A 1.9 m-long barbell has a 25 kg weight on its left end and a 37 kg weight on its right end. A) If you ignore the weight of the bar itself, how far from the left end of the barbell is the center of gravity? Express your answer using two significant figures. B) Where is the center of gravity if the 8.0 kg mass of the barbell itself is taken into account? Express your answer using two significant figures.

Question

Kathy Case

Physics

3 June, 17:07

A 1.9 m-long barbell has a 25 kg weight on its left end and a 37 kg weight on its right end. A) If you ignore the weight of the bar itself, how far from the left end of the barbell is the center of gravity? Express your answer using two significant figures. B) Where is the center of gravity if the 8.0 kg mass of the barbell itself is taken into account? Express your answer using two significant figures.

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Answers (1)

Know the Answer?

Brooke Ali · Answer 1

A. 1.13m

B. 1.12m

Explanation:

Parameters given:

Length of barbell = 1.9m

Mass of weight on the left = 25kg

Mass of weight on the right = 37kg

A. The centre of gravity is defined as the sum of moments divided by the total weight of a body.

Hence, ignoring the weight of the barbell,

CoG = (mx + MX) / (m + M)

Where m = mass on the left

x = distance of the left weight from origin

M = mass on the right

X = distance of the right weight from origin.

Choosing the left edge of the weight as the origin,

CoG = [ (25*0) + (37 * 1.9) ] / (25 + 37)

= (0 + 70.3) / 62

= 70.3/62

= 1.13m

Hence, the centre of gravity is 1.13 m from the left edge of the barbell.

B. Taking the 8kg mass of the barbell into consideration,

CoG = (mx + MX + wc) / (m + M + w)

Where w = mass of barbell

c = centre of barbell

CoG = [ (25 * 0) + (37 * 1.9) + (8 * 0.98) / (25 + 37 + 8)

= (0 + 70.3 + 7.84) / (70)

= 78.14/70

= 1.12m

Hence, the centre of gravity would be 1.12m from the left edge of the barbell, if we consider the mass of the barbell.