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maxonik [38]
2 years ago
7

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 muchB) three times as muchC) the sameD) one-third as muchE) one-Ninth as much
Physics
1 answer:
Mrac [35]2 years ago
7 0

Answer:

W'=\dfrac{W}{9}

Explanation:

The potential energy of the spring or the work done by the spring is given by :

W=\dfrac{1}{2}kd^2............(1)

k is the spring constant

d is the compression

When the spring is compressed a distance d' = d/3, let W' is the work is required to load the second dart. Then the work done is given by :

W'=\dfrac{1}{2}kd'^2

W'=\dfrac{1}{2}k(d/3)^2.............(2)

Dividing equation (1) and (2) :

\dfrac{W}{W'}=\dfrac{1/2kd^2}{1/2k(d/3)^2}

\dfrac{W}{W'}=9

W'=\dfrac{W}{9}

So, the work required  to load the second dart compared to that required to load the first is one-Ninth as much. Therefore, the correct option is (E).

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