Question

An engineer wants to design a circular racetrack of radius R such that cars of mass M can go around the track at speed U without the aid of friction or other forces other than the perpendicular contact force from the track surface.

Find an expression for the required banking angle θ of the track, measured from the horizontal. Express the answer in terms of M, R, U, and g.

Suppose the race cars actually round the track at a speed ω
>U. What additional radial force F_{r} is required to
keep the cars on the track at this speed? Express the answer in
terms of M, R, U, ω , and g.

Answer #1

An engineer wants to design an oval racetrack such that 3.20×103
lb3.20×103 lb racecars can round the exactly 1000 ft1000 ft radius
turns at 95 mi/h95 mi/h without the aid of friction. She estimates
that the cars will round the turns at a maximum of 175 mi/h.175
mi/h.
Find the banking angle ?θ necessary for the race cars to
navigate the turns at 95 mi/h95 mi/h without the aid of
friction.
This banking and radius are very close to the...

4. A designer plans to build a circular Indy 500 racetrack with
a bank angle of 12 degrees and it must keep cars moving at 150
miles per hour (242 km per hour) from sliding off the track even
when the track is slick. a) Draw a diagram showing all forces
acting on a racecar as it rounds the track. Neglect friction. b)
Choose an x-y coordinate system and write the components of the
forces. Why is the choice of...

Consider a satellite of mass m in a circular orbit of radius r
around the Earth of mass ME and radius RE.
1.
What is the gravitational force (magnitude and direction) on
the satellite from Earth?
2.
If we define g(r) to be the force of gravity on a mass m at a
radial distance r from the center of the Earth, divided by the mass
m, then evaluate the ratio g(r)/g(RE)to see how g varies with
radial distance. If...

6. A device for acclimating military pilots to the high
accelerations they must experience consists of a horizontal beam
that rotates horizontally about one end while the pilot is seated
at the other end. In order to achieve a radial acceleration of 35.1
m/s2 with a beam of length 5.39 m, what rotation frequency is
required?
? Hz
7. You want to design an oval racetrack such that 3200 lb
racecars can round the turns of radius 1000 ft at...

Learning Goal:
To understand how to apply the law of conservation of energy to
situations with and without nonconservative forces acting.
The law of conservation of energy states the following:
In an isolated system the total energy remains constant.
If the objects within the system interact through gravitational
and elastic forces only, then the total mechanical energy
is conserved.
The mechanical energy of a system is defined as the sum of
kinetic energy K and potential energy
U. For such...

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