Question

You are working for a shipping company. Your job is to stand at the bottom of a 7.1m -long ramp that is inclined at 39? above the horizontal. You grab packages off a conveyor belt and propel them up the ramp. The coefficient of kinetic friction between the packages and the ramp is ?k=0.30.

Answer 1

You need to draw a picture of what is going on. From this the following equation can be derived

F + mgsin Theta - ?k *mg cos Theta = 0

where F is the driving force , m is the mass of package, g is the acceleration due to gravity, ?k is the coefficient of kinetic friction, and theta is the angle of the ramp. The mgsin Theta represents component of weight acting with the driving force, and ?k *mg cos Theta represent the friction acting against the driving force.

F= mg (?k cos theta - sin theta)

F= 5*9.81 (0.31 *cos 12 - sin 12) = 49.05*(0.30302257-0.2079116908) = 4.675N

Work done = Force* distance moved

work done = 4.675 *1.5 = 7.0125J

From the force we can calculate the acceleration of the package by using F=ma

a= F/m= 4.675/5= 0.935 m/s.

We can calculate the velocity at the end of the slide by

v^2 = u^2 + 2as

where v and U are the final and initial velocity of parcel respectively , acceleration, s is distance.

v^2 = 2.2^2 + 2*0.935*1.5

v^2 = 4.84 +2.805

v^2= 7.645

v= 2.76 m/s.