- #1
shmoop
Homework Statement
Hi! I'm having issues with this practice problem. Any advice on what I'm doing wrong would help!
A 2.5 kg particle is projected with an initial speed of 3.3m/s along a surface for which the coefficient of friction is 0.7. Find the distance it travels given that the particle moves up a 26 degree incline.
Homework Equations
W=ΔKE
W=F*d
Ff=μFn
W=ΔKE+ΔPE
KE=1/2mv2
PE=mgh
The Attempt at a Solution
mg=2.5kg*-9.8m/s2=-24.5N
-24.5Nsin26=-10.74 N = mgx
-24.5Ncos26=-22.02N = mgy
ΣFy=0=Fn-mgy
Fn= 22.02 N
Ff = Fnμ
Ff = 22.02N*0.7
Ff=15.14 N
W= KEf-KEf+PEf-PEi
W=.5mv2-.5mv2+mgh-mgi
W=0.5*0.3kg*(3.3m/s)2-0+2.5kg*9.8*h-0
W=F*d
Here I assumed KEf was 0 because the final velocity is 0, and I assumed PEi was 0 because the inital height is 0.
The forces applied that aren't in equilibrium are mgx, and Ff.
W= (-15.14N-10.74N)*d
-26.15N*d=0.5*0.3kg*(3.3m/s)2-0+2.5kg*9.8*h
So instead of having 2 unknown variables, I made h equal to...
h= d*sin26
So.. I inserted that in the previous equation:
-26.15N*d=0.5*0.3kg*(3.3m/s)2-0+2.5kg*9.8*d*sin26
Factored out d...
d(-26.15+24.5sin26)=-13.6125
d=-13.6125/(-26.15+24.5sin16)
d=0.88m
And this answer is incorrect. I am unsure where I went wrong... Any thoughts? Thank you!
For an image of what my free body diagram looks like, I posted it below!
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