Ahockey puck sliding along frictionless ice with speed v to the right collides with a horizontal spring and compresses it by 1.0 cm before coming to a momentary stop. what will be the spring's maximum compression if the same puck hits it at a speed of 2v?

The spring's maximum compression will be 2.0 cm

Explanation:

There are two energies in this problem, kinetic energy and elastic potential energy (with m the mass, v the velocity, x the compression and k the spring constant. ) so the total mechanical energy at every moment is the sum of the two energies:

Here we have a situation where the total mechanical energy of the system is conserved because there are no dissipative forces (there's no friction), so:

Note that at the initial moment where the hockey puck has not compressed the spring all the energy of the system is kinetic energy, but for a momentary stop all the energy of the system is potential elastic energy, so we have:

(1)

Due conservation of energy the equality (1) has to be maintained, so if we let k and m constant x has to increase the same as v to maintain the equality. Therefore, if we increase velocity to 2v we have to increase compression to 2x to conserve the equality. This is  2(1.0) = 2.0 cm

relativism, roughly put, is the view that truth and falsity, right and wrong, standards of reasoning, and procedures of justification are products of differing conventions and frameworks of assessment and that their authority is confined to the context giving rise to them. more precisely, “relativism” covers views which maintain that—at a high level of abstraction—at least some class of things have the properties they have (e.g., beautiful, morally good, epistemically justified) not simpliciter, but only relative to a given framework of assessment (e.g., local cultural norms, individual standards), and correspondingly, that the truth of claims attributing these properties holds only once the relevant framework of assessment is specified or supplied. relativists characteristically insist, furthermore, that if something is only relatively so, then there can be no framework-independent vantage point from which the matter of whether the thing in question is so can be established.

relativism has been, in its various guises, both one of the most popular and most reviled philosophical doctrines of our time. defenders see it as a harbinger of tolerance and the only ethical and epistemic stance worthy of the open-minded and tolerant. detractors dismiss it for its alleged incoherence and uncritical intellectual permissiveness. debates about relativism permeate the whole spectrum of philosophical sub-disciplines. from ethics to epistemology, science to religion, political theory to ontology, theories of meaning and even logic, philosophy has felt the need to respond to this heady and seemingly subversive idea. discussions of relativism often also invoke considerations relevant to the very nature and methodology of philosophy and to the division between the so-called “analytic and continental” camps in philosophy. and yet, despite a long history of debate going back to plato and an increasingly large body of writing, it is still difficult to come to an agreed definition of what, at its core, relativism is, and what philosophical import it has. this entry attempts to provide a broad account of the many ways in which “relativism” has been defined, explained, defended and criticized.

explanation:

thermal energy is the answer