Question

Suppose the coefficient of static friction between a quarter and the back wall of a rocket car is 0.383. At what minimum rate would the car have to accelerate so that a quarter placed on the back wall would remain in place?

Answer 1

25.59 m/s²

Step-by-step explanation:

Using the formula for the force of static friction:

`f_s = \mu_s N` --- (1)

where;

`f_s =` static friction force

`\mu_s =` coefficient of static friction

N = normal force

Also, recall that:

F = mass × acceleration

Similarly, N = mg

here, due to min. acceleration of the car;

`N = ma_(min)`

From equation (1)

`f_s = \mu_s ma_(min)`

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,

`F = f_s`

`mg = \mu_s ma_(min)`

`a_(min) = (mg )/( \mu_s m)`

`a_(min) = (g )/( \mu_s )`

where;

`\mu_s = 0.383` and g = 9.8 m/s²

`a_(min) = (9.8 \ m/s^2 )/(0.383 )`

`\mathbf{a_(min)= 25.59 \ m/s^2}`