A) 18.4 m
B)
a) mass of the load
b) mass of the truck
Explanation:
A)
In order for the oad not to slide, its acceleration must be the same as the acceleration of the truck.
Since there is only one force acting on the load (the force of static friction), the acceleration of the load will be equal to the force of friction divided by the mass of the load (Newton's second law of motion):
[tex]a=\frac{F_f}{m}=\frac{-\mu mg}{m}=-\mu g[/tex] (1)
where
m is the mass of the load
[tex]\mu=0.400[/tex] is the coefficient of static friction
[tex]g=9.8 m/s^2[/tex] is the acceleration due to gravity
The acceleration of the truck (and the load) is also related to the stopping distance of the truck by the suvat equation:
[tex]v^2-u^2=2as[/tex] (2)
where
v = 0 is the final velocity of the car
u = 12.0 m/s is the initial velocity
a is the acceleration
s is the stopping distance
Since the acceleration must be the same, we can substitute (1) into (2), and solving for s we find:
[tex]v^2-u^2=-2\mu g s\\s=\frac{v^2-u^2}{-2\mu g}=\frac{0^2-12.0^2}{-2(0.400)(9.8)}=18.4 m[/tex]
B)
From part A, we see that the data that we have not used in the calculation are:
- The mass of the load
- The mass of the truck
Therefore, the two pieces of data unnecessary for the solution are
a) mass of the load
b) mass of the truck
