Circular motion, 2 different questions. A car is approaching the top of a hill o

Question

Circular motion, 2 different questions.

A car is approaching the top of a hill of radius of curvature R.

(a) If the normal force that the driver feels at the top of the hill is 1/3 of their weight, how fast is the car going?

(b) Check that the units of your answer to part a make sense.

(c) Check that the dependence of your answer on the variables makes sense.

An airplane is in a nosedive. In order not to crash, the pilot pulls up as much as she can. At the lowest point of the plane’s trajectory, the plane is in a circular arc of radius 300 m, and the pilot experiences an acceleration of 5.0g (so that her weight feels like six times normal).

What is the plane’s speed at this point?

Explanation / Answer

a)We know that at the top of the hill

N = W - Fc

where N is the normal force ; W is the weight ; Fc is the centripital force

1/3 mg = mg - m v^2/R

m v^2/R = mg (1 - 1/3)

v^2/R = 2/3g

v = sqrt (2Rg/3)

b)We know that, v has units of m/s

R is in m and g is in m/s

v = sqrt (m^2/s^2) = m/s

c)Yes they makes sense.

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