Question

Тіло масою 200 г коливається на мотузці довжиною 1 м. Якою буде сила натягу мотузки коли тіло буде проходити положення рівноваги зі швидкістю 2 м/с

Answer 1

Calculation of Tension Force in a Pendulum

To calculate the tension force in the string when the body is at equilibrium with a velocity of 2 m/s, we can use the principles of Newton's laws of motion.

In this case, the body is acting as a simple pendulum, oscillating back and forth on a string. The tension force in the string is responsible for keeping the body in motion and preventing it from falling.

The tension force in the string can be calculated using the following equation:

Tension force (T) = mass (m) x acceleration (a)

In this scenario, the body is at equilibrium, which means the net force acting on it is zero. Therefore, the acceleration is also zero.

Since the body is moving with a velocity of 2 m/s, we can assume that it has reached its maximum displacement and is momentarily at rest before changing direction. At this point, the acceleration is zero.

Given: - Mass of the body (m) = 200 g = 0.2 kg - Length of the string (L) = 1 m - Velocity of the body (v) = 2 m/s

To calculate the tension force, we need to find the acceleration of the body. The acceleration can be calculated using the centripetal acceleration formula:

Acceleration (a) = (velocity (v))^2 / radius (r)

In this case, the radius is equal to the length of the string (L).

Substituting the given values into the equation:

Acceleration (a) = (2 m/s)^2 / 1 m = 4 m/s^2

Now that we have the acceleration, we can calculate the tension force:

Tension force (T) = mass (m) x acceleration (a) = 0.2 kg x 4 m/s^2 = 0.8 N

Therefore, the tension force in the string when the body is at equilibrium with a velocity of 2 m/s is 0.8 N.