Law of conservation, and efficiency problem?

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SUMMARY

The discussion focuses on calculating the maximum speed of a pendulum bob using the law of conservation of energy, specifically for a 200g bob raised 22cm. The gravitational potential energy (PE) is calculated using the formula eg = mgh, resulting in 0.4312 joules. Since the efficiency is assumed to be 100%, this potential energy is entirely converted into kinetic energy (KE) at the lowest point, allowing for the calculation of maximum speed using the equation ek = (mv²)/2.

PREREQUISITES
  • Understanding of gravitational potential energy (PE) and kinetic energy (KE)
  • Familiarity with the law of conservation of energy
  • Basic algebra for solving equations
  • Knowledge of units of mass (kilograms) and height (meters)
NEXT STEPS
  • Calculate maximum speed using the formula v = sqrt(2 * eg / m)
  • Explore the impact of efficiency on energy conversion in pendulum systems
  • Investigate real-world applications of the conservation of energy in mechanical systems
  • Learn about energy loss factors in pendulum motion, such as air resistance and friction
USEFUL FOR

Students studying physics, educators teaching energy concepts, and anyone interested in understanding mechanical energy transformations in pendulum systems.

raininggently
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Homework Statement


A 2.0x10^2 g pendulum bob is raised 22cm above its rest position.The bob is released, and it reaches its maximum speed as it passes the rest position.

Calculate its maximum speed at that point by applying the law of conservation of energy and assuming that the efficiency is 100%.


Homework Equations


-eg=mgh
-ek=(mv^2)/2
-et=eg+ek
-eff=eoutput/einput x 100%


The Attempt at a Solution


-m=2.0 x 10^2 = 0.200 kg
-h=22cm=0.22 m
I know the law of conservation states when energy is changed from one form to another no energy is lost.

I tried using ek=(mv^2)/2 but I didn't know what ek so I coulden't solve for V.

eg=mgh
eg=(0.200kg)(9.8)(0.22)
eg=0.4312 j

I don't know what to do from here :o
eg=(
 
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raininggently said:

Homework Statement


A 2.0x10^2 g pendulum bob is raised 22cm above its rest position.The bob is released, and it reaches its maximum speed as it passes the rest position.

Calculate its maximum speed at that point by applying the law of conservation of energy and assuming that the efficiency is 100%.


Homework Equations


-eg=mgh
-ek=(mv^2)/2
-et=eg+ek
-eff=eoutput/einput x 100%


The Attempt at a Solution


-m=2.0 x 10^2 = 0.200 kg
-h=22cm=0.22 m
I know the law of conservation states when energy is changed from one form to another no energy is lost.

I tried using ek=(mv^2)/2 but I didn't know what ek so I coulden't solve for V.

eg=mgh
eg=(0.200kg)(9.8)(0.22)
eg=0.4312 j

I don't know what to do from here :o
eg=(

When a pendulum swings there is a repeated interchange of Kinetic Energy and Gravitaional Potential Energy.
When it was to the side - 22 cm higher than rest position, it was all PE.
When it swings past the middle position, all that energy has been transformed into KE.
 

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