force_right = (15,000 N) / (0.075 m²)
Force_right = 200,000 N
Now, since the left and right pistons are connected by a common fluid, the pressure exerted on the right piston will be transmitted to the left piston. Therefore, the pressure on the left piston will also be 200,000 N/m².
We can now calculate the force required on the left piston:
Force_left = Pressure_left * Area_left
Given that the area of the left piston is 25 cm², which is equivalent to 0.0025 m², we can calculate the force:
Force_left = (200,000 N/m²) * (0.0025 m²)
Force_left = 500 N
Therefore, the force that must be applied on the left piston is 500 N.
To solve this problem, we can apply Pascal's principle, which states that when a pressure is applied to an enclosed fluid, the pressure is transmitted undiminished to all portions of the fluid and the walls of its container.
In this case, the pressure on the left piston will be equal to the pressure on the right piston. We can use the formula:
Pressure = Force / Area
Let's calculate the pressure on the right piston first. The weight of the car and the right piston is given as 15,000 N. The area of the right piston is 750 cm^2. To calculate the pressure, we divide the force by the area:
Pressure on right piston = 15,000 N / 750 cm^2
Now we can use Pascal's principle to find the force on the left piston. The pressure on the left piston will be the same as the pressure on the right piston. The area of the left piston is given as 25 cm^2. We can rearrange the formula:
Force on left piston = Pressure x Area
Substituting the values we have:
Force on left piston = (15,000 N / 750 cm^2) x 25 cm^2
To calculate the answer, we simplify the expression and calculate the force on the left piston.