A lightweight test cart of mass moves on a circular section of track that is banked…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A lightweight test cart of mass 120kg moves on a circular section of track that is banked at 35∘ above the horizontal. The radius of curvature is 5.0m. The interaction between the cart’s wheels and the track provides a coefficient of static friction of 0.20. Air resistance is negligible.
(a) Construct a free-body diagram for the cart while it travels on the banked track.
(b) Derive expressions for the normal force N and the static friction force fs in terms of the cart’s speed v, the banking angle, and physical constants.
(c) Using the results from part (b), determine the maximum speed the cart can have without sliding up the banking.
(d) Determine the minimum speed the cart can have without sliding down the banking.
(e) Explain qualitatively how increasing the banking angle would affect the range of speeds found in parts (c) and (d).