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A man sets into motion on the surface, an object with mass m = 20 kg acting on it with a force of F = 50 N (Newton), whose direction makes with the horizontal angle ά = 37o (cos 37o = 0 8). Human action on the object takes 3 seconds. Neglecting friction forces, calculate the mechanic work performed by the man on the object.

A man sets into motion on the surface, an object with mass m = 20 kg acting on it with a force of F = 50 N (Newton), whose direction makes with the horizontal angle ά = 37o (cos 37o = 0,8). Human action on the object takes 3 seconds. Neglecting friction forces, calculate the mechanical work performed by the man on the object.

Solution:

a) For the calculation of the movement of the object, first we calculate the object's acceleration by using the fundamental relation of dynamics:

N + mg + F = ma  (rel. 4.4)

Designing rel. 4.4. the direction of movement (direction on Ox) we get:

Fx = F cos ά  = ma

then:

a = 50N * 0,8 / 20 kg = 2 m / s2

In 3 seconds the object has moved on the distance:

d = Vot + ½  * at2 = ½ * 2 * 9 = 9 m
Vo = 0

  1.  After we apply the relation, the mechanical work is:
L = Fd* cos ά => 50 * 9 * 0,8 = 360j (jouli)


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