Math  /  Algebra

Question22. (II) A flatbed truck is carrying a heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75 . What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?

Studdy Solution
Solve for maximum deceleration. Set the two expressions for the static frictional force equal to each other:
μsmg=mamax \mu_s \cdot mg = m \cdot a_{\text{max}}
Cancel the mass (m m ) from both sides:
μsg=amax \mu_s \cdot g = a_{\text{max}}
Substitute the given value of μs=0.75 \mu_s = 0.75 and g=9.8m/s2 g = 9.8 \, \text{m/s}^2 :
amax=0.759.8 a_{\text{max}} = 0.75 \cdot 9.8
Calculate the maximum deceleration:
amax=7.35m/s2 a_{\text{max}} = 7.35 \, \text{m/s}^2
The maximum rate at which the driver can decelerate without the crate sliding is:
7.35m/s2 \boxed{7.35 \, \text{m/s}^2}

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