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jenyasd209 [6]
3 years ago
15

A thin rod (length = 1.09 m) is oriented vertically, with its bottom end attached to the floor by means of a frictionless hinge.

The mass of the rod may be ignored, compared to the mass of the object fixed to the top of the rod.
The rod, starting from rest, tips over and rotates downward.

(a) What is the angular speed of the rod just before it strikes the floor?

(Hint: Consider using the principle of conservation of mechanical energy.)

(b) What is the magnitude of the angular acceleration of the rod just before it strikes the floor?
Physics
1 answer:
Murljashka [212]3 years ago
5 0

Answer:

a) w = 4.24 rad / s , b) α  = 8.99 rad / s²

Explanation:

a) For this exercise we use the conservation of kinetic energy,

Initial. Vertical bar

        Emo = U = m g h

Final. Just before touching the floor

       Emf = K = ½ I w2

As there is no friction the mechanical energy is conserved

       Emo = emf

       mgh = ½ m w²

The moment of inertial of a point mass is

        I = m L²

       m g h = ½ (m L²) w²

       w = √ 2gh / L²

The initial height h when the bar is vertical is equal to the length of the bar

         h = L

         w = √ 2g / L

Let's calculate

       w = RA (2 9.8 / 1.09)

       w = 4.24 rad / s

b) Let's use Newton's equation for rotational motion

         τ = I α

         F L = (m L²) α

The force applied is the weight of the object, which is at a distance L from the point of gro

         mg L = m L² α  

          α  = g / L

          α  = 9.8 / 1.09

          α  = 8.99 rad / s²

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2NaOH+H2SO4 Na2SO4+H2O the equation is balanced/unbalanced because the number of hydrogen atoms and oxygen/sodium is equal/not e
RUDIKE [14]
Your equation is:
2NaOH + H_{2}SO_{4}  ==\ \textgreater \  Na_{2}SO_{4} + H_{2}O

An equation is balanced only if there are the same number of atoms of each element on both sides of the arrow - aka same number of atoms of each element in both reactants (left of the arrow) and products (right of the arrow). 

It'll be easiest to tackle this by counting up the number of atoms of each element on the left and on the right and comparing those numbers. If there is a number in front of the entire compound, that means that number applies to all elements in the compound. If the number is a subscript (little number to the right of the element), that means that number only applies to the element that the subscript is attached to:
1) On the left, you have:
2NaOH + H_{2}SO_{4}\\
\\
Na:  \: 2 \: atoms\\
O: \: 2 + 4 = 6 \: atoms\\
H: \: 2 + 2 = 4 \: atoms\\
S:  \: 1 \: atom

2) On the right, you have:
Na_{2}SO_{4} + H_{2}O\\
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Na: \: 2 \: atoms\\ 
O: \: 4 + 1 = 5 \: atoms\\ 
H: \: 2 \: atoms\\ 
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You can see that the number of oxygen and hydrogen atoms aren't equal on both the left (reactants) and the right (products), so the equation is unbalanced.

Your final answer is "T<span>he equation is unbalanced because the number of hydrogen atoms and oxygen is not equal in the reactants and in the products."</span>


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svlad2 [7]
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Therefore, the higher the kinetic energy, the higher the thermal energy in the system and the higher the temperature.

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