CATAGORY: Mechanics QUESTION: A 10 Kg crate is pulled up a rough incline with an initial speed of 1.5 m/s. The pulling force is 100 N parallel to the incline, which makes an angle of 20 degrees with the horizontal. If the coefficient of kinetic friction is .4 and the crate is pulled a distance of 5 meters. a) what is the change in kinetic energy of the crate? b) what is the speed of the crate after it is pulled 5 meters? The text says the answer for a) is 150 Joules and for b)5.6 m/s. The wierd thing is that when I calculated these questions excluding friction those are the answers I got. When I formulated an equation including friction I got smaller numbers. Please help, I'm taking this independant study and have to figure everything out alone.Thanks.

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The figure below shows a SIDEWAYS  view of the incline

100N
\
\
rope \ \
\ \
\ \
blocks final       O \----> gravity force = mg
position            \b
\
\
\
10kg     \a=20 degrees
block-->O \
|
initial position
|
|

The angle b = 90 degrees - 20 degrees = 70 degrees.  The force of
gravity pulling the block down the incline is mgcos(b) = mgcos(70
degrees) = mg sin(20) and is directed down the incline.  The force of
friction is also directed down the incline and is equal to the normal
force which here is mg cos(20) times the coefficient of friction.  The
net force on the block in the direction of the incline is

(1) F(net) = 100N - mg sin(20) - Uk mg cos(20)

= 100N -10kg 9.8m/s^2 sin(20) - .4 10kg 9.8m/s^2 cos(20)

= 100N - 33.52N - 36.84N

= 29.91N

The work done on moving the block 5 meters up the
incline is then

(2) Work = F(net) x 5.00m = 149.55J

thus we have

(3) KE(initial) + PE(initial) - Non conservative work

= KE(final) + PE(final)

But

(4)   PE(final) - PE(initial) + Non conservative work

= Work = 149.55J ~ 150 J

so

(5)  KE(final)-KE(initial) =

PE(final) - PE(initial) + Non conservative work = 150 J

the final speed is given by solving (5) for KE(final) and then
for v(final)

(6) KE(final) = 150J -KE(initial)

= 150J - 1/2 10kg(1.5m/s)^2

= 138.75 J

thus since KE(final) = 1/2 m (v(final))^2 with m =10Kg

(7)  1/2 10Kg (v(final))^2 = 138.75 J

we have

(8) v(final) = 5.26 m/s

********************************
*                              *
* KE(final)-KE(initial) = 150J *
*                              *
*  v(final) = 5.26m/s          *
*                              *
********************************

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