Calculating Force of Static Friction on a Car

[Fire Slayer]

Homework Statement

When you take your 1100-kg car out for a spin, you go around a corner of radius 55m with a speed of 15m/s. Assuming your car doesn't skid, what is the force exerted on it by static friciton?

Homework Equations

f$$_{}c$$=ma$$_{}c$$
f$$_{}c$$=mv$$^{}2$$/r
$$\sumf=ma$$

The Attempt at a Solution

$$\sum$$f=ma
f$$_{}s$$=mv$$^{}2$$/r
f$$_{}s$$=300

300=$$\mu$$$$_{}s$$mg
300=$$\mu$$$$_{}s$$(1100)(908)
$$\mu_{}s$$=0.027

but apparantley it's supposed to be 4.5
what happened?

 

[learningphysics]

How did you get 300?

And why are you calculating the coefficient of friction? The question only asks for the force.

 

[m2003]

The equation you used, f_s = mv^2/r, is for centripetal force, which is the force required to keep an object moving in a circular path. This equation does not take into account the force of static friction on the car.

To calculate the force of static friction on the car, we need to use the equation f_s = \mu_s N, where \mu_s is the coefficient of static friction and N is the normal force exerted on the car by the road. The normal force is equal to the weight of the car, which is given by mg.

Therefore, the correct equation to use is f_s = \mu_s mg. Plugging in the values given in the problem, we get:

f_s = \mu_s (1100 kg)(9.8 m/s^2) = 10780 \mu_s

To solve for \mu_s, we need to know the value of f_s. We can calculate this using the equation for centripetal force, f_c = mv^2/r. Plugging in the given values, we get:

f_c = (1100 kg)(15 m/s)^2 / 55 m = 3000 N

Now we can solve for \mu_s:

3000 N = 10780 \mu_s
\mu_s = 0.278

This is the coefficient of static friction between the car and the road. To calculate the force of static friction, we simply multiply this value by the normal force, which is equal to the weight of the car:

f_s = (0.278)(1100 kg)(9.8 m/s^2) = 3003 N

This is the correct answer for the force of static friction on the car. It is not 4.5, because that value is the coefficient of friction between the car and the road, not the force of friction. It is important to carefully read and understand the problem and use the correct equations to solve it.