A mass m = 16 kg is pulled along a horizontal floor with NO friction for a dista

Question

A mass m = 16 kg is pulled along a horizontal floor with NO friction for a distance d = 7.7 m. Then the mass is pulled up an incline that makes an angle theta = 34 degree with the horizontal and has a coefficient of kinetic friction mu = 0.43. The entire time the massless rope used to pull the block is pulled parallel to the incline at an angle of theta = 34 degree (thus on the incline it is parallel to the surface) and has a tension T = 75 N. What is the work done by tension before the block goes up the incline? (On the horizontal surface.) What is the speed of the block right before it begins to travel up the incline? What is the work done by friction after the block has traveled a distance x = 3.6 m up the incline? (Where x is measured along the incline.) What is the work done by gravity after the block has traveled a distance x = 3.6 m up the incline? (Where x is measured along the incline.)

Explanation / Answer

1) Work done on the horizontal is W = F*S*cos(theta) = 75*7.7*cos(34) = 478.76 J

2) if it is starts from zero

Work done by the net force = change in kinetic energy

W = 0.5*m*(V^2-Vo^2)

478.76 = 0.5*16*(V^2-0^2)

V = 7.74 m/sec

3) work done by the frictional force is W = -fk*S = -mu_k*m*g*cos(34)*S

W = -mu_k*m*g*cos(theta)*S = -0.43*16*9.8*cos(34)*3.6 = -201.22 J

4) Work done by the gravitational force is W = -m*g*sin(34)*S = -16*9.8*sin(34)*3.6

W = -315.65 J

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