Exemplo de Physics, 6.2 Uniform Circular Motion

Comparing Centripetal Acceleration of a Car Rounding a Curve with Acceleration Due to Gravity

Problema e solução em inglês, como no livro original.

A car follows a curve of radius 500 m at a speed of 25.0 m/s (about 90 km/h). What is the magnitude of the car’s centripetal acceleration? Compare the centripetal acceleration for this fairly gentle curve taken at highway speed with acceleration due to gravity (g).

The diagram shows an illustration of a car driving clockwise around a circle with a radius r and an arrow pointing in the direction of the car labeled v and an arrow pointing opposite toward the radius labeled ac (centripetal acceleration). The point at the center of the circle and start of radius is labeled Center of rotation.

Resolva no papel primeiro. Depois abra a solução um passo de cada vez e pare assim que conseguir terminar sozinho.

Estratégia
Because linear rather than angular speed is given, it is most convenient to use the expression $a_{c} = \frac{v^{2}}{r}$ to find the magnitude of the centripetal acceleration.
Solução
Entering the given values of v = 25.0 m/s and r = 500 m into the expression for a_c gives

$\begin{matrix} a_{c} & = & \frac{v^{2}}{r} \\ = & \frac{{(25.0 m/s)}^{2}}{500 m} \\ = & 1.25 {m/s}^{2} . \end{matrix}$

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