Howdyy, I have another question. The teacher today showed me her answer but I couldn't really understand the reasoning behind it. You guys are smart so thank you!
A 600 kg car is merging onto a major highway via a curve banked at 7 degrees from the horizontal.
The radius of the curve is 240 m.
- What is the maximum safe speed for this car around the curve? -
Hey! A question from the new syllabus? How exciting!!
An object on a banked track does not use friction, but the velocity of the object to maintain its circular motion. If the velocity is too slow of too fast, the car will either "slip" and fall into the centre of the banked track or go over the top of the banked track. So I'm going to assume that the "safe speed" is the speed for the car to not move up or down the slope.
We know that with any object moving in a circle uniformly, the object travels in a circle at a constant speed due to a force accelerating it inwards, which is called centripetal force. We also know that the force of gravity acts on this car; I've made this diagram to visually help with this.
As you can see, both the gravitational force and the centripetal force are perpendicular, and the Normal force to any object is always perpendicular to the surface, we so know that the angle is 7 in this.
By then equating Tan (opposite over adjacent), we derive a formula (which does not have mass in it amazingly!)
Subbing that in, I get 16.9938 m/s
= 17m/s.
Let me know if i'm right, because "safe" is a broad term. Hope this helps!