1000-kg car (including the driver) traveling 20 m/s goes around a 125-m radius curve at constant speed. What is the work done by friction on the car as the car makes the turn, in Joules

Respuesta :

The work done by friction on the car as it makes the turn is [tex]2.514 \times 10^6 \ J[/tex].

The centripetal force on the car

The kinetic friction of the car produces the centripetal force needed to keep the car in the circular path.

[tex]Ff = F_c = \frac{mv^2}{r}\\\\ F_c = \frac{1000 \times 20^2}{125} \\\\F_c = 3200 \ N[/tex]

The distance around the curved path

[tex]d = 2\pi r\\\\d = 2\times 3.142 \times 125\\\\d = 785.5 \ m[/tex]

Work done by friction

The work done by friction on the car as it makes the turn is calculated as follows;

[tex]W = F_c d\\\\W = 3200 \times 785.5\\\\W = 2.514 \times 10^6 \ J[/tex]

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