Apparently an easy Dynamics question

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In summary: N = mg - m (50)^2/ 668.04= 160*32.2 - 160* (50)^2/ 668.04= 5152 - 3759.5= 1392.5 lbIn summary, during a high-speed chase, a 2400-lb sports car loses contact with the road at the crest of a hill. The radius of curvature of the vertical profile of the road can be determined using the formula an= v^2/p, and the force exerted on a 160-lb driver by the seat of his 3100-lb car can be found by summing the forces in the normal direction. The final answer is
  • #1
fluffypuffin
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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?
 

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  • #2
hi there, fluffypuffin! welcome to pf! :smile:

(try using the X2 and X2 icons just above the Reply box :wink:)
fluffypuffin said:
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? :smile:
 
  • #3
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!
 
  • #4
looks good! :biggrin:

(are you ok on the other parts?)
 
  • #5
Nope! Want to help me? :)
 
  • #6
if we sum the forces in the normal direction
wouldn't it be:
mg- N= m (50)^2/ 668.04

??
 
  • #7
fluffypuffin said:
mg- N= m (50)^2/ 668.04

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

1. What is Dynamics?

Dynamics is the branch of physics that deals with the study of motion and the forces that cause motion.

2. What is an easy Dynamics question?

An easy Dynamics question typically involves a simple scenario, such as a ball rolling down an inclined plane or an object being pushed across a surface with a certain force.

3. What are the key principles of Dynamics?

The key principles of Dynamics include Newton's laws of motion, the concept of mass and inertia, and the relationship between force, mass, and acceleration.

4. How does Dynamics relate to other branches of physics?

Dynamics is closely related to other branches of physics, such as kinematics, which deals with the description of motion without considering the forces causing the motion, and statics, which deals with the analysis of forces acting on stationary objects.

5. Why is understanding Dynamics important?

Understanding Dynamics is important because it helps us to understand and predict the motion of objects in our everyday lives, as well as in more complex systems such as vehicles, machines, and celestial bodies. It also forms the basis for many other areas of physics, including mechanics, thermodynamics, and electromagnetism.

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