What is the Kinetic Energy of a Pulley System with Bodies B1, B2, and B3?

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SUMMARY

The kinetic energy of a pulley system consisting of bodies B1, B2, and B3 can be calculated using the formulas for translational and rotational kinetic energy. Given the parameters, B1 has a mass of 32.2 lb and a speed of 5 ft/sec, while B2 and B3 also have respective masses of 32.2 lb and 96.6 lb. The calculated kinetic energy for B1 is 402.5 ft-lb, for B2 is 201.25 ft-lb, and for B3 is 1207.5 ft-lb. However, the total kinetic energy of the system is confirmed to be 25 ft-lb, indicating a misunderstanding in the calculations or unit application.

PREREQUISITES
  • Understanding of translational kinetic energy formula: K = 1/2mv²
  • Knowledge of rotational kinetic energy formula: K = 1/2Iw²
  • Familiarity with units of measurement, specifically foot-pounds (ft-lb)
  • Basic principles of mechanics related to pulley systems
NEXT STEPS
  • Review the principles of energy conservation in mechanical systems
  • Study the application of the rotational inertia (I) in kinetic energy calculations
  • Learn about the relationship between torque and energy units
  • Explore advanced topics in pulley systems and their dynamics
USEFUL FOR

Students in physics or engineering courses, educators teaching mechanics, and anyone interested in understanding kinetic energy calculations in pulley systems.

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Homework Statement


http://s2.webstarts.com/exploring-my-thought/index.html

Find the kinetic energy of the system of bodies B1, B2 and B3 at an instant when the speed of B1 is 5ft/sec (the image is linked above)

radius of B2 = 2ft
mass of B1 = 32.2lb
mass of B2 = 32.2lb
mass of B3 = 96.6lb

answer is 25ft-lb

Homework Equations


translational kinetic energy: K = 1/2mv2
rotational kinetic energy: K = 1/2Iw2

The Attempt at a Solution



B1 = 1/2(32.2)(5)^2 = 402.5 ft-lb
B2 = 1/2((mr^2)/2)(5/2) = 201.25 ft-lb
B3 = 1/2(96.6)(5)^2 = 1207.5 ft-lb

My answers are way off, what am I doing wrong?
 
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How can energy be measured in ft-lb? That doesn't make sense unit wise.

A ft-lb is a unit of torque...
 
Matterwave said:
How can energy be measured in ft-lb? That doesn't make sense unit wise.

A ft-lb is a unit of torque...


Work = force * distance right?

force unit:lb
distance unit :ft
 

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