The mathematical relationship between force and extension for a spring is F = -kx , where F is the restoring force, k is the spring constant and x is the extension. If a box that weighs 40 N is hung from a spring of content 400 N/m, then the extension is equal to x = -F / k = -400 / 40 = -10 cm. The negative sign simply shows the extension and restoring force are in opposite directions. The answer is 10 cm.
Answer:
0.0768 revolutions per day
Explanation:
R = Radius
= Angular velocity
As the mass is conserved the angular momentum is conserved
Moment of intertia for solid sphere
Moment of intertia for hollow sphere
Dividing the moment of inertia
From the first equation
The angular velocity, in revolutions per day, of the expanding supernova shell is 0.0768 revolutions per day
Answer: a) angular acceleration(alpha)=-14.8rad/s^2
b) time taken (t) = 1.52s
Explanation:
What we are given
Mass of the solid sphere m =225g = 0.225kg
Diameter D = 3.00cm = 0.0300m
Radius = D/2 = 0.01500m
Frictional Force = 0.0200N
a) to determine the angular acceleration, we first calculate the torque, then moment of inertia, before the angular acceleration.
Torque = -fr
= - (0.0200)(0.01500)
=-3.00X10^-4Nm
Moment of inertia I
= 2/5mr^2
=2/5(0.225)(0.01500)^2
=2.025X10^-5kgm^2
Angular acceleration (alpha)= torque/moment of inertia (I)
= -3.00X10^-4Nm/2.025X10^-5kgm^2
=-14.8rad/s^2
b) time taken (∆t) = w/alpha
w= -22.5rad/s
Angular acceleration (alpha) = -14.8rad/s^2
∆t = -22.5/-14.8
= -1.52s
.Water
Adequate water supplies of high quality are necessary both for community use and local ecosystems. Communities and jurisdictions must work together to assure an adequate water supply to meet future needs. This section presents resources to aid in that effort.Energy
Communities require energy. Nonrenewable sources for power generation, home and workplace, and transportation cause pollution and its harmful impacts. Energy conservation and the use of renewable fuels provide cost-effective and more sustainable alternatives. This section contains resources available to make energy use more efficient.Air and Climate
Both the natural ecosystem and human health can be adversely impacted by declining air quality and climatic change. Communities can preserve air quality by limiting or eliminating the discharge of harmful chemicals into the air and by minimizing the sources of air pollution. This section contains resources and approaches that address air quality and climate change.Biodiversity
Biodiversity is particularly important for creating sustainability because of the specialized roles each species plays in maintaining ecological balance. Communities can promote healthy wildlife by supporting integrative approaches for managing, protecting, and enhancing wildlife populations and habitats appropriate to their area. Some examples are given here.Land, Forests, and Ecosystems
While providing a protective covering for soil, water, and the atmosphere, forests are also renewable sources of an endless variety of products. In a healthy ecosystem, policies and programs must balance economic and conservation needs. This section highlights cases where communities have developed land use practices and businesses that both conserve ecosystems and enhance local economies.
