Answer:
[tex]v = 10.8 m/s^{2}[/tex]
Explanation:
The centripetal force experienced by the steel toolbox is provided by the friction between the toolbox and the bed of the truck.
Therefore,
[tex]\frac{mv^{2} }{r} = f[/tex]--------------------------------(1)
Here,
v - speed of truck
m - mass of toolbox
r - radius of curve around which the truck is turning
f - frictional force
[tex]f \leq[/tex] μmg
In order to obtain Vmax, frictional force must also be max
Thus,
f = μmg--------------------------------------------------(2)
Substitute (2) in (1)
[tex]\frac{mv^{2} }{r} =[/tex] μmg
[tex]v^{2} =[/tex] μgr
g - 9.8 m/[tex]s^{2}[/tex]
The standard value of coefficient of static friction between steel and steel is
μ ≈ 0.7
Therefore,
[tex]v = 10.8 m/s^{2}[/tex]
