- #1

RoboRaptor

- 3

- 1

- Homework Statement
- A 1050-kg car rounds a curve of radius 72m banked at an angle of 14°. If the car is traveling at 85 km/h, will a friction force be required? If so, how much and in what direction?

- Relevant Equations
- Centripetal Force = (m*v^2)/R

Normal Force = Cos(x) * mg

Sin(x) = opp/hyp

Cos(x) = adj/hyp

g = 9.8m/s^2

First I figured out the normal force being exerted on the car using the equation above.

Cos(40°)*(1050*9.8) = 7883N

Next, I tried to find out the horizontal component of the normal force by doing:

Cos(50) * 7883 = 5067N

I figured out the angle by using certain geometrical properties.

Next, I found the Centripetal Force using its corresponding equation:

F = 1050 * (23.6^2/72) = 8122 N

(I found 23.6 by dividing 85000 by 3600)

I figured out that the horizontal component of the Normal Force is not enough to give the object its circular motion so I found the difference between it and the Centripetal Force which gave me around 3055 more N needed to make the car go in a uniform circular motion.

Here is where I'm unsure of what to do. Will the frictional force of the car point directly to the center of the circular motion or will it point down towards the direction of the ramp?

Here are some pictures to better illustrate my doubts:

OR

Thanks in advance for the help!

Cos(40°)*(1050*9.8) = 7883N

Next, I tried to find out the horizontal component of the normal force by doing:

Cos(50) * 7883 = 5067N

I figured out the angle by using certain geometrical properties.

Next, I found the Centripetal Force using its corresponding equation:

F = 1050 * (23.6^2/72) = 8122 N

(I found 23.6 by dividing 85000 by 3600)

I figured out that the horizontal component of the Normal Force is not enough to give the object its circular motion so I found the difference between it and the Centripetal Force which gave me around 3055 more N needed to make the car go in a uniform circular motion.

Here is where I'm unsure of what to do. Will the frictional force of the car point directly to the center of the circular motion or will it point down towards the direction of the ramp?

Here are some pictures to better illustrate my doubts:

OR

Thanks in advance for the help!