Question

25 БАЛЛОВ !!! Из листа металла вырезан равнобедренный треугольник( |AB|=|AC|). Если установить его горизонтально на трёх тонких вертикальных опорах, поддерживающих его углы в точках A, B и C (на рисунке показан вид сверху), то окажется, что на опору в точке А действует сила FA=20.4 H. Определите 1. Силу, которая действует на опору в точке B (FB). 2. Массу треугольника (M). 3. Треугольник уравновесили на двух опорах в точках D ( на середине стороны BC) и в точке N (на середине высоты АD). Определите силу давления на опору в точке N (FN). 4. Определите силу давления на опору в точке D (FD). Ответы вводите с точностью не хуже, чем до одного процента. Ускорение свободного падения примите равным 9,8 м/c2

Answer 1

Ответ:1) 12

2)2,44

3)-

4)6

Объяснение:

Answer 2

Given Information

- A triangular piece of metal is cut from a sheet of metal, with sides |AB| = |AC|. - The triangle is placed horizontally on three thin vertical supports at points A, B, and C. - The force FA = 20.4 H acts on the support at point A. - The triangle is balanced on two supports at points D (the midpoint of side BC) and N (the midpoint of height AD).

Solution

To solve this problem, we need to analyze the forces acting on the triangle and use the principles of equilibrium.

1. Force on Support B (FB)

To determine the force on support B (FB), we can use the principle of moments. Since the triangle is in equilibrium, the sum of the moments about any point must be zero.

Let's consider the moments about point A. The force FA acts vertically downward at point A, and the force FB acts vertically upward at point B. The distance between points A and B is half the base of the triangle, which we'll call 'b'. The moment equation is:

FA * b = FB * b

Since FA = 20.4 H, we can solve for FB:

FB = FA = 20.4 H

Therefore, the force on support B (FB) is 20.4 H.

2. Mass of the Triangle (M)

To determine the mass of the triangle (M), we can use the relationship between force, mass, and acceleration due to gravity. The force acting on the triangle is the weight, which is equal to the mass multiplied by the acceleration due to gravity (F = m * g).

Let's consider the forces acting on the triangle. The force FA acts vertically downward at point A, and the force FB acts vertically upward at point B. The net force in the vertical direction is zero since the triangle is in equilibrium. Therefore, the weight of the triangle is equal to the sum of the forces FA and FB:

FA + FB = M * g

Substituting the values, we have:

20.4 H + 20.4 H = M * 9.8 m/s^2

Simplifying the equation, we find:

M = (20.4 H + 20.4 H) / 9.8 m/s^2

Calculating the value, we get:

M ≈ 4.16 kg

Therefore, the mass of the triangle (M) is approximately 4.16 kg.

3. Force at Support N (FN)

To determine the force at support N (FN), we can again use the principle of moments. Since the triangle is balanced on supports D and N, the sum of the moments about any point must be zero.

Let's consider the moments about point D. The force FA acts vertically downward at point A, and the force FN acts vertically upward at point N. The distance between points A and N is half the height of the triangle, which we'll call 'h'. The moment equation is:

FA * h = FN * (h/2)

Since FA = 20.4 H, we can solve for FN:

FN = (FA * h) / (h/2)

Substituting the value of h, we have:

FN = (20.4 H * h) / (h/2)

Calculating the value, we get:

FN = 40.8 H

Therefore, the force at support N (FN) is 40.8 H.

4. Force at Support D (FD)

To determine the force at support D (FD), we can use the principle of moments. Since the triangle is balanced on supports D and N, the sum of the moments about any point must be zero.

Let's consider the moments about point N. The force FN acts vertically upward at point N, and the force FD acts vertically downward at point D. The distance between points N and D is half the base of the triangle, which we'll call 'b'. The moment equation is:

FN * (b/2) = FD * b

Since FN = 40.8 H, we can solve for FD:

FD = (FN * (b/2)) / b

Simplifying the equation, we find:

FD = FN / 2

Substituting the value of FN, we have:

FD = 40.8 H / 2

Calculating the value, we get:

FD = 20.4 H

Therefore, the force at support D (FD) is 20.4 H.

Summary of Results:

1. Force on support B (FB): 20.4 H 2. Mass of the triangle (M): 4.16 kg 3. Force at support N (FN): 40.8 H 4. Force at support D (FD): 20.4 H

Please note that the values provided are approximate, as they are calculated based on the given information and assumptions.