Question

Шарик массой 1 кг подвешивают на пружине жесткостью 10^2Н/м.Затем пружину расиягивают на 5 см и отпускают.Используя теорему о кинетической энергии,определите скорость шарика в тот момент,когда он проходит положение равновесия

Answer 1

Mv2/2=kx2/2
v=kx/m
v=0,05×100/1
v=5=2,2

Answer 2

Calculating the Velocity of the Mass

To calculate the velocity of the mass as it passes through the equilibrium position, we can use the theorem of kinetic energy. The theorem of kinetic energy states that the work done on an object is equal to the change in its kinetic energy.

The potential energy stored in the spring when it is stretched by 5 cm can be calculated using the formula:

U = (1/2)kx^2

Where: - U is the potential energy - k is the spring constant (stiffness) = 10^2 N/m - x is the displacement from the equilibrium position = 0.05 m (5 cm)

The potential energy stored in the spring will be converted into kinetic energy as the mass moves through the equilibrium position. At the equilibrium position, all the potential energy will be converted into kinetic energy.

The kinetic energy of the mass can be calculated using the formula:

K.E. = (1/2)mv^2

Where: - K.E. is the kinetic energy - m is the mass = 1 kg - v is the velocity

Setting the potential energy equal to the kinetic energy, we can solve for the velocity of the mass at the equilibrium position.

Calculations

The potential energy stored in the spring: U = (1/2) * 10^2 * (0.05)^2 = 0.125 J

Setting the potential energy equal to the kinetic energy: 0.125 J = (1/2) * 1 kg * v^2

Solving for v: v^2 = 0.25 m^2/s^2 v = 0.5 m/s

Therefore, the velocity of the mass at the equilibrium position is 0.5 m/s.