Math  /  Algebra

Question39. (II) How large must the coefficient of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95 km/h95 \mathrm{~km} / \mathrm{h} ?

Studdy Solution
Solve for the coefficient of static friction μs \mu_s .
Cancel m m from both sides of the equation:
μsg=v2r \mu_s \cdot g = \frac{v^2}{r}
Solve for μs \mu_s :
μs=v2rg \mu_s = \frac{v^2}{rg}
Substitute the known values:
μs=(26.39)285×9.81 \mu_s = \frac{(26.39)^2}{85 \times 9.81}
μs696.6721833.85 \mu_s \approx \frac{696.6721}{833.85}
μs0.835 \mu_s \approx 0.835
The coefficient of static friction must be approximately:
0.835 \boxed{0.835}

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