Answer:
25.59 m/s²
Explanation:
Using the formula for the force of static friction:
[tex]f_s = \mu_s N[/tex] --- (1)
where;
[tex]f_s =[/tex] static friction force
[tex]\mu_s =[/tex] coefficient of static friction
N = normal force
Also, recall that:
F = mass × acceleration
Similarly, N = mg
here, due to min. acceleration of the car;
[tex]N = ma_{min}[/tex]
From equation (1)
[tex]f_s = \mu_s ma_{min}[/tex]
However, there is a need to balance the frictional force by using the force due to the car's acceleration between the quarter and the wall of the rocket.
Thus,
[tex]F = f_s[/tex]
[tex]mg = \mu_s ma_{min}[/tex]
[tex]a_{min} = \dfrac{mg }{ \mu_s m}[/tex]
[tex]a_{min} = \dfrac{g }{ \mu_s }[/tex]
where;
[tex]\mu_s = 0.383[/tex] and g = 9.8 m/s²
[tex]a_{min} = \dfrac{9.8 \ m/s^2 }{0.383 }[/tex]
[tex]\mathbf{a_{min}= 25.59 \ m/s^2}[/tex]
