Solving for Moving a 100kg Box on a Ramp | Static and Kinetic Friction

[skittlez411]

force! help me please =)

Homework Statement

It's moving day and you need to push a 100kg box up a 20 degree ramp into the truck. The coefficients of friction for the box on the ramp are Us=0.9 and Uk=0.6. Your largest pushing force is 1000N. Can you get the box into the truck without assistance if you get a running start at the ramp? If you stop on the ramp, will you be able to get the box moving again?

Homework Equations

Fk=Ukmg
F=mgsin20

The Attempt at a Solution

a) Fk=(0.6)(100)(9.8)
=588N

F=mgsin20
=335N

yes, my maximum pushing force is 1000N. 335N<1000N

b) Fs=Usmg
=882N

Yes. I will be able to get the box moving again because I have enough force to overcome the static force.

thank you!

 

[Doc Al]

Fk=Ukmg

Careful here! Fk = Uk N, where N is the normal force. Since the mass is on an incline, the normal force is not just mg.

 

[skittlez411]

ok... so i got

a) Fk=ukmgsin20
= 201.11 N

so if i get a running start i would be able to move the box up w/o assistance.

b) Fs= Usmgsin20
= 301.66 N

If i stop at the ramp, i will be able to get the box moving agian.. 301.66N<1000N

is that it? thanks!

 

[pcdagr8]

N is mgcos 20

 

[skittlez411]

N is mgcos 20

can i ask why? i thought it's sine...

 

[pcdagr8]

N is normal reaction ,component of gravity perpendicular to the surface
when you are taking the component of gravity parallel to the surface as mgsin20
how are you missing out that perpendicular component will be mg cos20
just draw a free body diagram and resolve the forces...

 

[skittlez411]

hmmm... i still don't quite get it. i know how sine and cosine are. but i don't quite get the diagram... sorry!

 

[Astronuc]

Try these

http://hyperphysics.phy-astr.gsu.edu/hbase/N2st.html

in particular

http://hyperphysics.phy-astr.gsu.edu/hbase/faia.html

with friction

http://hyperphysics.phy-astr.gsu.edu/hbase/faia2.html

 

[pcdagr8]

well...i can't help u with this.i don't have any software to make a diagram for you...may be someone else can help...

 

[skittlez411]

ok thanks austronuc and pcdagr8! i get that part now!

a) Fk=Ukmgcos20
= 552.5N

b) Fs=Usmgcos20
=828.8N

so this is what i have right now.

 

[ImsoFly]

good job

 

[skittlez411]

yay! i got it? thanks!