Coriolis Force on a Race Car at 45 Degrees North

In summary, the magnitude of the Coriolis force on a racing car of mass 10 metric tons traveling due south at a speed of 400km/hr at a latitude of 45 degrees north is 110 N west.
  • #1
OmegaKV
22
1

Homework Statement



Find the magnitude and direction of the Coriolis force on a racing car of mass 10 metric tons traveling due south at a speed of 400km/hr at a lattitude of 45 degrees north.

Homework Equations



[tex]F_{cor}=-2m\omega\times v[/tex]

The Attempt at a Solution



[tex]\omega=2\pi/(24*3600 \quad seconds)[/tex]
[tex]v=400km/hr=400/3600 \quad km/second[/tex]
[tex]m=10000[/tex]
[tex]-2 m\omega\times v=-2m\omega v sin(45) \quad Newtons \quad east = -114.27 \quad Newtons \quad east = 114.27 \quad Newtons \quad west[/tex]

The answer in the back of my book says "41 nt west"
 
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  • #2
OmegaKV said:
[tex]v=800km/hr=800/3600 \quad km/second[/tex]
v = 400 km/hour according to the problem statement.
I do not see you account for the mass of the race car.
Math not checked.
 
  • #3
jbriggs444 said:
v = 400 km/hour according to the problem statement.
I do not see you account for the mass of the race car.
Math not checked.

Updated my post to fix those mistakes. I mistyped 800km/hr in my post but I used 400km/hr in my calculation. Taking mass into account my answer is scaled by a factor of 10000, so it's still different from the answer in the back of the book.
 
  • #4
My result matches yours. Note that the race car mass is only given to two significant figures. Our result should be reported as 110 N (or 1.1x102N)
 

FAQ: Coriolis Force on a Race Car at 45 Degrees North

1. What is the Coriolis force on a race car?

The Coriolis force on a race car is a fictitious force that appears to act on an object due to its motion in a rotating reference frame. It is caused by the rotation of the Earth and can affect the path of a race car as it moves.

2. How does the Coriolis force affect a race car?

The Coriolis force can cause a race car to veer to the right in the northern hemisphere and to the left in the southern hemisphere. This is due to the fact that the Earth's rotation causes objects to appear to deflect to the right in the northern hemisphere and to the left in the southern hemisphere.

3. Can the Coriolis force be felt by a race car driver?

No, the Coriolis force is a very small force and is only noticeable on large scales, such as the movement of weather systems or ocean currents. It does not have a significant effect on the movement of a race car and cannot be felt by a driver.

4. How does the Coriolis force affect the speed of a race car?

The Coriolis force does not directly affect the speed of a race car. However, it can affect the direction in which the car is moving, which can indirectly impact its speed. For example, if the car is deflected to the right by the Coriolis force, it may have to adjust its steering and slow down to maintain its intended path.

5. Is the Coriolis force the same on all race cars?

The Coriolis force is not dependent on the type of car, but rather on its location on the Earth's surface. Therefore, the force will be the same on all race cars at the same location, regardless of their size or design.

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