- #1
TomW17
- 10
- 2
Homework Statement
A car makes a left turn from a stopped position, increasing its speed at a rate of 2 m/s/s. If a book is on the dashboard of the car, at what time will the book begin to slide if the static coefficient of friction [itex]\mu_s = 0.3[/itex]? The radius of the curve of the motion is 7m.
Seems straight forward enough but the answer I get is different to the one my teacher put in the tutorial sheet, and would just like a 2nd opinion on this to make sure I'm not going mad.
Homework Equations
Normal force on a particle in circular motion: [itex]F_n = m\frac{v^2}{R}[/itex]
Maximum frictional force between the box and dash board: [itex]F_f = N\mu_s = mg \mu_s[/itex]
Constant acceleration equations: [itex]v = v_0 + at[/itex]
The Attempt at a Solution
Let the book have mass [itex]m[/itex]. Just as the book is about to slide: [tex]F_f = F_n \implies m\frac{v^2}{R} = m\frac{(at)^2}{R} = mg \mu_s \implies t = \frac{\sqrt{gR\mu_s}}{a}[/tex]
Plugging in the numbers, I get [itex]t\approx 2.27 \text{s}[/itex] whereas my teacher's put [itex]t= 1.94\text{s}[/itex]
Thanks for the help.
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