A package of dishes (mass 60.0 kg) sits on the flatbed of a pickup truck with an
ID: 1364708 • Letter: A
Question
A package of dishes (mass 60.0 kg) sits on the flatbed of a pickup truck with an open tailgate. The coefficient of static friction between the package and the truck's flatbed is 0.370, and the coefficient of kinetic friction is 0.180.
(a) The truck accelerates forward on level ground. What is the maximum acceleration the truck can have so that the package does not slide relative to the truck bed? Correct: Your answer is correct.
(b) The truck barely exceeds this acceleration and then moves with constant acceleration, with the package sliding along its bed. What is the acceleration of the package relative to the ground? Correct: Your answer is correct.
(c) The driver cleans up the fragments of dishes and starts over again with an identical package at rest in the truck. The truck accelerates up a hill inclined at 6.0° with the horizontal. Now what is the maximum acceleration the truck can have such that the package does not slide relative to the flatbed?
(d) When the truck exceeds this acceleration, what is the acceleration of the package relative to the ground?
(e) For the truck parked at rest on a hill, what is the maximum slope the hill can have such that the package does not slide?
(f) Is any piece of data unnecessary for the solution in all the parts of this problem?
The coefficient of static friction
The mass of the package
The coefficient of kinetic friction
Explanation / Answer
Here
a)
maximum acceleration of truck , a = us * g
a = 0.37 * 9.8
a =3.63 m/s^2
the maximum acceleration of the truck is 3.63 m/s^2
b)
for the acceleration realtive to ground ,
a = 0.18 * 9.8
a = 1.76 m/s^2
the acceleration of the package relative to graound is 1.76 m/s^2
c)
for the truck to go up the incline
a = 0.37 * 9.8 - 9.8 * sin(6)
a = 2.60 m/s^2
the maximum acceleration is 2.6 m/s^2
d)
accelration relative to ground = 0.18 * 9.8 - 9.8 * sin(6)
accelration relative to ground = 0.74 m/s^2
e)
for the parked truck
tan(theta) = us
theta = arctan(0.37)
theta = 20.3 degree
f)
the mass of package is unecessary
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