Home Expression

Home Expression
Derive an expression for home much work kinetic friction does on the block…?

At time t1 = 0, a 2.00 kg block is initially moving horizontally in a straight line at 3.00 m/s on a surface where the coefficient of kinetic friction between the block and surface is μk = 0.40. The block comes to a stop after traveling a distance D at some time t2 > 0.

(a) Derive an expression for how much work kinetic friction does on the block between t1 = 0 and the time t2 at which the block stops.

(b) Using the Work-Energy Theorem, calculate D.

(c) Now calculate D using constant acceleration formulas. The answer should be the same as in part (b).

Any help would be appreciated!!

for a)
the object starts with an initial kinetic energy of 1/2*m*v^2
=1/2*2*3^2=9J
then object end with a KE of 0J because it is at rest. so the net change in kinetic energy is 0-9 = -9J
Now, remember that W=⌠Fdx=Fx because the force does not change.
So F=-Wµk=-mgµk=2*9.81*.4=-7.848N
so FD=-9
-7.848D=-9
D=1.147m
for c) F=-7.848N=ma=2a, a=-3.924m/s^2,
0=Vo+at, 0=3-3.924t
t=.7645 seconds.
So X=Xo+Vot+1/2at^2
X=0+3* .7645+1/2*3.924* .7645^2
X=1.147m
I hope this helps!

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