A spring which has a spring constant of k, needs 19 J of energy to be compressed [math: x] m. How much energy is needed for the same spring to be compressed by 5[math: x] m?

Question

BlackTom AI · Accepted Answer

Start by recalling the energy stored in a spring: E = (1/2) k x^2, where x is the compression.
From the given information, when the compression is x meters, the energy is 19 J, so we have 19 = (1/2) k x^2. This relation defines the product (1/2) k x^2 as 19.
Now consider a new compression of 5x meters. The energy at this compression is E' = (1/2) k (5x)^2 = (1/2) k * 25x^2 = 25 * (1/2) k x^2.
Since (1/2) k x^2 equals 19 J from the initial condition, E' becomes 25 * 19 J.
Calculating 25 times 19 gives 25*20 - 25 = 500 - 25 = 475. Therefore, the energy required for a compression of 5x meters is 475 J.

A spring which has a spring constant of k, needs 19 J of energy to be compressed [math: x] m. How much energy is needed for the same spring to be compressed by 5[math: x] m?数值题

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