Trig Help: Deriving a Friction Equation from Circular Motion Example

  • Thread starter Thread starter CINA
  • Start date Start date
  • Tags Tags
    Trig
AI Thread Summary
The discussion revolves around deriving a friction equation from a circular motion example, specifically focusing on the transition from sine and cosine functions to tangent in the equation. The user is struggling to understand the mathematical steps involved in this derivation, suspecting that a trigonometric identity is used but unable to identify which one. They mention considering a sum/difference identity but find it unhelpful. A suggestion is made to multiply the top and bottom of the equation by 1/cosθ to aid in the derivation process. Clarification on this mathematical approach is sought to complete the homework assignment effectively.
CINA
Messages
60
Reaction score
0

Homework Statement



Well I'm following an example problem on this site:
http://www.batesville.k12.in.us/physics/PhyNet/Mechanics/Circular Motion/banked_with_friction.htm
I just need some help on the derivation math. I'll just host the image below.

Homework Equations


This is the problem equation:
http://img105.imageshack.us/img105/3449/frictioneqn4.th.gif

On the last line when it goes from sines and cosines to tangants I can't follow what the person did.


The Attempt at a Solution



I'm assuming he used some type of trig Identity but I can't find one that is apt. I thinking it's a sum/difference trig identity but it just doesn't help. What could he be doing?

Any help at all is GREATLY apperciated!

Thanks
 
Last edited by a moderator:
Physics news on Phys.org
Multiply top and bottom by 1/cosθ
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

How Does Mass, Radius, and Tension Affect Frequency in Circular Motion?
Replies
2
Views
3K
Derive trig equations 4, 5, and 6 from 1, 2, and 3
Replies
13
Views
3K
Deriving the Formula for Banked Roads: No Friction
Replies
11
Views
3K
Uniform Circular Motion; Need help with deriving equations.
Replies
4
Views
9K
Finding Optimal Elevation Angles for a Field Goal: A Kinematics Trig Problem
Replies
5
Views
3K
What distance is needed for a body to spin in circular motion with a spring?
Replies
26
Views
4K
Finding the Velocity and Acceleration of a Car in Circular Motion
Replies
1
Views
5K
How Does Radius Affect Centripetal Force in Your Experiment?
Replies
4
Views
30K
Aeroplane follows circular trajectory-Tension? (geometry)
Replies
6
Views
2K
Need help deriving the general maximum height equation
Replies
3
Views
8K

Hot Threads

Recent Insights

Back
Top