Question

Балка массой 1200 кг и длиной 3 м лежит на опо­рах, равноудаленных от ее концов. Расстояние между опорами 2 м. Какую силу, перпендикулярную балке и направленную вертикально вверх, нужно прило­жить, чтобы приподнять балку за один из ее краев?

Answer 1

Расстояние от короткой части балки до опоры = (3-2)/2=0,5 метра
Масса этой части уравновешивает такую же часть с другой стороны опоры
т. е. 1 метр балки уравновешен и не требует силы для сдвига
остается еще 2/3 балки, а это 800 кг
центр масс этих 800 кг находится на расстоянии (3-1)/2+0,5=1,5 метра от опоры
а расстояние от точки приложения силы до опоры = 2,5 метра
по правилу моментов получаем
сила = 10*800*1,5/2,5=4800 Н = 4,8 кH

Answer 2

Calculation of the Force Required to Lift the Beam

To calculate the force required to lift the beam, we can use the principle of moments. The moment of a force is the product of the force and the perpendicular distance from the point of rotation (in this case, the support) to the line of action of the force.

In this scenario, the beam is supported at two equidistant points, each 1 meter away from the center of the beam. The total length of the beam is 3 meters. Therefore, the distance from each support to the end of the beam is 1.5 meters.

To lift the beam at one of its ends, we need to apply a force that creates a moment equal to the weight of the beam multiplied by the distance from the support to the end of the beam.

Given that the beam has a mass of 1200 kg, we can calculate its weight using the formula:

Weight = mass x gravitational acceleration

The gravitational acceleration is approximately 9.8 m/s^2.

Let's calculate the weight of the beam:

Weight = 1200 kg x 9.8 m/s^2 = 11760 N

Now, let's calculate the moment created by the weight of the beam at one of its ends:

Moment = Weight x Distance

The distance from the support to the end of the beam is 1.5 meters.

Moment = 11760 N x 1.5 m = 17640 Nm

Therefore, to lift the beam at one of its ends, we need to apply a force that creates a moment of 17640 Nm.

Please note that this calculation assumes that the beam is in equilibrium and neglects any other external forces acting on the beam.