Question

Труба массой 70 кг лежит на двух горизонтальных опорах. Длина трубы 5 м, одна опора находится у конца трубы, вторая на расстоянии 2 м от второго конца трубы. Определите силы реакции опор.

Answer 1

70 кг : 5 м * 2 м = 28 м

Answer 2

Problem Analysis

We have a pipe with a mass of 70 kg lying on two horizontal supports. The length of the pipe is 5 m, with one support located at the end of the pipe and the other support located 2 m away from the other end. We need to determine the reaction forces at the supports.

Solution

To solve this problem, we can consider the equilibrium of forces acting on the pipe. Since the pipe is in equilibrium, the sum of the forces in the vertical direction and the sum of the moments about any point must be equal to zero.

Let's assume that the reaction forces at the supports are R1 and R2, with R1 being the reaction force at the end of the pipe and R2 being the reaction force at a distance of 2 m from the other end.

Equilibrium in the Vertical Direction

In the vertical direction, the sum of the forces must be zero. Since the pipe is at rest, the sum of the vertical forces is equal to zero. We can write the equation as:

R1 + R2 - mg = 0,

where m is the mass of the pipe and g is the acceleration due to gravity.

Equilibrium in the Moments

To analyze the moments, we need to choose a point about which we will calculate the moments. Let's choose the point where the second support is located (2 m from the other end of the pipe).

The sum of the moments about this point must be zero. We can write the equation as:

R1 * 5 - mg * (5/2) + R2 * 0 = 0.

Simplifying this equation, we get:

5R1 - (5/2)mg = 0.

Now we have two equations with two unknowns (R1 and R2). We can solve these equations simultaneously to find the values of R1 and R2.

Solving the Equations

Let's solve the equations using the given values and calculate the reaction forces at the supports.

From the equation R1 + R2 - mg = 0, we can rearrange it to solve for R1:

R1 = mg - R2.

Substituting this value of R1 into the equation 5R1 - (5/2)mg = 0, we get:

5(mg - R2) - (5/2)mg = 0.

Simplifying this equation, we get:

5mg - 5R2 - (5/2)mg = 0.

Combining like terms, we have:

(5/2)mg - 5R2 = 0.

Now we can solve this equation for R2:

R2 = (5/2)mg / 5.

Substituting the given values of m = 70 kg and g = 9.8 m/s^2, we can calculate R2:

R2 = (5/2) * 70 * 9.8 / 5.

Calculating this expression, we find:

R2 = 686 N.

Finally, we can substitute the value of R2 into the equation R1 = mg - R2 to find R1:

R1 = 70 * 9.8 - 686.

Calculating this expression, we find:

R1 = 0 N.

Answer

The reaction force at the support located at the end of the pipe is 0 N, and the reaction force at the support located 2 m from the other end of the pipe is 686 N.