I\'m reviewing past quiz problems and would really appreciate help on solving. T
ID: 1434368 • Letter: I
Question
I'm reviewing past quiz problems and would really appreciate help on solving. Thank you.
A box of auto parts rests in the middle of the bed of a truck The coefficients of static and kinetic friction between the truck bed and the box mu_s = 0.7 and = 0.35. respectively. A. If the truck is traveling along a horizontal road, what is the maximum acceleration the truck can stop with and keep the box from sliding in the bed? B. If the truck is driving down a hill which makes an angle of 25degree with the horizontal, what is the maximum acceleration the truck can stop with and keep the box from sliding in the bed? C. If the truck now exceeds that acceleration, what is the acceleration of the box as measured by an observer on the side of the road?Explanation / Answer
A) maximum force on box is static friction only.
maximum static friction = us N = us M g
Using Fnet = ma
Fmax = m a_max
us M g = M a
a =us g = 0.7 x 9.8 = 6.68 m/s^2
B) in this case,
N - mgcos@ = 0
N = mgcos@
and along the incline,
f - mgsin@ = ma
us mgcos@ - mgsin@ = ma
a = 9.8 ( 0.7cos25 - sin25) = 2.08 m/s^2
C) If block starts moving then kinetic friction will work.
now f = uk N = uk mg
f = ma
uk m g = ma
a = uk g = 0.35 x 9.8 = 3.43 m/s^2