"Provide calculations to show the force and pressure required to lift the weight of each draw bridge (or the load that is on the bridge)"
A syringe is used as the hydraulic system which is pushed (via the plunger) to draw up the bascule and pulled back to draw the bascule back to its original position.
The area of the syringe used to push liquid (or air), in this case, is 5.65cm^2, and the area of the bascule which the syringe needs to push liquid to, to lift, is 238cm^2 (17cm by 14cm by 0.12cm).
So we have:
Area of bascules: 238cm^2 (unfortunately, there is no weight provided for the bascules)
Area of plunger (back of syringe which can pull and push): 5.65cm^2
Weight of the entire bridge (including towers): 200g
Weight of the load that the bridge is able to carry: 2000g (per bascule) * 2 = 4000g altogether
Speed of gravity/earth's downward acceleration: 9.8m/s^2
Unfortunately, we are not also given the mass of the object. Is there any way to calculate the force and pressure needed to lift 4000g of weight with this information? I'm also aware of the Pascal's Principle, but am not sure how to use it without the force. Any help is appreciated, thanks.
To calculate the force and pressure required to lift the weight on the drawbridge, we can use Pascal's Principle, which states that the pressure applied to an enclosed fluid is transmitted equally in all directions.
Here's a step-by-step calculation:
1. Convert the weight of the load that the bridge can carry to kilograms:
Weight = 4000g = 4 kg
2. Calculate the force needed to lift this weight:
Force = Mass x Acceleration due to gravity
Force = 4 kg x 9.8 m/s^2
Force = 39.2 N
3. Determine the ratio of the areas of the two surfaces (bascule and plunger):
Area ratio = Area of bascule / Area of plunger
Area ratio = 238 cm^2 / 5.65 cm^2
Area ratio = 42.12
4. Utilize Pascal's Principle: The pressure applied to an enclosed fluid is transmitted equally.
Therefore, the force applied to the plunger will be multiplied by the area ratio to calculate the force on the bascule.
Force on the bascule = Force on the plunger x Area ratio
Force on the bascule = 39.2 N x 42.12
Force on the bascule = 1650.14 N
5. Finally, compute the pressure required to lift the load:
Pressure = Force on the bascule / Area of bascule
Pressure = 1650.14 N / 238 cm^2
Pressure ≈ 6.93 N/cm^2
Therefore, to lift the weight of 4000g (4 kg), a force of approximately 39.2 N is required, which translates to a pressure of approximately 6.93 N/cm^2 on the bascule.
To calculate the force and pressure required to lift the weight, we can use the concept of Pascal's Principle. According to Pascal's Principle, pressure applied to an enclosed fluid is transmitted equally in all directions.
First, let's convert the weights from grams to kilograms for consistency. The weight of the entire bridge is 0.2 kg, and the load the bridge can carry is 4 kg (4000 g).
Since we are given the area of the syringe's plunger (5.65 cm^2) and the area of the bascule (238 cm^2), we can determine the force required to lift the weight using the equation:
Force = Pressure * Area
However, we don't know the pressure or force directly. We can calculate the force needed by considering the weight of the load. The force can be determined using the equation:
Force = Mass * Acceleration
In this case, the mass is the weight of the load, which is 4 kg, and the acceleration due to gravity is 9.8 m/s^2. So the force required is:
Force = 4 kg * 9.8 m/s^2 = 39.2 N
Now, we can use Pascal's Principle to calculate the pressure required. Since the pressure is transmitted equally in all directions, the pressure applied to the syringe will be the same as the pressure needed to lift the load.
Pressure = Force / Area
Pressure = 39.2 N / 238 cm^2
We need to convert the area from square centimeters to square meters to maintain consistency with the force in Newtons.
1 cm^2 is equal to 0.0001 m^2.
Pressure = 39.2 N / (238 cm^2 * 0.0001 m^2/cm^2)
Pressure = 0.1647 N/m^2 or 0.1647 Pa (Pascal)
Therefore, the force required to lift the weight of the load is 39.2 Newtons, and the pressure required is approximately 0.1647 Pascal.