Physics $223-$ Test Circular Oynamies and Rotational Motion

For all questions, show your reasonme and calculations

Question $1-40$ Points

This question is about motion of a car on a horizontal flat road, and the speed limit signs that you see when going around in a curved road. On a snowy day, when the coefficient of static friction between a car's tires and the road is ${}_s=0\mathrm{.}50,$ the maximum speed that a car can go around a curve is $10\frac{m}{s}($car is going a constant maximum speed$).$ The question is "What is the maximum speed at which the car can take the same curve on a sunny summer day when ${}_s=0\mathrm{.}90?"$

Step $1)$ Draw a sketch of the situation, a view from above of a car going around a portion of a circle during a turn

Step $2)$ Show the coordinate axis for circular motion $(r-$axis, $z-$axis, and $t-$axis$)$

Step $3)$ Draw a force diagram or free$-$body diagram, showing forces along $r-$axis and $z-$axis acting on the car

Step $4)$ Write down Newton's Second Law equations for the forces on the car and accelerations along radial$-$axis and the z$-$axis perpendicular to the plane containing the circ trajectory

Step $5)$ From these equations find an equation relating the maximum speed to static fr coefficient between the road and tires.

Step $6)$ Answer the question above