If a car takes a banked curve at less than a given speed, friction is needed to keep it from sliding toward the inside of the cu
rve (a real problem on icy mountain roads). (a) Calculate the minimum speed, in meters per second, required to take a 84 m radius curve banked at 16° so that you don't slide inwards, assuming there is no friction. (b) What is the minimum coefficient of friction needed for a frightened driver to take the same curve at 16 km/h?
2 answers:
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This question is incomplete, the missing image is uploaded along this answer.
Answer:
the coefficient of friction is 0.32
Explanation:
Given the data in the question;
we make use of kinematic equation of motion;
ω = ω₀ + ∝t
we substitute
ω = ( 0 rad/s ) + ( 0.4 rad/s² )( 9.903 s )
ω = 3.9612 rad/s
The centripetal force acting on the sample is;
Fc = mrω²
from the image; r = 200 mm = 0.2 m
so we substitute
Fc = m(0.2 m ) ( 3.9612 rad/s )²
Fc = (3.13822 m/s²)m
we know that the frictional force between the two materials should be providing the necessary centripetal force to rotate the sample object;
f = Fc
μN = Fc
μmg = (3.13822 m/s²)m
μ = (3.13822 m/s²)m / mg
μ = (3.13822 m/s²) / g
acceleration due to gravity g = 9.8 m/s²
so
μ = (3.13822 m/s²) / 9.8 m/s²
μ = 0.32
Therefore, the coefficient of friction is 0.32
