physics basic help?

Question

Losing Cargo. A box of mass 12.3 kg rests on the flat floor of a truck. The coefficients of friction between the box and floor are U_s = 0.190 and U_k = 0.140 . The truck stops at a stop sign and then starts to move with an acceleration of 2.23 m/s^2.

a) If the box is a distance 1.83 m from the rear of the truck when the truck starts, how much time elapses before the box falls off the truck? Take the free fall acceleration to be 9.8 m/s^2

b) How far does the truck travel in this time?
Take the free fall acceleration to be 9.8 m/s^2

Answer 1

a) It will slide if we overcome static friction
f_s=U_s m g<=ma

ma= 12.3 x 2.23 m/s^2=27.4 N
U_s m g= 0.190 x 12.3 x 9.8=22.9 N
I guess it will slide!

Ft= F- f_k
Ft= ma - U_k mg= 27.4 - 0.140 x 12.3 x 9.8
Ft= 10.5N
since S=0.5at^2
t=sqrt(2S/a) and a= Ft/m
t=sqrt(2Sm/F)
t=sqrt(2 x1.8 x 12.3/10.5)=2.0 sec

b)
again S=0.5 a t^2
S= 0.5 x 2.23 x (2)^2=4.46 m

IHIH