A dart is loaded into a spring-loaded toy dart gun by pushing the spring in by a 
distance d. For the next loading?the spring is compressed a distance d/3. How much 
work is required to load the second dart compared to that required to load the first?

A)nine times as much
B)three times as much
C)the same
D)one-third as much
E)one-Ninth as much

E. Didn't I respond to this earlier?

To compare the amount of work required to load the second dart to that required to load the first, we can use the concept of work done by a spring.

The work done by a spring is given by the formula:

Work = (1/2) * k * x^2

Where "k" is the spring constant and "x" is the displacement of the spring.

Let's assume that the spring constant (k) remains the same for both loadings. Therefore, we only need to consider the displacement of the spring.

For the first loading, the displacement of the spring is "d".

So, the work required to load the first dart is:

Work1 = (1/2) * k * d^2

Now, for the second loading, the displacement of the spring is (d/3).

Therefore, the work required to load the second dart is:

Work2 = (1/2) * k * (d/3)^2
= (1/2) * k * (d^2/9)
= (1/18) * k * d^2

To compare the two works, we can calculate their ratio:

Work2 / Work1 = [(1/18) * k * d^2] / [(1/2) * k * d^2]
= (1/18) / (1/2)
= 1/9

Therefore, the work required to load the second dart is one-ninth (1/9) of the work required to load the first dart.

So the answer is E) one-Ninth as much.