Apparently an easy Dynamics question

[fluffypuffin]

During a high-speed chase, a 2400-lb sports car traveling
at a speed of 100 mi/h just loses contact with the road as it
reaches the crest A of a hill. a) Determine the radius of
curvature r of the vertical profile of the road at A. b)
Using the value of r found in a part a), determine the
force exerted on a 160-lb driver by the seat of his 3100-lb
car as the car, traveling at a constant speed of 50 mi/h,
passes through A.

Homework Equations

an= v^2/p, p is what we are searching from, but it if we are not given an equation of the hill, it seems unlikely that it can be solved.
p can also be found using derivatives of the position function...


Is this even solve-able?

 

[tiny-tim]

hi there, fluffypuffin! welcome to pf!

(try using the X² and X₂ icons just above the Reply box )

an= v^2/p, p is what we are searching from

contact is lost when the reaction force is zero …

so do F = ma for the driver, using your centripetal acceleration formula …

what do you get? ​

 

[fluffypuffin]

You'd have to make some conversions because velocity is in seconds. So
100 mi/h= 146.6 ft/s then
p= 146.6 ^2/ 32.2

Correct?

Thank you so much!

 

[tiny-tim]

looks good!

(are you ok on the other parts?)

 

[fluffypuffin]

Nope! Want to help me? :)

 

[fluffypuffin]

if we sum the forces in the normal direction
wouldn't it be:
mg- N= m (50)^2/ 668.04

??

 

[tiny-tim]

mg- N= m (50)^2/ 668.04

yes (except you need to convert the 50 into ft/s )