What Is the Angle of Inclination for a Car on a Banked Track?

In summary, a car with a mass of 1000kg is traveling at a constant speed of 108km/h around a banked track with a horizontal radius of 100m. To calculate the angle of inclination of the track, we can use the equation theta = tan^-1(900/(100 x g)), where g is the acceleration due to gravity (approximately 9.8 m/s²). This results in an angle of approximately 5.7 degrees.
  • #1
chrisridgwell
11
0
a car of mass 1000kg moves round a banked track at a constant speed of 108km/h. the reaction of the wheels is at right angles to the track, the horizontal radius is 100m. calculate the angle of inclination of the track.



Homework Equations


tan(theta)= V^2/rg



The Attempt at a Solution


108km/h = 30m/s
(theta)= Tan^-1(900/(100 x g))

im confused as to what g actually stands for
 
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  • #2
chrisridgwell said:
im confused as to what g actually stands for
g is the acceleration due to gravity; g ≈ 9.8 m/s².
 
  • #3
so the equation should read:
theta= tan^-1(900/(100x9.8))
 
  • #4
Yes.
 
  • #5
Thankyou very much, I am sure i will return
 

What is the angle of inclination?

The angle of inclination, also known as the tilt angle, is the angle between a reference line and a line or surface measured from horizontal. It is usually measured in degrees.

How is the angle of inclination calculated?

The angle of inclination can be calculated using basic trigonometric functions such as sine, cosine, and tangent. The formula for calculating the angle of inclination is arctan (opposite/adjacent), where the opposite side is the height and the adjacent side is the distance from the reference line.

Why is the angle of inclination important in science?

The angle of inclination is an important concept in science as it helps us understand the orientation of objects and surfaces in relation to a reference point. It is used in various fields such as astronomy, geology, and physics to determine the angle of tilt of planetary orbits, the slope of landforms, and the angle of deflection of objects in motion.

What factors affect the angle of inclination?

The angle of inclination can be affected by various factors such as the shape and orientation of the surface or object, the force of gravity, and the presence of other external forces. For example, the angle of inclination of a hill will vary depending on its slope and the angle of inclination of a pendulum will change depending on the strength of the gravitational force.

How does the angle of inclination relate to the Earth's axis?

The Earth's axis is tilted at an angle of approximately 23.5 degrees from its orbital plane around the sun. This tilt, known as the axial tilt or obliquity, is responsible for the changing seasons on Earth. The angle of inclination of other planets in our solar system also affects their seasons and climate.

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