State a two-part conclusion in which you describe the effect of the inclined angle upon the …

• amount of force required to pull the cart up the hill at a constant speed.

• amount of work done when pulling the cart up the hill at a constant speed.


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Respuesta :

Answer:

*he force to climb a plane inlcinado with constant velicad is equal to the cosine of the weight of the body

*he force to climb a plane inlcinado with constant velicad is equal to the cosine of the weight of the body

Explanation:

When a car is going up an inclined plane with constant speed, we can solve the problem using the translational equilibrium equation

Let's locate one axis parallel to the plane and the other perpendicular

     F - W x = 0

      F = W cos tea

       

therefore wes ee that the force to climb a plane inlcinado with constant velicad is equal to the cosine of the weight of the body

Work is defined by

       W = F. l

in this case the force and displacement are constant

       W = F L

where L is the length of the plane

       W = mgL cos tes

we see that the work is equal to the cosine of the force times the distance on the plane

The angle of inclination of the plane increases the force and work required to pull the cart up the hill increases.

  • Let the angle of inclination of the plane = θ
  • Let the force required to pull a cart up the hill = F
  • Let the work done when pulling the cart up the hill = W
  • Let the coefficient of friction between the cart and the hill = μ
  • Let the mass of the cart = m
  • Let acceleration due to gravity = g

The force required the pull the cart up at a constant speed is determined by applying Newton's second law of motion;

[tex]\Sigma F = 0\\\\-F -F_f = 0\\\\-F = F_f\\\\F=- \mu F_n\\\\F= -\mu mgcos\ \theta[/tex]

The work done when pulling the cart up the hill is calculated as;

[tex]W = -F\times d\\\\W = - \mu mg\ cos(\theta) \times d[/tex]

Thus, we can conclude that as the angle of inclination of the plane increases the force and work required to pull the cart up the hill increases.

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