Question

Тело массой 100 кг, подвешенное на канате и движущееся вертикально вниз со скорость 6 м/с , останавливается через 4 с. Определите силу натяжения каната. Можно дано и решение и рисунок,пожалуйста

Answer 1

1) сила натяжения каната до торможения равна (при условии равномерного спуска со скоростью 6 м/с) :
Fн=-mg
2) при торможении его в течении 4х секунд возникает ускорение, это ускорение равно:
a= 6/4=1.5 м/с, где 6 - это изменение скорости от 6 м/с до 0 ( то есть остановки) , а 4 - это время за которое произошло изменение в скорости.
3) тогда сила натяжения каната будет равна:
Fн=-m(g+a)=-100(10+1,5)=-1150 Н
пс: знак минус говорит о направлении противоположном направлению свободного падения, то есть сила натяжения каната направленна вверх.

Answer 2

Problem Analysis

We are given the following information: - Mass of the body: 100 kg - Initial velocity: 6 m/s downward - Time taken to stop: 4 seconds

We need to determine the tension force in the rope.

Solution

To solve this problem, 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 body is moving vertically downward and comes to a stop. Therefore, the net force acting on the body is equal to the tension force in the rope.

We can calculate the acceleration of the body using the formula:

acceleration = (final velocity - initial velocity) / time

Given that the final velocity is 0 m/s (since the body comes to a stop), the initial velocity is 6 m/s downward, and the time taken to stop is 4 seconds, we can substitute these values into the formula to find the acceleration.

Next, we can calculate the tension force using the formula:

tension force = mass * acceleration

Substituting the mass and acceleration values, we can find the tension force.

Calculation

Let's calculate the acceleration first:

acceleration = (0 - 6) / 4 = -1.5 m/s^2

Now, we can calculate the tension force:

tension force = 100 kg * (-1.5 m/s^2) = -150 N

Since the tension force is acting upward to counterbalance the weight of the body, the negative sign indicates that the tension force is directed upward.

Therefore, the tension force in the rope is 150 N and it acts upward.

Diagram

Unfortunately, I am unable to provide a diagram in this text-based format. However, you can visualize the situation as a body with a mass of 100 kg hanging from a rope, moving vertically downward with an initial velocity of 6 m/s. The body comes to a stop after 4 seconds, and the tension force in the rope acts upward to counterbalance the weight of the body.

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