Question

Шарик,подвешанный на длинной нити, отклонили от положения равновесия на 5 см, и отпустили. Какую скорость будет иметь шарик при прохождение положения равновесия.

Answer 1

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Answer 2

Calculation of the Ball's Velocity

To determine the velocity of the ball as it passes through the equilibrium position, we can use the principle of conservation of mechanical energy. The ball is initially displaced by 5 cm from the equilibrium position and then released. At the equilibrium position, the ball will have zero potential energy and maximum kinetic energy.

The formula for the potential energy of an object in simple harmonic motion is given by:

PE = (1/2)kx^2

where PE is the potential energy, k is the spring constant, and x is the displacement from the equilibrium position.

The formula for the kinetic energy of an object is given by:

KE = (1/2)mv^2

where KE is the kinetic energy, m is the mass of the object, and v is the velocity.

Since the ball is released from rest, its initial velocity is zero. Therefore, all the potential energy at the maximum displacement is converted into kinetic energy at the equilibrium position.

Using the principle of conservation of mechanical energy, we can equate the potential energy at the maximum displacement to the kinetic energy at the equilibrium position:

(1/2)kx^2 = (1/2)mv^2

Simplifying the equation, we can solve for the velocity:

v = sqrt((k/m)x^2)

Now, we need to find the values of the spring constant (k) and the mass of the ball (m) to calculate the velocity.

Unfortunately, the provided search results do not contain the necessary information to determine the values of k and m. Therefore, we are unable to calculate the exact velocity of the ball at the equilibrium position without additional information.

If you have the values of the spring constant and the mass of the ball, please provide them, and I will be able to calculate the velocity for you.