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Jim Jefferies wishes to lift a 2m barbell that is loaded with:

- Two 20kg plates on its left side, positioned 20cm and 25cm from the end of the bar.
- One 20kg plate and two 10kg plates on its right side, with the 20kg plate 26cm from the end, and the two 10kg plates 21cm and 17cm from the end.

The unloaded mass of the barbell is 20kg. The axis of rotation is at the center of the bar.

Where is the center of gravity of the loaded barbell?

Answer :

Final answer:

The centre of gravity of the loaded barbell is located approximately 0.257m from the axis of rotation.

Explanation:

To find the centre of gravity of the loaded barbell, we need to calculate the moments of each plate and sum them up. The moments can be calculated by multiplying the mass of each plate by its distance from the axis of rotation.

Let's calculate the moments of the plates on the left side:

  • The moment of the first 20kg plate is 20kg * 0.2m = 4kgm
  • The moment of the second 20kg plate is 20kg * 0.25m = 5kgm

Now, let's calculate the moments of the plates on the right side:

  • The moment of the 20kg plate is 20kg * 0.26m = 5.2kgm
  • The moment of the first 10kg plate is 10kg * 0.21m = 2.1kgm
  • The moment of the second 10kg plate is 10kg * 0.17m = 1.7kgm

To find the centre of gravity, we need to sum up the moments and divide by the total mass of the barbell:

Total moment = (4kgm + 5kgm + 5.2kgm + 2.1kgm + 1.7kgm) = 18kgm

Total mass = 20kg + 20kg + 10kg + 10kg + 10kg = 70kg

Centre of gravity = Total moment / Total mass = 18kgm / 70kg = 0.257m

Therefore, the centre of gravity of the loaded barbell is located approximately 0.257m from the axis of rotation.

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