Question

Тело массой 5 кг, подвешенное на нити, равномерно вращается по окружности. Определите модуль центростремительного ускорения, если сила нятяжения нити 4Н и нить образуют с вертикалью угол а=30 градусов

Answer 1

Calculation of Centripetal Acceleration

To determine the centripetal acceleration of a body with a mass of 5 kg, hanging on a string and rotating uniformly in a circle, we need to consider the tension force in the string and the angle it forms with the vertical.

The centripetal acceleration is given by the formula:

a = v^2 / r

where: - a is the centripetal acceleration, - v is the linear velocity of the body, and - r is the radius of the circular path.

In this case, the tension force in the string is given as 4 N, and the angle between the string and the vertical is 30 degrees.

To find the linear velocity, we can use the relationship between the tension force, the angle, and the weight of the body:

Tension force = Weight * cos(angle)

Rearranging the equation, we have:

Weight = Tension force / cos(angle)

The weight of the body is given by:

Weight = mass * gravitational acceleration

where the gravitational acceleration is approximately 9.8 m/s^2.

Substituting the values, we can find the weight of the body:

Weight = 5 kg * 9.8 m/s^2

Now, we can calculate the linear velocity:

Tension force / cos(angle) = mass * gravitational acceleration

4 N / cos(30 degrees) = 5 kg * 9.8 m/s^2

Simplifying the equation, we get:

Linear velocity = (4 N / cos(30 degrees)) / (5 kg * 9.8 m/s^2)

Once we have the linear velocity, we can calculate the centripetal acceleration using the formula mentioned earlier.

Let's perform the calculations:

Weight = 5 kg * 9.8 m/s^2 = 49 N

Linear velocity = (4 N / cos(30 degrees)) / (5 kg * 9.8 m/s^2)

Using a calculator, we find that the linear velocity is approximately 2.041 m/s.

Now, we can calculate the centripetal acceleration:

Centripetal acceleration = (2.041 m/s)^2 / r

Unfortunately, the radius of the circular path is not provided in the question. Without this information, we cannot calculate the exact value of the centripetal acceleration.

Please provide the radius of the circular path so that we can complete the calculation.