Workbook Physics

$7-7$ Minimum$/$Maximum Problems

For each problem, draw the free$-$body diagram and show all your work.

A car in a chase scene speeds over the hills of San Francisco.

a$)$ If the car goes too fast, it will be on the verge of launching off the road. What is the value of $F_N$ at this critical speed?

b$)$ What is this critical speed if the hill has a radius of $25$ meters?

Bad Albert ties an $0\mathrm{.}90$ kg cat to a string and swings it in a vertical circle $1\mathrm{.}5$ m in radius. The string has a breaking strength of $90\mathrm{.}0$ N $.$

a$)$ He swings the cat faster and faster. Will the string break at the top of the circle or at the bottom? Why?

b$)$ Find the maximum possible velocity of the cat that will not break the string.

A car on a level road is making a turn with a radius of $50\mathrm{.}0$ meters. It is rainy, so the coefficient of friction between the tires and road is ${}_S=0\mathrm{.}60.$

a$)$ How fast can the driver go and still make the turn?

b$)$ Oh no$!$ The driver goes too fast. Sketch the driver's path on the diagram above.

$195$