A hydraulic lift office chair has its seat attached to a piston with an area of 11.4 cm2. The chair is raised by exerting force on another piston, with an area of 4.2 cm2. If a person sitting on the chair exerts a downward force of 220 N, what force needs to be exerted on the small piston to lift the seat?
i need help
Well, isn't this a piston predicament we have here! Let's calculate the force needed to lift the seat of this hydraulic lift office chair.
First, let's find the pressure exerted on the larger piston. Pressure is equal to the force divided by the area. So, the pressure on the larger piston is 220 N divided by 11.4 cm².
Now, to lift the seat, we need to find the force that needs to be exerted on the smaller piston. We can calculate this by multiplying the pressure on the larger piston by the area of the smaller piston.
But before we proceed, let me tell you a little joke to keep things light: Why don't scientists trust atoms? Because they make up everything!
Now, back to our calculation. We multiply the pressure (which we calculated earlier) by the area of the smaller piston (4.2 cm²) to find the force needed on the smaller piston. Ta-da!
I hope this helps, and remember, laughter is the best hydraulic lift for the soul!
To find the force needed to lift the seat, we can use the principle of Pascal's law, which states that the pressure applied to a fluid in a closed container is transmitted equally in all directions.
Step 1: Calculate the pressure exerted by the person on the seat.
Pressure = Force / Area
The area of the seat piston is 11.4 cm².
The force applied by the person is 220 N.
Pressure = 220 N / 11.4 cm²
Step 2: Calculate the pressure needed to lift the seat.
According to Pascal's law, the pressure exerted by the person is transmitted equally to the small piston.
Pressure = Force / Area
The area of the small piston is 4.2 cm².
Pressure = Force / 4.2 cm²
Step 3: Equate the pressures between the two pistons.
Since the pressure exerted is the same on both pistons:
220 N / 11.4 cm² = Force / 4.2 cm²
Step 4: Solve for the force needed to lift the seat.
Cross multiply and solve for Force:
(220 N)(4.2 cm²) = (11.4 cm²)(Force)
Force = (220 N)(4.2 cm²) / 11.4 cm²
Therefore, the force that needs to be exerted on the small piston to lift the seat is approximately 81.93 N.
To find the force exerted on the small piston to lift the seat, we can use Pascal's law, which states that the pressure exerted at any point in an enclosed fluid is transmitted equally in all directions.
First, let's find the pressure exerted by the person sitting on the chair. Pressure is defined as force divided by area:
Pressure = Force / Area
The area of the seat's piston is given as 11.4 cm², so the pressure exerted by the person is:
Pressure = 220 N / 11.4 cm²
Next, we can use Pascal's law to find the force needed to lift the seat. According to Pascal's law, the pressure exerted on the small piston will be the same as the pressure exerted by the person sitting on the seat.
The area of the small piston is given as 4.2 cm², so the force needed to lift the seat can be calculated as:
Force = Pressure x Area
Force = (220 N / 11.4 cm²) x 4.2 cm²
Simplifying the equation:
Force = 220 N x (4.2 cm² / 11.4 cm²)
Force = 220 N x 0.3684
Finally, calculating the force:
Force = 81.048 N
Therefore, a force of approximately 81.048 N needs to be exerted on the small piston to lift the seat.