A problem about mechanics, moments, balance, calculations, mathematics.

Analysis: If an object with a mass of m kilograms is added to the thin end of object b, the mass of a and b multiplied by the length can be equal.

At this time, the center of gravity of object b is located at a distance of l from the thick end

Then there is 35*

For object b, the equilibrium condition is 30*(l *4 l) (the center of gravity of the later b object is the axis).

The later B object refers to the composition of the original B object with the added mass m of the object.

From the above two types of joint, after finishing to obtain 8 * m 2 233 * m 210 0

Solve m 7 8 kg, (substituting the value of m into one of the equations to get l m).

That is, an object with a mass of kilograms should be added to the thin end of the original B object in order to make the product of the mass and length of a and b equal.

The so-called "mass multiplied by length" in the problem is actually the (gravitational) moment of the object to the left end, and only the mass of the right end of object B can be satisfied.

The center of gravity can be understood as the center of mass. Therefore, the value of "mass multiplied by length" in the original question can be understood as the moment of mass on the left end.

a: m=b rod at the right end plus a mass of the mass of p, p to the left end of the moment p 4ab mass multiplied by the length of the value is equal, so.

b: p 4 to get p kg

Hope it helps! Hope.

Summary. If the algebraic sum of the resultant moment of the force experienced by an object is 0, then it is said that the object is in a state of moment equilibrium, the length of the power arm * the length of the power arm = the length of the resistance arm * the resistance arm is the state of moment equilibrium, and this formula can be calculated by applying the principle of balance, rocker, lever and so on.

The title is pro.

See. Question No.

Two questions. A question can only be counted as one question at a time.

Good. That first question.

What about people. 5 sin20° 400=g 400 solution g=5sin20° If the algebraic sum of the net force of the force on an object is 0, then it is said that the object is in a state of moment equilibrium, the length of the power arm * the power arm = the length of the resistance arm * the width of the resistance arm * the resistance at this time is the state of moment equilibrium.

According to the meaning of the title, ab l, bc l 3, the weight of the plate is g

Analysis: The force on the plate is analyzed, there is gravity G (at the midpoint of the plate), the support force Fa at A (vertically upward), the supporting force Fb (vertically upward) at B, and the supporting force Fc (vertically upward) at C.

Since the plate is stationary (equilibrium state), there is a resultant force of 0 and a resultant moment of 0.

g fa fb fc is obtained from a resultant force of 0

It is obtained by the resultant moment of 0.

G*(L2) FC* [L(L3)]FB* L (with A-end as axis).

Fa*LG* (L2) FC* (L3) (with B-terminus as axis).

Fa* [l ( l 3 ) g * [l 2) (l 3 )] fb*(l 3) (axis at point c).

Note: There are four equations above, only three of which are independent, and the fourth equation can be derived from three of them.

3.As shown in Figure 3, when the wooden board is fixed and hinged on three fulcrums, it is a superstatically determined structure, and the two-span continuous beam, because the stiffness of the beam is the same, the bending moment of the B support can be solved by using the three-bending moment equation, and then the support reaction force is solved. Due to the asymmetry of the load, there is no ready-made ** to check.

This solution is not unique, the listed system of equations is not ranked, and a solution to a linear equation is obtained.

Positive and negative are relative, you can choose to be positive clockwise and negative counterclockwise, or you can choose negative clockwise and positive counterclockwise, as long as all the moments in a moment balance equation are the same standard selection symbol.

Taking the moment balance equation in the figure as an example, if the clockwise is negative and counterclockwise is positive, then the moment of fb*4a is counterclockwise and positive, and the moments of p*2a, 2aq*a and m are clockwise and negative.

Let the length of the timber be L, and the distance from the center of gravity of the timber to the two ends is L1 and L2 respectively, L=L1+L2

gl1=650*l

gl2=480*l

Add the two formulas. g(l1+l2)=(650+480)lg=650+480=1130n

Yes. Take the point in the lower right corner as the fulcrum, and the height and width of the object as the force arm. Note that the length of the arm changes as the center of gravity of the object tilts.

The critical force f that rotates the object around point b should be satisfied on the following conditions: f to point b moment = gravitational force to point b moment, i.e.: = , i.e.: f = gml (2h), .,

If the object does not move, the maximum static friction is >f, i.e. ugm > f,..Substitute : ugm > gml (2h), i.e., static coefficient of friction u >l (2h).

Make the hinge, the thin rod, and the guessing ball watch cover as a whole, and compare the balance equation of the point O column moment and the balance equation of the force: rf-mgl+nl=0, f=n, and get m=f(r +l) gl, when pushing to the left, let the thrust force be f, and the elastic force of the board is n, then mgl+fr=nr, f=n, and bring in the solvable f=f(r +l) (r-r).