Question

На малый поршень гидравлического пресса действует сила 500 Ньютонов. При этом малый поршень опускается на 13 см а большой поднимается на 6 определить силу действующую на большой поршень гидравлического пресса

Answer 1

дано:

F1=500 Н

h1=13 см

h2=6 см

найти:

F2- ?

решение:

F1*h1=F2*h2

F2=F1*h1/h2=500*2,1≈1050н

ответ: 1050н

Answer 2

Calculating the Force on the Large Piston of a Hydraulic Press

To calculate the force acting on the large piston of a hydraulic press, we can use the principle of Pascal's law, which states that the pressure applied to a fluid is transmitted undiminished throughout the fluid in all directions.

Given: - Force on the small piston (F1) = 500 Newtons - Distance the small piston descends (d1) = 13 cm - Distance the large piston ascends (d2) = 6 cm

Calculating the Force on the Large Piston

We can use the formula:

F1 / A1 = F2 / A2

Where: - F1 = Force on the small piston - A1 = Area of the small piston - F2 = Force on the large piston - A2 = Area of the large piston

Calculating the Area of the Pistons

The area of the piston can be calculated using the formula:

A = π * r^2

Where: - A = Area of the piston - π is a constant approximately equal to 3.14159 - r = radius of the piston

Calculating the Force on the Large Piston

First, let's calculate the area of the small piston (A1) and the large piston (A2) using the given information.

The radius of the small piston (r1) can be calculated using the formula:

r1 = d1 / 2

The radius of the large piston (r2) can be calculated using the formula:

r2 = d2 / 2

Then, we can use the calculated areas to find the force on the large piston (F2) using the formula:

F2 = (F1 * A2) / A1

Calculation Steps

1. Calculate the radius of the small piston (r1): - r1 = d1 / 2 - r1 = 13 cm / 2 - r1 = 6.5 cm

2. Calculate the area of the small piston (A1): - A1 = π * r1^2 - A1 = 3.14159 * (6.5 cm)^2 - A1 ≈ 132.732 cm^2

3. Calculate the radius of the large piston (r2): - r2 = d2 / 2 - r2 = 6 cm / 2 - r2 = 3 cm

4. Calculate the area of the large piston (A2): - A2 = π * r2^2 - A2 = 3.14159 * (3 cm)^2 - A2 ≈ 28.274 cm^2

5. Calculate the force on the large piston (F2): - F2 = (F1 * A2) / A1 - F2 = (500 N * 28.274 cm^2) / 132.732 cm^2 - F2 ≈ 106.63 N

Result

The force acting on the large piston of the hydraulic press is approximately 106.63 Newtons.