Energy Loss & Height of Thrown Ball & Marble Fired from Cannon

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Homework Help Overview

The discussion revolves around two problems involving energy loss and projectile motion. The first problem concerns a ball thrown vertically and the effects of air resistance on its maximum height, while the second problem involves a marble fired horizontally from a cannon and the distance needed to hit a target.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between kinetic energy and gravitational potential energy in the context of air resistance. Questions arise about calculating energy loss and determining maximum height without resistance. In the second problem, there is inquiry into the necessary compression of the spring to achieve a successful hit.

Discussion Status

Some participants have offered initial thoughts on how to approach the problems, particularly regarding the energy loss in the first scenario. There is an ongoing exploration of the concepts involved, with no clear consensus yet on the methods to be used.

Contextual Notes

The problems involve assumptions about air resistance and gravitational effects on different celestial bodies, as well as the constraints of a classroom setting where specific methods may be expected.

Kuro
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1. A ball with a mass of 0.5 kg is thrown straight up with an initial speed of 20 m/s. The ball reaches a maximum height of 15 m. (a) Give the energy loss due to air resistance. (b) What height would the ball have reached without air resistance? (c) What height would the ball have reached on the moon (where gravity is only 0.17 that of earth)?

2. Two children are playing a game in which they try to hit a small box on the floor with a marble fired horizontally from a spring-loaded cannon that is mounted on a table. The target box is 2.40 m from the edge of the table. Alex compresses the spring 1.10 cm, but the marble falls 36 cm short. How far should Ben compress the spring to score a hit?
 
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How would you think to approach either of these problems?
 
In the first problem, I think that the energy loss is between the 1/2mv^2 - mgh?
 
Kuro said:
In the first problem, I think that the energy loss is between the 1/2mv^2 - mgh?

Not exactly, if you're looking for air resistance, though certainly that's the energy exchange in throwing a ball in the air.

Maybe consider how high it would go without any resistance using the relationship you suggested?
 

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