Question

A spring-loaded gun shoots a plastic ball with a speed of 4 m/s. If the spring is compressed twice as far, the ball's speed will be

Answer 1

Answer:

v' = 8

Explanation:

Given:

Speed v = 4 m/s

Find:

New compressed speed

Computation:

1/2(k)(x)² = 1/2(m)(v)²

v = √kx²/m = 4

If x become double

v' = √k(2x)²/m

v' = 2√kx²/m

v' = 2(4)

v' = 8

Answer 2

The ball's speed will be "8 m/s".

According to the question,

• Speed, v = 4 m/s

As we know,

→ $\frac{1}{2}kx^2 = \frac{1}{2}mv^2$

→       $v = \sqrt{\frac{kx^2}{m} }$

           $= 4$

then,

→ $v' = \sqrt{\frac{k(2x)^2}{m} }$

By substituting the values, we get

       $= 2 \sqrt{\frac{kx^2}{m} }$

       $= 2\times 4$

       $= 8 \ m/s$

Thus the response above is appropriate.

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