Friction and Banked road question

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SUMMARY

The discussion revolves around two physics problems involving friction and banked curves. The first problem requires calculating the coefficient of kinetic friction and the tension in a string connecting two masses (m1 = 3.90 kg and m2 = 9.40 kg) with an acceleration of 1.77 m/s². The second problem focuses on a car navigating a banked curve, requiring the determination of speed ranges without slipping and the minimum static friction coefficient necessary for the car to remain stationary. Newton's second law is emphasized as a critical tool for solving these problems.

PREREQUISITES
  • Understanding of Newton's second law of motion
  • Knowledge of kinetic and static friction coefficients
  • Familiarity with banked curves and circular motion
  • Basic algebra for solving equations
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  • Calculate the coefficient of kinetic friction using the formula involving acceleration and mass
  • Determine tension in a string using Newton's second law for connected masses
  • Analyze the dynamics of banked curves to find speed ranges using static friction
  • Explore the effects of varying the banking angle and radius on car stability
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Physics students, educators, and anyone interested in understanding the principles of motion, friction, and dynamics in real-world applications.

msq126
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Hello Everybody. I am having a very difficult time with these two questions.

The first question:

The system shown in Figure 4.54 has an acceleration of magnitude 1.77 m/s2, where m1 = 3.90 kg and m2 = 9.40 kg. Assume that the coefficient of kinetic friction between block and incline is the same for both inclines.


Figure 4.54
http://www.webassign.net/serpop/p4-54alt.gif

a)Find the coefficient of kinetic friction.?

b)Find the tension in the string. (N)

The Second Question:

A car rounds a banked curve as in the figure below. The radius of curvature of the road is R, the banking angle is θ, and the coefficient of static friction is μs.

http://www.webassign.net/serpop/5-13.gif

a)Determine the range of speeds the car can have without slipping up or down the banked surface. (Use theta for θ, mu for μs, R and g as necessary.)

vmin =

vmax=



b)Find the minimum value for μs such that the minimum speed is zero. (Use theta for θ, and R and g as necessary.)

μs =


c)What is the range of speeds possible if R = 100 m, θ = 10.0°, and μs = 0.110 (slippery conditions)?

vmin =


vmax=

-----------------------------

I would really appreciate it if someone could help me.
Thanks in Advance...
 
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Welcome to PF!

Hi msq126! Welcome to PF! :smile:

Hint: try good ol' Newton's second law for both questions. :wink:

Anyway, show us what you've tried, and where you're stuck, and then we'll know how to help. :smile:
 

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