Speed of a pendulum at lowest point

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SUMMARY

The speed of a pendulum bob at the lowest point of the swing, given an initial angle of θ=5.7° and a period of 2.5 seconds, can be calculated using the formula v=√(2gL(1-cosθ). The length of the pendulum was determined to be 1.552 meters using the equation T=2∏√(L/g) with g=9.81 m/s². The correct speed at the lowest point is v=0.388 m/s, achieved by ensuring the calculator is set to degrees when calculating trigonometric functions. The initial miscalculation of v=2.244 m/s was due to using radians instead of degrees.

PREREQUISITES
  • Understanding of pendulum mechanics and energy conservation principles
  • Familiarity with trigonometric functions and their applications in physics
  • Knowledge of the equations for kinetic energy (K.E.) and potential energy (P.E.)
  • Ability to perform calculations involving gravitational acceleration (g=9.81 m/s²)
NEXT STEPS
  • Review the derivation of the pendulum period formula T=2∏√(L/g)
  • Learn about the effects of angle on pendulum motion and energy conservation
  • Explore the use of trigonometric functions in physics calculations
  • Investigate common mistakes in calculator settings when performing physics calculations
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and energy conservation, as well as educators seeking to clarify pendulum motion concepts.

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Homework Statement



I am told to find the speed of a pendulum bob at the lowest point of the swing where the initial angle of displacement is θ=5.7° and the period of the pendulum is 2.5 seconds.

Homework Equations



K.E.=.5mv2, T=2∏√(L/g), P.E.=mgh, h=L-Lcosθ=L(1-cosθ)

The Attempt at a Solution



So I found the length of the pendulum first by plugging in 9.81 m/s2 for g and 2.5 s for T into the equation T=2∏√(L/g) to get 1.552 m.

Next, we know that the height displacement in a pendulum bob is equal to L-Lcosθ, so I plug this into P.E.=mgh, and also from conservation of energy we know P.E. can be set as .5mv2, so the final equation I used is:
v=√(2gL(1-cosθ))=√(2(9.81)(1.553(1-cos(5.7)))) which got me the answer v=2.244 m/s.

However the answer is apparently v=0.388 m/s. My teacher is kind of notorious for being wrong a lot of the time, so if somebody could let me know which answer is right and why that would be awesome, thanks.
 
Physics news on Phys.org
Did you set your calculator to degrees (DEG) to calculate sin(5.7°)?
 
Wow I feel stupid. Got the answer now, thanks.
 

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