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guajiro [1.7K]
3 years ago
13

A cat walks along a plank with mass M= 7.00 kg. The plank is supported by two sawhorses. The center of mass of the plank is a di

stance d1= 0.850 m to the left of sawhorse B. When the cat is a distance d2= 1.11 m to the right of sawhorse B, the plank just begins to tip.If the cat has a mass of 3.6 kg, how far to the right of sawhorse B can it walk before the plank begins to tip?
Physics
1 answer:
solong [7]3 years ago
5 0

Answer:

Before the plank will tip cat will walk 1.652 m

Explanation:

Mass of the cat along with plank m_1=7kg

Center of mass of the plank d_1=0.850m

Mass of cat m_2=3.6kg

We have to find how far right of sawhorse B.

Plank will tip when weight of the cat about B is greater than the torque by the weight of the plank.

Balancing the the torque

m_1gd_1=m_1gd_2

7\times 9.8\times 0.850=3.6\times 9.8\times d_2

d_2=1.652m

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Explanation:

To answer this question, let's analyze the problem. Let's use conservation of energy

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notice that we include the kinetic energy of translation and rotation

         

energy is conserved

        Em₀ = Em_f

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angular and linear velocity are related

         v = w r

         w = v / r

we substitute

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          v² = 2 gh   \frac{m}{m+ \frac{I}{r^2} }

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this is the velocity at the bottom of the plane ,, indicate that it stops from rest, so we can use the kinematics relationship to find the acceleration in the axis ax (parallel to the plane)

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         a = g \ \frac{h}{L} \  \frac{1}{1+ \frac{I}{m r^2 } }

let's use trigonometry

         sin θ = h / L

         

we substitute

         a = g sin θ   \ \frac{h}{L} \  \frac{1}{1+ \frac{I}{m r^2 } }

the moment of inertia of each object is tabulated, let's find the acceleration of each object

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      I = m r²

we look for the acerleracion

      a₁ = g sin θ    \frac{1}{1 + \frac{mr^2 }{m r^2 } }1/1 + mr² / mr² =

      a₁ = g sin θ    ½

b) solid cylinder

       I = ½ m r²

       a₂ = g sin θ  \frac{1}{1 + \frac{1}{2}  \frac{mr^2}{mr^2} } = g sin θ   \frac{1}{1+ \frac{1}{2} }

       a₂ = g sin θ   ⅔

c) hollow sphere

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     a₃ = g sin θ   \frac{1}{1 + \frac{2}{3} }

     a₃ = g sin θ \frac{3}{5}

d) solid sphere

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     a₄ = g sin θ  \frac{1 }{1 + \frac{2}{5} }

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a) a₁ = g sin θ ½ = g sin θ      \frac{105}{210}

b) a₂ = g sinθ ⅔ = g sin θ     \frac{140}{210}

c) a₃ = g sin θ \frac{3}{5}= g sin θ       \frac{126}{210}

d) a₄ = g sin θ \frac{5}{7} = g sin θ      \frac{150}{210}

the order of acceleration from lower to higher is

   

     a₁ <a₃ <a₂ <a₄

acceleration are

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