A crate of mass 5kg is pushed up a rough incline by means of a horizontal pushing force of constant magnitude 50N. The incline makes an angle 30° with respect to the horizontal and has a coefficient of kinetic friction 0.2 with the surface of the crate. The crate moves a distance 3m along the incline. Find a) the work done on the crate by gravity. b) the work done on the crate by the pushing force. c) the work done on the crate by the normal force. d) the work done on the crate by friction. e) the final speed of the crate if the crate started from rest

Explanation:

a ) work done by gravity = - mg sinθ x d

= - 5 x 9.8 x sin 30 x 3 = - 73.5 J

b ) Work done by pushing force

= 50 con 30 x d = 50 cos 30 x 3 = 130 J approx .

c ) work done by normal force on crate will be zero as it is acting normal to the displacement .

d ) work done by friction

-  mg cos 30 x μ x d where μ is coefficient of friction .

= - 5 x 9.8 x .866 x .2 x 3 = - 25.4 J

e ) net force on the crate = F con30 - mg sin 30 - mg cos 30 x .2

= 50 x .866 - 5 x 9.8 x .5 - 5 x 9.8 x .866 x .2

= 43.3 - 24.5 - 8.5

= 10.3 N

acceleration = 10.3 / 5 = 2.06

v² = u² + 2 a s

v² = u² + 2 x 2.06 x 3

v² = 12.36

v = 3.5 m /s

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