How Do You Calculate Mechanical Energy and Work for a Thrown Ball?

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SUMMARY

The discussion focuses on calculating mechanical energy and work for a thrown rubber ball with a mass of 0.50 kg, reaching a height of 20 m and traveling at 15 m/s. The kinetic energy (Ek) is calculated as 56 J using the formula Ek = 1/2 mv². The gravitational potential energy (Eg) is determined to be 98 J using Eg = mgh. The work done in throwing the ball is derived from the change in energy, resulting in an initial speed (Vi) of approximately 19.8 m/s when leaving the ground.

PREREQUISITES
  • Understanding of kinetic energy calculation (Ek = 1/2 mv²)
  • Knowledge of gravitational potential energy (Eg = mgh)
  • Familiarity with work-energy principles (W = fd)
  • Basic understanding of kinematic equations (Vf² = Vi² + 2ad)
NEXT STEPS
  • Study the principles of energy conservation in mechanical systems.
  • Learn more about kinematic equations and their applications in projectile motion.
  • Explore the relationship between work and energy in physics.
  • Investigate the effects of air resistance on the motion of thrown objects.
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Students studying physics, educators teaching mechanics, and anyone interested in understanding the principles of energy and motion in thrown objects.

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Please help... with Mechanical Energy Question

Homework Statement



A 0.50 kg rubber ball is thrown into the air. At a height of 20 m above the ground, it is traveling at 15 m/s.
a. what is the balls kinetic energy
b. What is its gravitational potential energy relative to the ground?
c. how much work was done by someone at ground level throwing the ball into the air?
d. What was the speed of the ball when it left the ground?


The Attempt at a Solution



a. Ek = 1/2 mv2
Ek = 1/2 (0.50kg)(15m/s)
Ek = 1/2 (0.50 kg)(225 m2/s2)
Ek = 1/2 (112.5 J)
Ek = 56 J

b. Eg = mgh
Eg = (0.50kg)(9.80 N/kg)(20m)
Eg = 98 J

c. W = fd
HELP ME PLEASE
 
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....d. Vf^2 = Vi^2 + 2ad Vf = 0m/s Vi = ? a = 9.8 m/s2 (acceleration due to gravity) d = 20m 0m/s = Vi2 + (2)(9.8 m/s2)(20m) Vi2 = -392 m2/s2 Vi = 19.8 m/s
 

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