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ame: Third Test, Page 3 of 5 April 4, 2018 3. The track shown has only a small r

ID: 2035737 • Letter: A

Question

ame: Third Test, Page 3 of 5 April 4, 2018 3. The track shown has only a small rough section, of lgth0.600m that offers friction between the track and the box with a coefficient of kinetic friction,H- 0.600. The track is otherwise smooth. After the rough patch, the track ends on a spring with a force constant k, 1666. /m lenght A box of mass m 93.75kg, initially at rest, is released from a height h 2.400m (I) (5 points) Draw the forces acting on the box as it moves through the rough patch, make a free body diagram for the box and find the value of the friction force, f (do not confuse with (II) (15 points) Find the speed of the box after leaving the rough patch.

Explanation / Answer

part I.

forces acting on the body area:

weight of the body=93.75*9.8=918.75 N, in vertically downward direction

normal force, in vertically upward direction=weight of the body=918.75 N

friction force=friction coefficient*normal force

=551.25 N

it is acting in direction opposite to the motion , hence to the left side.

free body diagram:

part II.

before the mass enters the rough patch:

let speed of the mass be m kg.

using conservation of energy principle:

initial potential energy+initial kinetic energy=final potential energy+final kinetic energy

==>mass*g*initial height+0.5*mass*initial speed^2=mass*g*final height+0.5*mass*final speed^2

==>93.75*9.8*2.4+0.5*93.75*0=93.75*9.8*0+0.5*93.75*v^2

==>v=6.8586 m/s

after the mass has passed through the rough patch:

let speed after it has gone through the rough patch is v m/s.

using work-energy principle:

kinetic energy before entering the rough patch -work done against friction=kinetic energy after the rough patch

==>0.5*93.75*6.8586^2-friction force*distance=0.5*93.75*v^2

==>2205-551.25*0.6=0.5*93.75*v^2

==>v=6.3233 m/s

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