Is the Slope of the Wheelchair Ramp Too Steep for Young Children?

[homevolend]

Homework Statement

There was a new wheelchair ramp installed at a nurserey. It was built for young children with wheelchairs to go up instead of the stairs and it was made to not be too difficult to get up. If the required force is not more than 50N like the testers say. If the weight of one child+wheelchair is 30kg, and the slope of the ramp is 5degrees, is the slope too steep? The friction with everything regarding wheels is by coefficient of uk = .10

Homework Equations

Fg=mg
Fnet=Fa-Ff-F||
F||=Fgsintheta
Fperpen=Fgcostheta

The Attempt at a Solution

I have found fg by using Fg=mg
Fg=30(9.8)
Fg=294.3

then I found the F||=Fgsintheta
F||=294.3sin5
F||=25.6

Fperpen=Fgcostheta
Fperpen=294.3cos5
Fperpen=293.2


So now I was thinking to use the Fnet=Fa-Ff-F||


But I don't know what to find or anything to actually know if its too step or not, I don't know if that above equation is correct.



thanks

 

[tiny-tim]

hi homevolend!

(have a mu: µ and a theta: θ and a degree: ° and try using the X₂ icon just above the Reply box )

I have found fg by using Fg=mg
Fg=30(9.8)
Fg=294.3

then I found the F||=Fgsintheta
F||=294.3sin5
F||=25.6

Fperpen=Fgcostheta
Fperpen=294.3cos5
Fperpen=293.2


So now I was thinking to use the Fnet=Fa-Ff-F||

yes, that's fine , except i don't understand what your F_a is

now use the normal force and µ to find the friction force

 

[homevolend]

Ok I am still not sure if I am using the correct formula to do the Fnet.

I did Fnet=Fa-Ff-F||

Fnet=50-29.43-25.6

Fnet=14.7


But that does not seem correct, I do not think I am using the right formula, Then once I have the fnet I do not know how or what else to find to say if it is steep enough or not.

 

[tiny-tim]

hi homevolend!

(just got up :zzz: …)

I did Fnet=Fa-Ff-F||

Fnet=50-29.43-25.6

oh i see … F_a is the applied force

no, you're misunderstanding the question, F_a is not 50, F_a is the minimum force needed to keep the wheelchair moving …

so find what F_a is from your F_net = 0 formula, and then answer yes/no is it > 50 (which would mean the slope is too steep)?

 

[homevolend]

Got it I used the 0=Fa-Fk-F||

Got 55, so yes it is too steep because it cannot be more than 55.
"Can be no more than 50N" so does that mean its too steep?

 

[tiny-tim]

Got it I used the 0=Fa-Fk-F||

Got 55, so yes it is too steep because it cannot be more than 55.
"Can be no more than 50N" so does that mean its too steep?

Yup!

overcoming both gravity and friction would require 55 N, so the slope is too steep for someone who can only apply 50 N

 

[homevolend]

Thanks for the help tim.