Question

Объясните просто как надо решать, принцип решения, решу сама.Если груз лежит на левой чашке неравноплечих весов, его уравновешивают гири массой 9 кг на правой чашке, если же груз положить на правую чашку, его уравновешивают гири массой 25 кг на левой чашке. Какова масса груза? На сколько одно плечо рычага длиннее другого если общая их длина равно 60 см?

Answer 1

Если груз лежит на левой чашке неравноплечих весов, его уравновешивают гири массой 9 кг на правой чашке, если же груз положить на правую чашку, его уравновешивают гири массой 25 кг на левой чашке. Какова масса груза? На сколько одно плечо рычага длиннее другого если общая их длина равно 60 см?
Дано m1=9 кг   m2=25 кг    L=60 см                         M- ?  ΔL - ?

из условия рановесия
m1*g*L1=M*g*L2
M*g*L1=m2*g*L2
m1/M=M/m2
M=√m1*m2=√9*25=15 кг

2)  m1*L1=M*(L-L1)
9*L1=15*(0,6-L1)
3*L1=3-5*L1
8*L1=3
L1=0,373 м=37,5 cм
L2=60-37,5=22,5
ΔL=15 см

Answer 2

Problem Analysis

To solve this problem, we need to determine the mass of the load and the difference in length between the two arms of the lever. We are given that when the load is placed on the left side of the lever, it is balanced by a weight of 9 kg on the right side. When the load is placed on the right side, it is balanced by a weight of 25 kg on the left side. We are also given that the total length of the two arms of the lever is 60 cm.

Solution

Let's assume the mass of the load is x kg and the length of one arm of the lever is y cm. Since the total length of the two arms is 60 cm, the length of the other arm can be expressed as (60 - y) cm.

When the load is placed on the left side of the lever, it is balanced by a weight of 9 kg on the right side. This can be represented by the equation:

x * y = 9 * (60 - y)

When the load is placed on the right side of the lever, it is balanced by a weight of 25 kg on the left side. This can be represented by the equation:

x * (60 - y) = 25 * y

We can solve this system of equations to find the values of x and y.

Let's solve the first equation for x:

x = (9 * (60 - y)) / y

Substituting this value of x into the second equation:

((9 * (60 - y)) / y) * (60 - y) = 25 * y

Simplifying the equation:

9 * (60 - y) = 25 * y

Expanding and rearranging the equation:

540 - 9y = 25y

34y = 540

y = 540 / 34

y ≈ 15.88 cm

Now, we can substitute this value of y back into the first equation to find the value of x:

x = (9 * (60 - 15.88)) / 15.88

x ≈ 24.12 kg

Therefore, the mass of the load is approximately 24.12 kg and one arm of the lever is approximately 15.88 cm long.

Conclusion

The mass of the load is approximately 24.12 kg and one arm of the lever is approximately 15.88 cm long.