A crate of mass 11.5 kg is pulled up a rough incline with an initial speed of 1.

Question

A crate of mass 11.5 kg is pulled up a rough incline with an initial speed of 1.50 m/s. The pulling force is 100 N parallel to the incline, which makes an angle of 16.0° with the horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled 4.30 m.

(a) How much work is done by gravity?
J
(b) How much mechanical energy is lost due to friction?
J
(c) How much work is done by the 100 N force?
J
(d) What is the change in kinetic energy of the crate?
J
(e) What is the speed of the crate after being pulled 4.30 m?
m/s

Explanation / Answer

( a )

W grav = - mgh

W grav = - mg * 4.3 sin 16 ;

W grav = - 11.5 * 9.8 * 4.3 sin 16 ;

W grav = -133.576 J <--------------ans

( b )

N = mg sin 16 ;

N = 11.5 * 9.8 * sin 16

N = 31.064 N ;

f = N ;

f = 0.4 * 31.064 = 12.4257 ,

E lost due to friction = 12.4257 * 4.3 = 53.4306 J ; <-----------ans

( c )

W = 100 * 4.3 = 430 J <------------ans

( d )

Work energy theorem ;

K = Wnet

K = W grav + W friction + W ( by 100N )

K = -133.576 + -53.4306 + 430

K = 242.9934 J ; <--------------ans

( e )

K = 242.9934 ;

m/2 [ v2^2 - v1^2 ] = 242.9934 ;

0.5 * 11.5 * ( v2^2 - 1.5^2 ) = 242.9934 ;

v2 = 6.671 m /s <---------ans

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