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When a slice of buttered toast is accidentally pushed over the edge of a counter, it rotates as it falls. Suppose the distance to the floor is 79 cm and the toast rotates less than 1 rev.

(a) What is the smallest angular speed that causes the toast to hit and then topple to be butter-side down?


(b) What is the largest angular speed that causes the toast to hit and then topple to be butter-side down?

Respuesta :

boffeemadrid

Answer:

3.91407 rad/s

11.742 rad/s

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement = 79 cm

g = Acceleration due to gravity = 9.81 m/s² = a

[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow 0.79=0t+\frac{1}{2}\times 9.81\times t^2\\\Rightarrow t=\sqrt{\frac{0.79\times 2}{9.81}}\\\Rightarrow t=0.40132\ s[/tex]

If the bread is rotating 1 side of a rotation would be 0.25 as there are 4 sides

Angular speed is given by

[tex]\omega_{min}=\dfrac{\Delta\theta}{\Delta t}\\\Rightarrow \omega_{min}=\dfrac{0.25\times 2\pi}{0.40132}\\\Rightarrow \omega_{min}=3.91407\ rad/s[/tex]

The minimum angular speed is 3.91407 rad/s

[tex]\omega_{max}=\dfrac{\Delta\theta}{\Delta t}\\\Rightarrow \omega_{max}=\dfrac{0.75\times 2\pi}{0.40132}\\\Rightarrow \omega_{max}=11.742\ rad/s[/tex]

The maximum angular speed is 11.742 rad/s