The total mechanical energy of the system at any time t is the sum of the kinetic energy of motion of the ball and the elastic potential energy stored in the spring:

where m is the mass of the ball, v its speed, k the spring constant and x the displacement of the spring with respect its rest position.
Since it is a harmonic motion, kinetic energy is continuously converted into elastic potential energy and vice-versa.
When the spring is at its maximum displacement, the elastic potential energy is maximum (because the displacement x is maximum) while the kinetic energy is zero (because the velocity of the ball is zero), so in this situation we have:

Instead, when the spring crosses its rest position, the elastic potential energy is zero (because x=0) and therefore the kinetic energy is at maximum (and so, the ball is at its maximum speed):

Since the total energy E is always conserved, the maximum elastic potential energy should be equal to the maximum kinetic energy, and so we can find the value of the maximum speed of the ball:


(a) The amount of work required to change the rotational rate is 0.0112 J.
(b) The decrease in the rotational inertia when the outermost particle is removed is 64.29%.
<h3>
Moment of inertia of the rod</h3>
The moment of inertia of the rod from the axis of rotation is calculated as follows;
I = md² + m(2d)² + m(3d)²
where;
- m is mass = 10 g = 0.01 kg
- d = 3 equal division of the length
d = 6/3 = 2 cm = 0.02 m
I = md²(1 + 2² + 3²)
I = 14md²
I = 14(0.01)(0.02)²
I = 5.6 x 10⁻⁵ kg/m³
<h3>Work done to change the rotational rate</h3>
K.E = ¹/₂Iω²
K.E = ¹/₂(5.6 x 10⁻⁵)(60 - 40)²
K.E = ¹/₂(5.6 x 10⁻⁵)(20)²
K.E = 0.0112 J
<h3>Percentage decrease of rotational inertia when the outermost particle is removed</h3>
I₂ = md² + m(2d)²
I₂ = 5md²
ΔI = 14md² - 5md²
ΔI = 9md²
η = (ΔI/I) x 100%
η = (9md²/14md²) x 100%
η = 64.29 %
Learn more about rotational inertia here: brainly.com/question/14001220
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Answer:
se me hace que son 8 protones
(16.8 kW) means (16,800 joules/second)
Energy in 1 hour = (1 hour) x (16,800 J/s) x (3,600 s/hour)
Energy = (16,800 x 3,600) J
Energy = 60,480,000 Joules
Energy = 60.48 MJ