Spring powered dart gun conceptual question

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Homework Help Overview

The discussion revolves around a conceptual question regarding a spring powered dart gun that fires two different darts, one regular and one with twice the mass, and their respective times to reach the ground after being fired. The subject area includes concepts of mechanics, specifically focusing on forces, mass, and acceleration in the context of projectile motion.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between mass and time of fall, questioning whether the mass affects the time taken for both darts to reach the ground. There is also discussion on the role of the spring's energy in accelerating the darts.

Discussion Status

The discussion has seen participants confirming their understanding of the concepts involved, with some guidance provided regarding the effects of mass on acceleration. However, there is no explicit consensus on the final answer to the original question, as participants are still exploring the implications of their reasoning.

Contextual Notes

Participants are navigating assumptions about the effects of mass on acceleration and the conservation of energy in the context of the problem. There is an indication that the original poster may have been seeking validation of their reasoning rather than a definitive answer.

freshcoast
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1. Problem statement.
A spring powered dart gun fires darts straight downward towards the Earth from the same height each time. First it fired a regular dart, then a dart with twice the mass. Which dart takes the least time to reach the ground after exiting the gun?

A) the regular dart
B) the weighted dart
C) each takes the same time
D) there is insufficient information to answer the question.

2. Related equations
conservation of energy

3. Attempt at solution
Just to make sure I got the correct answer, would both darts take the same time to reach the floor since the energy is conserved and the mass has no effect on the velocities?
 
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The mass has no effect in the free fall. What about the motion in the gun, when masses are accelerated by the spring?
 
Oh I see, if I use the equation work done by spring = force x d, convert the f into ma, solve for a, the heavier mass would have a lower acceleration since the energy from the spring is being divided by the heavier mass?
 
Your conclusion is correct. So what's the answer to the original question?
 
So the regular dart will take less time to reach the ground
 
Good!
 

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