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Trava [24]
3 years ago
5

Un bloque de 750 kg es empujado hacia arriba por una pista inclinada 15º respecto de la horizontal. El coeficiente de rozamiento

es 0.4. Determinar la fuerza necesaria para iniciar la subida del bloque por la pista.
Physics
1 answer:
kotegsom [21]3 years ago
8 0

Answer:

4776.98 N is the minimum force to start the rise.  

Explanation:

We can use the first Newton's law to find the minimum force to move the block.

So we will have:

F-W_{x}-F_{f}=0

Where:

  • F is the force
  • W(x) is the weight of the block in the x direction, W = mg*sin(15)
  • F(f) is the static friction force (F(f) = μN), μ is the static friction coefficient 0.4.

F=W_{x}+F_{f}=mgsin(15)+\mu N

F=mgsin(15)+\mu mgcos(15)

F=mg(sin(15)+\mu cos(15))

F=750*9.81(sin(15)+0.4*cos(15))

F=4776.98 N

Therefore 4776.98 N is the minimum force to move the block.

I hope it helps you!

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Answer:

(a) Ascend at 0.8 vertical meter/meter

(b) Descend at -0.2·√2 vertical meter/meter

(c) In the (-0.6, -0.8) direction. The path begins at 45° to the horizontal

Explanation:

The given equation of the shape of the hill is z = 2000 - 0.005·x² - 0.01·y²

The current location = (60, 40, 1966)  

The direction of the positive x-axis = east

The direction of the positive y-axis = north

(a) Walking due south = Reducing the y-value 40

From the equation, the elevation varies inversely with the motion towards the north

Therefore, walking south increases the elevation, and we ascend

The rate is given by the partial derivative at in the -j direction, which is 0.02

The rate is therefore 40 × 0.02 = 0.8

(b)The unit vector in the northwest direction u = 1/√2·(-1, 1)

∴ The rate = (-0.01(60), -0.02(40))·u = (-0.6, -0.8)·1/√2·(-1, 1) = -0.2·√2

Therefore we descend

(c) The slope is largest in the grad of the function at the point (60, 40) which is given as follows;

d(2000 - 0.005·x² - 0.01·y² )/dx, d(2000 - 0.005·x² - 0.01·y² )/dy = (-0.6, -0.8)

Therefore, the direction is tan⁻¹(-0.8/-0.6) ≈ S 36.87° W

The slope =(√((-0.4)² + (-0.8)²) = 1

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A red train travelling at 72 km/h and a green train travelling at 144 km/h are headed toward each
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Answer:

  Collision will occur.

  Speed of red train when they collide = 0 m/s.

  Speed of green train when they collide = 10 m/s.

Explanation:

Speed of red train = 72 km/h = 20 m/s

Speed of green train = 144 km/h = 40 m/s.

Deceleration of trains = 1 m/s²

For red train:-

    Equation of motion v = u + at

              u = 20 m/s

              v = 0 m/s

              a = -1 m/s²

    Substituting

             0 = 20 - 1 x t

             t = 20 s.

    Equation of motion s = ut + 0.5at²

              u = 20 m/s

              t = 20 s

              a = -1 m/s²    

    Substituting

             s = 20 x 20 - 0.5 x 1 x 20² = 200 m

   So red train travel 200 m before coming to stop.

For green train:-

    Equation of motion v = u + at

              u = 40 m/s

              v = 0 m/s

              a = -1 m/s²

    Substituting

             0 = 40 - 1 x t

             t = 40 s.

    Equation of motion s = ut + 0.5at²

              u = 40 m/s

              t = 40 s

              a = -1 m/s²    

    Substituting

             s = 40 x 40 - 0.5 x 1 x 40² = 800 m

   So green train travel 800 m before coming to stop.

 Total distance traveled = 800 + 200 = 1000 m>950 m.

  So both trains collide.

  Distance traveled by green train when red train stops(t=20s)

     Equation of motion s = ut + 0.5at²

              u = 40 m/s

              t = 20 s

              a = -1 m/s²    

    Substituting

             s = 40 x 20 - 0.5 x 1 x 20² = 600 m

    Total distance after 20 s = 600 + 200 = 800 m< 950m . So they collide after red train stops.

  Speed of red train when they collide = 0 m/s.

  Distance traveled by green train when they collide = 950 - 200 = 750 m

  Equation of motion v² = u² + 2as

              u = 40 m/s

              s= 750 m

              a = -1 m/s²    

    Substituting  

              v² = 40² - 2 x 1 x 750 = 100

               v = 10 m/s

  Speed of green train when they collide = 10 m/s.

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