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An object with mass m = 20 kg, is moving with V = ct (constant velocity) on the distance d = 60 m on a horizontal surface. The friction coefficient is μ = 0.45. Force applied to the object makes an angle ά = 30° with the horizontal

An object with mass m = 20 kg, is moving with V = ct (constant velocity) on the distance d = 60 m on a horizontal surface. The friction coefficient is μ = 0.45. Force applied to the object makes an angle ά = 30° with the horizontal.

find out:

a) the force applied to the object;
b) the mechanical work, made by force of traction upon the object (g = 10 m / s2)


Solution

a) the force applied to the object:

F = m (a + μg) / cos ά + μ * sin ά                  we know that     a = ct

=> F = μmg / cos ά + μ *sin ά
=> F  = 0,45 * 20 * 10 m / s2 / cos 30o + 0,45 * sin 30o
=> F  = 0,45 * 20 * 10 m / s2 / √3/2 + 0,45 * 0,5
=> F  ≈ 83 N (newton)


b) the mechanical work, made by force of traction upon the object (g = 10 m / s2):

L = F * d * cos ά
L = 83 N * 60 m * cos 30o

L = 4280 j (joul)

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