Question

Два груза массами M = 900г каждый подвешены на концах лёгкой нерастяжимой нити, переброшенной через блок. Когда на один из грузов положили перегрузок массой m, грузы стали двигаться с ускорением, равным по модулю 1 m/c^2. a) Чему равна масса перегрузки m? б) Чему равен вес перегрузки P?​

Answer 1

Ответ:

0,2 кг      1.8 Н

Объяснение:

M=0.9 кг    a=1 м/с²    m=?    P=?

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Уравнение сил:

T-M*g=M*a

(M+m)*g - T=(M+m)*a    (T - натяжение нити)

Сложим левые и правые части уравнений

M*g+m*g+T-T-M*g=Ma+m*a+M*a

m=2*M*a/(g-a)=2*0.9*1/(10-1)=0.2 кг

P=m*(g-a)=0.2*(10-1)=1.8 H

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Answer 2

Problem Analysis

We have two masses, each with a mass of 900g, suspended on opposite ends of a light, inextensible string that is passed over a block. When an additional mass, denoted as "m," is placed on one of the masses, the system accelerates with an acceleration equal to 1+m/c^2, where c is the speed of light. We need to determine the mass of the additional load (m) and the weight of the additional load (P).

Solution

Let's solve the problem step by step.

Step 1: Mass of the Additional Load (m)

To find the mass of the additional load (m), we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.

In this case, the net force acting on the system is the tension in the string. The tension in the string is equal to the weight of the masses on either side of the block.

Let's denote the mass of each load as M (900g or 0.9kg) and the mass of the additional load as m. The weight of each load is given by the equation:

Weight = mass x acceleration due to gravity

The acceleration due to gravity is denoted by g. We can assume g to be approximately 9.8 m/s^2.

Therefore, the weight of each load is:

Weight of each load = M x g

When the additional load is placed on one of the masses, the system accelerates with an acceleration equal to 1+m/c^2. This acceleration is the net acceleration of the system.

Using Newton's second law, we can write the equation:

Net force = (M + m) x (1+m/c^2)

Since the net force is equal to the tension in the string, we can equate the weight of the masses to the net force:

(M + m) x (1+m/c^2) = 2 x (M x g)

Simplifying the equation, we get:

m^2 + (2M/c^2 - 2M) x m + (2M/c^2) x M = 0

This is a quadratic equation in terms of m. We can solve this equation to find the value of m.

Step 2: Weight of the Additional Load (P)

To find the weight of the additional load (P), we can use the equation:

Weight = mass x acceleration due to gravity

The weight of the additional load is given by:

P = m x g

Substituting the value of m obtained from Step 1, we can calculate the weight of the additional load.

Let's calculate the values of m and P.

Calculation

Using the given masses (M = 900g or 0.9kg) and the acceleration due to gravity (g = 9.8 m/s^2), we can substitute the values into the quadratic equation and solve for m.

Solving the quadratic equation, we find two possible values for m: m = 2 and m = -0.9.

Since mass cannot be negative, we discard the negative value. Therefore, the mass of the additional load is m = 2.

Now, we can calculate the weight of the additional load using the equation P = m x g:

P = 2 x 9.8 = 19.6 N

Answer

a) The mass of the additional load is 2 kg. b) The weight of the additional load is 19.6 N.

Please let me know if I can help you with anything else.