Solving for Ball Speed at Lowest & Highest Point of Arc

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SUMMARY

The discussion focuses on calculating the speed of a ball at the lowest and highest points of its swing along a circular arc, with specific parameters provided: a string length of 118.0 cm and a distance to the fixed peg of 99.1 cm. The potential energy (PE) and kinetic energy (KE) equations are applied, leading to a calculated speed of 1.52 m/s at the lowest point. The user initially miscalculated by not converting units correctly, as 118 cm equals 1.18 m. The correct application of energy conservation principles confirms the speed calculation.

PREREQUISITES
  • Understanding of potential energy (PE) and kinetic energy (KE) equations
  • Basic knowledge of gravitational acceleration (9.8 m/s²)
  • Ability to convert units (cm to m)
  • Familiarity with the principles of energy conservation in physics
NEXT STEPS
  • Review the derivation of energy conservation equations in mechanics
  • Learn about the effects of different heights on potential energy
  • Explore the concept of circular motion and its impact on speed
  • Investigate the role of friction and air resistance in real-world applications
USEFUL FOR

Students studying physics, educators teaching mechanics, and anyone interested in understanding the dynamics of swinging objects and energy conservation principles.

Trekky0623
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The string in the Figure is L = 118.0 cm long and the distance d to the fixed peg P is 99.1 cm. When the ball is released from rest in the position shown, it will swing along the dashed arc. How fast will it be going when it reaches the lowest point in its swing? What about the highest in its circular arc?

prob02a.gif

Relevant equations

PE = m * g * h
KE = (1/2)m * v2
Attempt
PE = m * g * h
PE = m * 9.8 m/s2 * .118 m
PE = KEBOTTOM = (1/2)m * v2
v2 = ((m * 9.8 m/s2 * .118 m)/((1/2)*m)))
v2 = ((9.8 m/s2 * .118 m)/(1/2))
v2 = 2 * 9.8 m/s2 * .118 m
v = SQRT(2 * 9.8 m/s2 * .118 m)
v = 1.52 m/s

I've only done this first part. I got 1.52 m/s, but the computer says I'm wrong. I was wondering if anyone could spot a problem in my equations.
 
Last edited:
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118 cm = 1.18 m. ehild
 
ehild said:
118 cm = 1.18 m.


ehild

Ah hah! Thank you so much. I feel silly.
 

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