A Very Light Ideal Spring with a Spring Constant (Force

question 138

Short Answer

A very light ideal spring with a spring constant (force constant) of 2.5 N/cm pulls
horizontally on an 18-kg box that is resting on a horizontal floor. The coefficient of static
friction between the box and the floor is 0.65, and the coefficient of kinetic friction is 0.45.
(a) How long is the spring just as the box is ready to move?
(b) If the spring pulls the box along with a constant forward velocity of 1.75 m/s, how long
is the spring?
(c) How long is the spring if it pulls the box forward at a constant 2.75 m/s?

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Definitions:

Marginal Utility

The additional enjoyment or gain achieved by consuming another unit of a good or service.

Total Utility

The total satisfaction or benefit derived from consuming a given quantity of goods or services.

Budget

An estimate of income and expenditure for a set period of time, often used by governments, businesses, and individuals to allocate resources.

Utility-maximizing Combination

The selection of goods and/or services that provides the highest utility (satisfaction) for a consumer subject to their income and the prices of the goods/services.