Question

Помогите решить: Щоб зважити монету, хлопчик склав аркуш паперу а4 у вигляді смужки, поклав на стіл, поставив монету і врівноважив усе у хиткій рівновазі на краю столу. Край столу розділив смужку аркуша на відрізки 8см і 22см. Відстань від краю монети до краю столу - 6см. Знайди масу монети, якщо маса аркуша паперу а4 - 5г.

Answer 1

Відповідь :

2, 5 грам

Пояснення : тут вирішується за певною формулою.

Answer 2

To solve this problem, we can use the principle of moments. The principle of moments states that for an object to be in equilibrium, the sum of the clockwise moments must be equal to the sum of the anticlockwise moments.

Let's break down the information given in the problem:

- The boy placed a strip of A4 paper on the table and balanced it on the edge of the table using a coin. - The strip of paper was divided into segments of 8 cm and 22 cm. - The distance from the edge of the coin to the edge of the table is 6 cm. - The mass of the A4 paper is 5 g.

We need to find the mass of the coin.

Applying the Principle of Moments

To apply the principle of moments, we need to consider the moments acting on the system. The moment of an object is the product of its mass and the distance from a reference point.

Let's assume the coin is at a distance of x cm from the 8 cm segment and y cm from the 22 cm segment. The distance from the coin to the edge of the table is given as 6 cm.

The moments acting on the system are as follows:

1. Moment due to the 8 cm segment: (8 - x) * 5 g 2. Moment due to the 22 cm segment: (22 - y) * 5 g 3. Moment due to the coin: x * m, where m is the mass of the coin.

According to the principle of moments, the sum of the clockwise moments must be equal to the sum of the anticlockwise moments.

Setting up the Equation

Since the system is in equilibrium, the sum of the clockwise moments must be equal to the sum of the anticlockwise moments.

Clockwise moments: - Moment due to the 8 cm segment: (8 - x) * 5 g - Moment due to the 22 cm segment: (22 - y) * 5 g

Anticlockwise moments: - Moment due to the coin: x * m

Setting up the equation:

(8 - x) * 5 g + (22 - y) * 5 g = x * m

Solving the Equation

To solve the equation, we need another equation to eliminate one of the variables. We can use the fact that the system is in equilibrium to set up another equation.

Since the system is in equilibrium, the sum of the clockwise moments must be equal to the sum of the anticlockwise moments.

Clockwise moments: - Moment due to the 8 cm segment: (8 - x) * 5 g - Moment due to the 22 cm segment: (22 - y) * 5 g

Anticlockwise moments: - Moment due to the coin: x * m - Moment due to the A4 paper: 6 cm * 5 g

Setting up the equation:

(8 - x) * 5 g + (22 - y) * 5 g = x * m + 6 cm * 5 g

Simplifying the equation:

40 g - 5x g + 110 g - 5y g = x * m + 30 g

150 g - 5x g - 5y g = x * m

Solving for the Mass of the Coin

Now we have two equations:

(8 - x) * 5 g + (22 - y) * 5 g = x * m 150 g - 5x g - 5y g = x * m

We can solve these equations simultaneously to find the values of x, y, and m.

However, without the specific values of x and y, we cannot determine the exact mass of the coin. We need additional information to solve the problem.

Please provide any additional information or clarify any missing details so that we can assist you further.