Question

На столе лежит брусок массой 2 кг, к которому привязаны нити, перекинутые через невесомые блоки, укрепленные на обоих концах стола.К свободным концам нитей подвешены грузы , масса которых равна соответсвенно 0,85 кг и 0,2 кг.Вследствие этого брусок приходит в движение и за первые 3 с проходит расстояние 0,81 м.Определить коэффициент трения скольжения бруска о стол и силы натяжения нитей.

Answer 1

Ответ: 1,85

Объяснение:

Дано:

m1=2кг

m2=0,82+0,2кг

t=3c

S=0,81м

----------------

μ-?

S=Vot+at²/2

at²/2=S

a*3²/2=0,81

а=0,18м/с²

Составим систему уравнений:

{m1*a=m1*g-T

{m2*a=T-μm2*g

Решаем систему методом алгебраического сложения

m1a+m2a=m1g-μm2g

а(m1+m2)=g(m1-μm2)

Подставляем значения

0,18(2+0,85+0,2)=10*2-10*μ*(0,85+0,2)

0,549=20-10,5μ

μ=(20-0,549)/10,5=1,85

Answer 2

Problem Analysis

We have a block with a mass of 2 kg on a table. The block is connected to two weights via strings that pass over frictionless pulleys. The masses of the weights are 0.85 kg and 0.2 kg. The block moves and covers a distance of 0.81 m in the first 3 seconds. We need to determine the coefficient of sliding friction between the block and the table, as well as the tension in the strings.

Coefficient of Sliding Friction

To determine the coefficient of sliding friction between the block and the table, we can use Newton's second law of motion. The net force acting on the block is equal to the product of its mass and acceleration. The net force can be calculated by considering the forces acting on the block.

The forces acting on the block are: 1. The tension in the string connected to the 0.85 kg weight. 2. The tension in the string connected to the 0.2 kg weight. 3. The force of sliding friction between the block and the table.

Since the block is moving, the net force acting on it is non-zero. We can write the equation for the net force as:

Net force = Tension1 - Tension2 - Frictional force

The frictional force can be calculated using the equation:

Frictional force = coefficient of sliding friction * Normal force

The normal force is equal to the weight of the block, which can be calculated as:

Normal force = mass of the block * acceleration due to gravity

By substituting the values and rearranging the equation, we can solve for the coefficient of sliding friction.

Tension in the Strings

To determine the tension in the strings, we can use the equations of motion. The block is subjected to two forces in the vertical direction: the weight of the block and the tension in the strings. The net force in the vertical direction is equal to the product of the mass of the block and its acceleration.

We can write the equation for the net force in the vertical direction as:

Net force in the vertical direction = Tension1 + Tension2 - Weight of the block

By substituting the values and rearranging the equation, we can solve for the tension in the strings.

Calculation

Let's calculate the coefficient of sliding friction and the tension in the strings.

Given: - Mass of the block (m) = 2 kg - Mass of the weight connected to the first string (m1) = 0.85 kg - Mass of the weight connected to the second string (m2) = 0.2 kg - Distance covered by the block in the first 3 seconds (s) = 0.81 m

Acceleration of the block (a) can be calculated using the equation of motion:

s = ut + (1/2)at^2

where u is the initial velocity (which is 0 in this case) and t is the time.

By rearranging the equation, we can solve for acceleration:

a = (2s) / t^2

Substituting the given values, we find:

a = (2 * 0.81) / (3^2) = 0.18 m/s^2

Now, let's calculate the coefficient of sliding friction:

The net force acting on the block is equal to the product of its mass and acceleration:

Net force = m * a

The normal force is equal to the weight of the block:

Normal force = m * g

where g is the acceleration due to gravity.

The frictional force can be calculated using the equation:

Frictional force = coefficient of sliding friction * Normal force

By substituting the equations, we can write:

m * a = Tension1 - Tension2 - coefficient of sliding friction * m * g

Rearranging the equation, we can solve for the coefficient of sliding friction:

coefficient of sliding friction = (Tension1 - Tension2 - m * a) / (m * g)

Now, let's calculate the tension in the strings:

The net force in the vertical direction is equal to the product of the mass of the block and its acceleration:

Net force in the vertical direction = m * a

By substituting the equations, we can write:

m * a = Tension1 + Tension2 - m * g

Rearranging the equation, we can solve for the tension in the strings:

Tension1 + Tension2 = m * a + m * g

Calculation Results

Using the given values and the equations above, we can calculate the coefficient of sliding friction and the tension in the strings.

- Acceleration of the block (a) = 0.18 m/s^2 - Mass of the block (m) = 2 kg - Mass of the weight connected to the first string (m1) = 0.85 kg - Mass of the weight connected to the second string (m2) = 0.2 kg - Acceleration due to gravity (g) = 9.8 m/s^2

Using the equation for the coefficient of sliding friction:

coefficient of sliding friction = (Tension1 - Tension2 - m * a) / (m * g)

Substituting the values, we find:

coefficient of sliding friction = (Tension1 - Tension2 - 2 * 0.18) / (2 * 9.8)

Using the equation for the tension in the strings:

Tension1 + Tension2 = m * a + m * g

Substituting the values, we find:

Tension1 + Tension2 = 2 * 0.18 + 2 * 9.8

Now, let's calculate the values:

coefficient of sliding friction = (Tension1 - Tension2 - 2 * 0.18) / (2 * 9.8)

Tension1 + Tension2 = 2 * 0.18 + 2 * 9.8

Unfortunately, I couldn't find the specific values for Tension1 and Tension2 in the search results. However, you can use the equations provided above to calculate the coefficient of sliding friction and the tension in the strings once you have the values for Tension1 and Tension2.