Question

Кулю підвісили до пружини, довжина якої при цьому збільшилася на 15 см. Знайдіть масу кулі, якщо коефіціент жорсткості пружини становить 400 Н/м

Answer 1

F = kx

F = 400н/м * 0.15м = 60Н = 6кг вага 

Answer 2

Calculation of the Mass of the Ball Suspended from the Spring

To calculate the mass of the ball suspended from the spring, we can use the formula for the potential energy stored in a spring, which is given by the equation:

U = (1/2) * k * x^2

Where: - U is the potential energy stored in the spring - k is the spring constant (in this case, 400 N/m) - x is the displacement of the spring from its equilibrium position

Given that the length of the spring increased by 15 cm (or 0.15 m) when the ball was suspended, we can use this information to calculate the mass of the ball.

Calculation Steps

1. Calculate the potential energy stored in the spring using the given displacement. 2. Equate the potential energy to the gravitational potential energy of the ball to solve for its mass.

Step 1: Calculate Potential Energy Stored in the Spring

Using the formula for potential energy stored in a spring, we have:

U = (1/2) * k * x^2

Substitute the given values: U = (1/2) * 400 N/m * (0.15 m)^2

Step 2: Equate Potential Energy to Gravitational Potential Energy

The potential energy stored in the spring is converted to gravitational potential energy when the ball is suspended. The gravitational potential energy is given by the formula:

U = m * g * h

Where: - m is the mass of the ball - g is the acceleration due to gravity (approximately 9.81 m/s^2) - h is the displacement of the ball from its equilibrium position

By equating the potential energy stored in the spring to the gravitational potential energy, we can solve for the mass of the ball.

Solution

Equating the potential energy stored in the spring to the gravitational potential energy, we have:

(1/2) * 400 N/m * (0.15 m)^2 = m * 9.81 m/s^2 * h

Solving for the mass m: m = (1/2) * 400 N/m * (0.15 m)^2 / (9.81 m/s^2)

Result

After performing the calculation, the mass of the ball suspended from the spring is approximately 0.153 kg.

This calculation is based on the provided information and the principles of potential energy in a spring system.