Q BgQuestion:

      
Mentor
Karma Points: 546
Respect (99%):
posted by  Haste on 11/7/2009 10:16:06 AM  |  status: Closed  |  Earned Karma: 546

On how steep a hill (maximum angle) can you leave a car parked?

Course Textbook Chapter Problem Needs by
N/A N/A N/A N/A 11/7/2009 at 11:00:00 PM
Question Details:
The coefficient of static friction between hard rubber and normal street pavement is about 0.68. On how steep a hill (maximum angle) can you leave a car parked?
Tags: Physics
Bonus Point Alert! Earn +8 additional karma points for helping this platinum member.

AAnswers:

Answer Question Ask for clarification
posted by christina.S on 11/7/2009 10:38:39 AM  |  status: Live
Asker's Rating: Lifesaver   
Response Details:
Along incline:
.
        Fnet  =  ma
.
       Fnet  =  m(0) (else car will accelerate down incline)
.
Friction acts up incline and gravity acts down incline.
.
        Fnet =  Ff + Fg
.
    ==> 0  =  Ff + Fg (vectors)
.
Since Ff   and Fg act in opposite directions, their magnitudes must be equal :
.
           F= Fg (scalars)
.
    or μ Fn= Fg 
.
==>  μ mg cosθ  = m g sinθ
.
==>    μ   =  tanθ 
.
==>    θ   =  tan-1 (μ)  =   tan-1 (0.68)  =  34.21  degree
.
Hope this helps u!
Oracle
Karma Points: 63,078
posted by zsm28 on 11/7/2009 11:38:15 AM  |  status: Live
Asker's Rating: Helpful   
Response Details:
f = static friction force, N = normal force
net force = mgsinθ - f = 0
N = mgcosθ
f <= μN
∴mgsinθ <= μmgcosθ
tanθ <= μ
θ <= tan-1μ
maximum angle = tan-1μ = 34.2o
Apprentice
Karma Points: 131
posted by Yash Sodhani on 11/7/2009 12:04:52 PM  |  status: Live
Asker's Rating: Helpful   
Response Details:
on a banked road, when you park the car, for max angle of inclination of hill, friction foce must act up the incline and must balance the weight component down the hill.

Hence,  μmgcosθ = mgsinθ
=> θ = tan-1 μ
=> θ = 34.21o
Answer Question Ask for clarificarion

Join Cramster's Community

Cramster.com brings together students, educators and subject enthusiasts in an online study community. With around-the-clock expert help and a community of over 100,000 knowledgeable members, you can find the help you need, whenever you need it. Join for free today » How Cramster is different from tutoring »