Question

Coefficients of friction between the flat bed of the truck and crate are ${\mu }_s=0.8$ and ${\mu }_k=\mathrm{0.7.}$ The coefficient of kinetic friction between the truck tires and the road surface is $0.9$. If the truck stop from an initial speed $15m/s$ with maximum braking (wheels skidding). Determine where on the bed the crate finally comes to rest. (Take $g=10m/s^2$)

• A. $2.77m$
• B. $2.37m$
• C. $3m$
• D. $1.77m$

Answer 1

The correct option is A $2.77m$

let the mass of the truck be $M$ then friction force on it is

$F=\mu Mg=Ma$

$a=\mu g=0.9g$

time for truck to come at rest

$V_f=V_i+at$

$0=15-0.9gt$

$t=\frac{5}{3}s$

friction between crate and truck surface is

$F=m{\mu }_{k}g$

$a=0.7g=7m/s^2$

so relative acceleration is $9-7=2m/s^2$

the distance the crate will travel is

$S=ut+\frac{1}{2}a{t}^2$

$S=0+\frac{1}{2}\times 2\times (\frac{5}{3}{)}^2$

$S=2.77m$