Question

Малый поршень гидравлического пресса опустился на 25 см под действием силы 650 Н. К площадь малого поршня равна 3 см², а площадь большего 15 см². Какая сила приложена на большой поршень и на какую высоту он переместился?

Answer 1

Ответ: 3250Н; 5см

Объяснение:

Дано:

h1=25см

F1=650Н

S1=3cм²

S2=15cм²

--------------

F2-?; h2-?

F1/S1=F2/S2

F2=F1*S2/S1=650*15/3=3250Н

V1=V2

S1*h1=S2*h2

h2=S1*h1/S2=3*25/15=5cм

Answer 2

Calculation of Force on the Large Piston:

To calculate the force applied to the large piston, we can use Pascal's law, which states that the pressure exerted on a fluid in a closed system is transmitted equally in all directions. In this case, the pressure exerted on the small piston is transmitted to the large piston.

The formula to calculate the force on the large piston is:

Force on Large Piston = Force on Small Piston * (Area of Large Piston / Area of Small Piston)

Given: - Force on Small Piston = 650 N - Area of Small Piston = 3 cm² - Area of Large Piston = 15 cm²

Converting the areas to square meters: - Area of Small Piston = 3 cm² = 3 * 10^(-4) m² - Area of Large Piston = 15 cm² = 15 * 10^(-4) m²

Now we can substitute the values into the formula:

Force on Large Piston = 650 N * (15 * 10^(-4) m² / 3 * 10^(-4) m²)

Simplifying the equation:

Force on Large Piston = 650 N * 5

Force on Large Piston = 3250 N

Therefore, the force applied to the large piston is 3250 N.

Calculation of Height Displacement of the Large Piston:

To calculate the height displacement of the large piston, we can use the principle of fluid displacement. The volume of fluid displaced by the small piston is equal to the volume of fluid displaced by the large piston.

The formula to calculate the height displacement of the large piston is:

Height Displacement of Large Piston = (Volume of Fluid Displaced by Small Piston) / (Area of Large Piston)

Given: - Height Displacement of Small Piston = 25 cm = 0.25 m - Area of Large Piston = 15 cm² = 15 * 10^(-4) m²

Converting the height displacement to cubic meters: - Height Displacement of Small Piston = 0.25 m

Now we can substitute the values into the formula:

Height Displacement of Large Piston = (0.25 m) / (15 * 10^(-4) m²)

Simplifying the equation:

Height Displacement of Large Piston = 0.25 m / 15 * 10^(-4) m²

Height Displacement of Large Piston = 0.25 m / 0.0015 m²

Height Displacement of Large Piston = 0.1667 m

Therefore, the large piston has been displaced by a height of 0.1667 m.

To summarize: - The force applied to the large piston is 3250 N. - The large piston has been displaced by a height of 0.1667 m.