30.0-kg child sits on one end of a long uniform beam having a mass of 20.0 kg, and a 40.0-kg child sits on the other end. the beam balances when a fulcrum is placed below the beam a distance 1.10 m from the 30.0-kg child. how long is the beam? a 30.0-kg child sits on one end of a long uniform beam having a mass of 20.0 kg, and a 40.0-kg child sits on the other end. the beam balances when a fulcrum is placed below the beam a distance 1.10 m from the 30.0-kg child. how long is the beam? 2.07 m 1.93 m 2.12 m 2.20 m 1.98 m

Question

08-11-2022
Physics

Answered

30.0-kg child sits on one end of a long uniform beam having a mass of 20.0 kg, and a 40.0-kg child sits on the other end. the beam balances when a fulcrum is placed below the beam a distance 1.10 m from the 30.0-kg child. how long is the beam? a 30.0-kg child sits on one end of a long uniform beam having a mass of 20.0 kg, and a 40.0-kg child sits on the other end. the beam balances when a fulcrum is placed below the beam a distance 1.10 m from the 30.0-kg child. how long is the beam? 2.07 m 1.93 m 2.12 m 2.20 m 1.98 m

Answer :

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Qwbox Qwbox · Answer 1 · 2022-11-14T12:04:04-05:00

The length of the beam on which the the two boys are lying is 1.01 m.

The mass of one kid is 30 kg and the mass of the beam is 20kg, the beam is balanced at a distance of 1.10 m from the 30 kg boy when a 40kg boy was sitting at the other end of the beam.

If the beam is balanced at 1.10 m from the 30kg boy it means that there lies the center of mass of the system.

So, let us assume the length of the beam to be X meters and the assume the center of mass to be at center.

So,

0 = M₁X₁ + M₂X₂/M₁+M₂

M₁ is 30kg and X₁ is 1.10m.

M₂ is 40kg and the X₂ is (X-1.10)m.

Putting values,

0 = 30 x 1.1 + 40 x (X-1.1)

(1.1 - X)40 = 3.3

X = 1.01 m.

So, the length of the Beam is 1.01 m.

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