Conservation of Mechanical Energy

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SUMMARY

The discussion focuses on the conservation of mechanical energy in projectile motion, specifically analyzing a 1.0 kg projectile fired at a 45° angle with an initial velocity of 30 m/s. The key equations involved are the total mechanical energy equation and the kinetic energy formula KE = 1/2 mv². The kinetic energy at the highest point of the trajectory is determined by the initial kinetic energy minus the potential energy at that height. The work done in firing the projectile can be calculated using the work-energy principle.

PREREQUISITES
  • Understanding of projectile motion principles
  • Familiarity with kinetic energy (KE) and potential energy (PE) equations
  • Knowledge of the work-energy theorem
  • Basic trigonometry for resolving forces and angles
NEXT STEPS
  • Calculate the maximum height of the projectile using kinematic equations
  • Explore the derivation of the work-energy theorem in detail
  • Study the effects of air resistance on projectile motion
  • Learn about energy conservation in different physical systems
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and energy conservation principles, as well as educators seeking to enhance their teaching of projectile motion concepts.

domtar
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Homework Statement



A 1.0 kg projectile is fired from a point on the Earth's surface at an angle θ = 45° with the horizontal and with an initial velocity v = 30 m/s. Neglect any effects due to air resistance and find:

a) What is the kinetic energy of the projectile when it reaches the highest point on its trajectory?
b) How much work was done in firing the projectile?

Homework Equations



total mechanical energy = KE + PE

KE_i + PE_i + W = KE_f + PE_f

The Attempt at a Solution



I'm not sure how to start this problem, or how to tackle it. I'm assuming I have to use the second equation? I let KE = 1/2 mv^2, m=1.0kg, v=30m/s. Then PE=mgh, m=1.0kg, g=9.81m/s/s, h=?. Then W=Fdcosθ, F=?, d=? cosθ=cos45°. Then I'm sort of stuck... There's a lot of values missing and I'm not sure how to solve or where to start.

Any help would be appreciated, thank you.
 
Physics news on Phys.org
Hi domtar,

The keyword is "projectile". What do you know about projectile motion?

ehild
 

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