Mechanics Problem Involving Newton's Laws

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SUMMARY

The discussion centers on a mechanics problem involving Newton's Laws, specifically analyzing the effect of doubling the average force exerted on an arrow by a bow. The initial speed of the arrow is 19.5 m/s, and when the force is doubled, the acceleration also doubles, leading to an increased final velocity. The key takeaway is that while the acceleration increases, the final velocity is not simply double the initial speed due to the time interval remaining constant. The relationship between force, mass, and acceleration is crucial in determining the new speed of the arrow.

PREREQUISITES
  • Understanding of Newton's Second Law (f=ma)
  • Basic knowledge of kinematics and velocity
  • Familiarity with concepts of force and acceleration
  • Ability to analyze motion under constant acceleration
NEXT STEPS
  • Calculate the new speed of the arrow using the formula v = u + at, where u is the initial speed, a is the acceleration, and t is the time interval.
  • Explore the implications of constant acceleration in projectile motion.
  • Study the relationship between force, mass, and acceleration in various scenarios.
  • Review examples of similar mechanics problems involving force and motion.
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the application of Newton's Laws in real-world scenarios, particularly in mechanics and motion analysis.

OpticalFreeze
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Homework Statement


An arrow, starting from rest, leaves the bow with a speed of 19.5 m/s. If the average force exerted on the arrow by the bow were doubled, all else remaining the same, with what speed would the arrow leave the bow?




Homework Equations


f=ma


The Attempt at a Solution


I know that when the force is doubled, so is the acceleration and therefore the rate of change in velocity is increased. I know that the velocity is not simply doubled as the acceleration increases the velocity over time. I'm not sure where to go with this problem because every possible solution I can think of would involve me knowing the time or the displacement, which I can't figure out how to get from the problem.

Any help would be greatly appreciated.
 
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I think that the key phrase in the question is "all else being the same" So if the acceleration before doubling was calculated using a time interval T , you would use the same interval T in calculating the acceleration after the force is doubled. If T stays the same and a is doubled, what must happen to v?
 

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