You are a member of an alpine resue team and must get a box of supplies, with a
ID: 1320929 • Letter: Y
Question
You are a member of an alpine resue team and must get a box of supplies, with a mass 2.50kg, up an incline of constant slope angle 30.0 degrees so that it reaches a stranded skier who is a vertical distance 2.50m above the bottom of the incline. There is some friction present; the kinetic coefficient of friction is 6.00 x 10 -2. Since you can't walk up the incline, you give the box a push that gives it an intitial velocity; then the box slides up the incline, slowing down under the forces of friction and gravity. Take acceleration due to gravity to be 9.81 m/s2. What is the velocity?
Explanation / Answer
the box is moving upwards
resolve force components on the box
incline of constant slope angle 30.0 degrees
force on the box due to gravity
=mg
=2.5*9.8
=24.5N
resolve force parllel and perpendicular to inclined plane
parllel component
=mgsin(theta)
=24.5*0.5
=12.25N
PERPENDICULAR COMPONENT
=mg cos(theta)
=24.5*0.866
=21.21N
normal component is canceled by perpendicularcomponent
force due to friction
=mu*FN
=0.06*
=1.2726N
net force equals to
Fnet=12.25-1.272
=10.978
accelration of box
Fnet=ma
a=Fnet/m
=10.978/2.5
=4.39m/s2
assuming intial velocity=0
h=0.5at2
2.5=0.5at2
t=1.066seconds
v=u+at
v=at
=4.39*1.066
=4.683m/s
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