Question

Помогите решить задачу по физике. Шар диаметром 2,8 см и весом 0,3 кг катится с периодом 0,25 секунд, найти кинетическую энергию движения. Заранее спасибо)

Answer 1

Кинетическая энергия будет равняться сумме энергии вращения и энергии поступательного движения.
W = m*v^2/2 + J*w^2/2
v = 2*pi*r/T
w = 2*pi/T
J шара = 2/5*m*r^2
W = m*r^2*4*pi^2/(2*T^2) + 2/5*m*r^2*4*pi^2/2*T^2
W = m*r^2*4*pi^2/(2*T^2)(1+2/5)
подставляем значения (r = 0.5*d = 1.4 см)
W = 0.3*0.14^2*4*3.14^2/(2*0.25^2)(1+0.4) = 2.60 Дж

Answer 2

Problem Analysis

To find the kinetic energy of the rolling ball, we need to use the formula for rotational kinetic energy. The formula is given by:

Rotational Kinetic Energy = (1/2) * I * ω^2

Where: - I is the moment of inertia of the ball - ω is the angular velocity of the ball

To calculate the moment of inertia, we need to know the mass and radius of the ball. The moment of inertia for a solid sphere rotating about its diameter is given by:

I = (2/5) * m * r^2

Where: - m is the mass of the ball - r is the radius of the ball

We are given the diameter of the ball, so we need to calculate the radius using the formula:

r = d/2

Where: - d is the diameter of the ball

Once we have the moment of inertia and the angular velocity, we can calculate the rotational kinetic energy using the formula mentioned above.

Calculation

Given: - Diameter of the ball (d) = 2.8 cm - Mass of the ball (m) = 0.3 kg - Period of rotation (T) = 0.25 seconds

To find the radius (r) of the ball, we use the formula: r = d/2 = 2.8/2 = 1.4 cm = 0.014 m

To find the angular velocity (ω), we use the formula: ω = 2π/T = 2π/0.25 = 8π rad/s

To find the moment of inertia (I), we use the formula: I = (2/5) * m * r^2 = (2/5) * 0.3 * (0.014)^2 = 0.0002352 kg·m^2

Finally, to find the rotational kinetic energy (KE), we use the formula: KE = (1/2) * I * ω^2 = (1/2) * 0.0002352 * (8π)^2 ≈ 0.059 J

Therefore, the kinetic energy of the rolling ball is approximately 0.059 Joules.

Answer

The kinetic energy of the rolling ball is approximately 0.059 Joules.