# A spring

A spring has a nonlinear force law such that the force necessary to compress the spring is given by:

F=k'(e^(ax)-1)

where k' = 200 N is a constant, α = 1.0 m−1 and x is the distance measured from the spring’s equilibrium position in meters. How much work is done compressing the spring from x = 0 m to x = 0.25 m? Compare this to the amount of work necessary to compress a spring that obeys Hooke’s Law with k = 200 N/m over the same distance.

What is the chance that 1 item out of 30 would remain as 1 of the last 2 items if an item is removed 1 at a time?

The Murphy family and the Rodriguez family each used their sprinklers last summer. The water output rate for the Murphy family's sprinkler was 30L per hour. The water output rate for the Rodriguez family's sprinkler was 25L per hour. The families used their sprinklers for a combined total of 50 hours, resulting in a total water output of 1400L How long was each sprinkler used?

F=k'(e^(ax)-1)

where k' = 200 N is a constant, α = 1.0 m−1 and x is the distance measured from the spring’s equilibrium position in meters. How much work is done compressing the spring from x = 0 m to x = 0.25 m? Compare this to the amount of work necessary to compress a spring that obeys Hooke’s Law with k = 200 N/m over the same distance.

What is the chance that 1 item out of 30 would remain as 1 of the last 2 items if an item is removed 1 at a time?

The Murphy family and the Rodriguez family each used their sprinklers last summer. The water output rate for the Murphy family's sprinkler was 30L per hour. The water output rate for the Rodriguez family's sprinkler was 25L per hour. The families used their sprinklers for a combined total of 50 hours, resulting in a total water output of 1400L How long was each sprinkler used?

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