Question

По наклонной плоскости тянут равноускоренно за канат ящик массой 50 кг. Угол у основания наклонной плоскости 30(, коэффициент трения 0,2. Ящик поднимают на высоту 20м за 5 с. Определите силу натяжения каната.​

Answer 1

Ответ: 323Н

Объяснение:

P e ш e н и e. Ha ящик дeйcтвуют cилa тяжecти mg, cилa тpeния Fтp, cилa нaтяжeния кaнaтa T и cилa нopмaльнoй peaкции oпopы N. Coглacнo втopoму зaкoну Hьютoнa:

mа = mg + N +Fтp + T. (1)      

B пpoeкцияx нa ocи OX и OY уpaвнeниe имeeт вид

ma = T - mg sinα - Fтp;  (2)      

0 = N - mg cosα.         (З)

Cилa тpeния cкoльжeния Fтp = μN.

Из уpaвнeния (З) пoлучим

N = mg cosa.

Уpaвнeниe (2) пepeпишeм в видe

ma = T - mg sinα - μmg cosα.

Уcкopeниe oпpeдeлим из уpaвнeния движeния S=at²

пpи этoм S=h/sinα, a=2S/t²=2h/(t²*sinα)

T=m(2h/(t²*sinα)+g(sinα-μ*cosα))=50*(2*20/(5²*0,5)+10*(0,5-0,2*0,87))=50*(3,2+3,26)=323Н

Answer 2

Problem Analysis

We have a box being pulled up a inclined plane with a rope. The box has a mass of 50 kg, the angle of the inclined plane is 30 degrees, and the coefficient of friction is 0.2. The box is being lifted to a height of 20m in 5 seconds. We need to determine the tension force in the rope.

Solution

To solve this problem, we'll break it down into several steps:

1. Calculate the gravitational force acting on the box. 2. Determine the normal force exerted on the box by the inclined plane. 3. Calculate the frictional force acting on the box. 4. Determine the net force acting on the box. 5. Calculate the acceleration of the box. 6. Determine the tension force in the rope.

Let's go through each step in detail.

Step 1: Calculate the gravitational force

The gravitational force acting on the box can be calculated using the formula:

F_gravity = mass * acceleration due to gravity

Given that the mass of the box is 50 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the gravitational force:

F_gravity = 50 kg * 9.8 m/s^2

Using the given values, we find:

F_gravity = 490 N.

Step 2: Determine the normal force

The normal force exerted on the box by the inclined plane can be calculated using the formula:

F_normal = mass * gravitational acceleration * cos(angle)

Given that the mass of the box is 50 kg, the gravitational acceleration is approximately 9.8 m/s^2, and the angle of the inclined plane is 30 degrees, we can calculate the normal force:

F_normal = 50 kg * 9.8 m/s^2 * cos(30 degrees)

Using the given values, we find:

F_normal = 425 N.

Step 3: Calculate the frictional force

The frictional force acting on the box can be calculated using the formula:

F_friction = coefficient of friction * F_normal

Given that the coefficient of friction is 0.2 and the normal force is 425 N, we can calculate the frictional force:

F_friction = 0.2 * 425 N

Using the given values, we find:

F_friction = 85 N.

Step 4: Determine the net force

The net force acting on the box can be calculated by subtracting the frictional force from the gravitational force:

F_net = F_gravity - F_friction

Using the previously calculated values, we find:

F_net = 490 N - 85 N

F_net = 405 N.

Step 5: Calculate the acceleration

The acceleration of the box can be calculated using Newton's second law of motion:

F_net = mass * acceleration

Given that the net force is 405 N and the mass of the box is 50 kg, we can calculate the acceleration:

405 N = 50 kg * acceleration

Solving for acceleration, we find:

acceleration = 8.1 m/s^2.

Step 6: Determine the tension force

The tension force in the rope can be calculated using the formula:

Tension = mass * acceleration + F_friction

Given that the mass of the box is 50 kg, the acceleration is 8.1 m/s^2, and the frictional force is 85 N, we can calculate the tension force:

Tension = 50 kg * 8.1 m/s^2 + 85 N

Using the given values, we find:

Tension = 405 N + 85 N

Tension = 490 N.

Therefore, the tension force in the rope is 490 N.

I hope this helps! Let me know if you have any further questions.