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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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Answer:

The total momentum before and after collision is 72000 kg-m/s.

Explanation:

Given that,

Mass of car = 1200 kg

Velocity of car = 10 m/s

Mass of truck = 2000 kg

Velocity of truck = 30 m/s

Using conservation of momentum

The total momentum before the collision is equal to the total momentum after collision.

m_{1}v_{1}+m_{2}v_{2}=(m_{1}+m_{2})V

Where, m_{1}=mass of car

v_{1} =velocity of car

m_{1}=mass of truck

v_{1} =velocity of truck

Put the value into the formula

1200\times10+2000\times30=(1200+2000)V

V=\dfrac{1200\times10+2000\times30}{(1200+2000)}

V = 22.5\ m/s

Now, The total momentum before collision is

P=m_{1}v_{1}+m_{2}v_{2}

P=1200\times10+2000\times30

P=72000\ kg-m/s

The total momentum after collision is

P=(m_{1}+m_{2})v_{2}

P=(1200+2000)\times22.5

P= 72000 kg-m/s

Hence, The total momentum before and after collision is 72000 kg-m/s.

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a ball of mass 0.80 kg moving at a speed of 2.5 m/s along a straight line collided with a mass 2.5 kg which was initially statio
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The speed of the 0.8 kg ball immediately after collision is 0.625 m/s in opposite direction to the stationary ball.

The given parameters;

  • mass of the ball, m₁ = 0.8 kg
  • speed of the ball, u₁ = 2.5 m/s
  • mass of the object at rest, m₂ = 2.5 kg
  • final velocity of the object at rest, v₂ = 1 m/s

Let the final velocity of the 0.8 kg ball immediately after collision = v₁

Apply the principle of conservation of linear momentum;

m₁u₁ + m₂u₂ = m₁v₁  +  m₂v₂

(0.8 x 2.5) + (2.5 x 0) = (0.8)v₁  +  2.5(1)

2 = 2.5 + (0.8)v₁

-0.5 = (0.8)v₁

v_1 = \frac{-0.5}{0.8} \\\\v_1 = -0.625 \ m/s

Thus, the speed of the 0.8 kg ball immediately after collision is 0.625 m/s in opposite direction to the stationary ball.

Learn more here: brainly.com/question/7694106

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2 years ago
Suppose that a tiny space invader (m=0.47 kg) and the new space station orbit Earth at the same height from Earth’s surface. Whi
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The tiny space invader and the new space station will have equal orbital speed.

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The orbital speed of satellite on Earth surface is given as;

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where;

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Since the two objects are at the same height from Earth's surface, the distance from the central point (r) will be the same. Thus, the two objects will have equal orbital speed.

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The sun delivers an average power of 1.499 w/m2 to the top of neptune's atmosphere. find the magnitudes of vector e max and vect
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Suppose we hang a heavy ball with a mass 13 kg (so the weight is ) from a steel wire 3.9 m long that is 3.1 mm in diameter (radi
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Answer:

1.635×10^-3m

Explanation:

Young modulus is the ratio of the tensile stress of a material to its tensile strain.

Young modulus = Tensile stress/tensile strain

Tensile stress = Force/Area

Given force = 130N

Area = Πr² = Π×(1.55×10^-3)²

Area = 4.87×10^-6m²

Tensile stress = 130/4.87×10^-6 = 8.39×10^7N/m²

Tensile strain = extension/original length

Tensile strain = e/3.9

Substituting in the young modulus formula given young modulus to be 2×10¹¹N/m²

2×10¹¹N/m² = 8.39×10^7/{e/3.9)}

2×10¹¹ = (8.39×10^7×3.9)/e

2×10¹¹e = 3.27×10^8

e = 3.27×10^8/2×10¹¹

e = 1.635×10^-3m

The stretch of the steel wire will be

1.635×10^-3m

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4 years ago
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