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KengaRu [80]
3 years ago
10

A dart is inserted into a spring-loaded dart gun by pushing the spring in by a distance x. For the next loading, the spring is c

ompressed a distance 2x. How much faster does the second dart leave the gun compared to the first? The book gives an answer of "two times as much" but I not totally clear on what equation this is coming from. Is it the equation: W(ext) = 1/2mvf^2 - 1/2mvi^2 where the initiial velocity would be 0?
Physics
1 answer:
bezimeni [28]3 years ago
7 0

Answer:

The second dart leaves the gun two times as faster than the first one.

Explanation:

Assuming no energy loss during the spring-dart energy transfer, we have by the conservation of energy principle

U_s = K_d \\ \frac{1}{2} kx^2 = \frac{1}{2}mv^2 \\ v = \sqrt{\frac{k}{m}x^2}.

Given an arbitrary x and its double, 2x, launch velocities are

v_1 = \sqrt{\frac{k}{m}x^2} \text{ and} \\ v_2 = \sqrt{\frac{k}{m}\left(2x\right)^2} = \sqrt{\frac{k}{m}4x^2} = 2\sqrt{\frac{k}{m}x^2} = \mathbf{2v_1}.

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Answer:TEP 1: State the Problem

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EXAMPLE: The lamp does not come on when you flip the switch.

Your problem may be something that you observe around you or it can be determined by researching a topic and attempting to repeat an experiment of another scientist based on what you are working with.

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An observation is the act of recognizing and recording something that is happening. Observing often involves the use of measurements and instruments to take measurements with.

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You make these observations based on the things you see, hear, and in other ways notice going on around you. You may also base your observations on information you found from researching the topic. Maybe you found the manual for the lamp and read about how it is supposed to work. You might have searched for information about Thomas Edison and his invention of the light bulb. These works of others are called background research.

 

STEP 3: Form a Hypothesis

A hypothesis is an educated guess meaning an explanation for something that happens based on facts that can then be tested to try and find logical answers.

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Having more than one hypothesis is fine. There could be a number of reasons why the lamp is not lit and testing them all might be the only way to find an answer. Before beginning to experiment, use logical reason to determine if any of your hypotheses can be eliminated. Maybe the fuse is blown or the outlet is bad. The switch could be wired wrong or broken. These are all testable hypotheses that could be looked into if the light bulb is not the problem.

 

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<span>fossil compaction                (answer)</span>

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Next, we should solve the problem by performing the multiplication on the right side of the equation.

v2 = 330 m/s

Therefore, the final velocity reached by the object is 330 m/s.

Hope this helps!

7 0
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