Friction on an inclined plane

In summary: F=ma:Friction is not the only force acting on the car. Static friction also applies.The normal force is perpendicular to the plane, but m*g*cos20 is correct. What happened to the cos20?The normal force is orthogonal to the plane.
  • #1
PascalPanther
23
0
I am suppose to find the initial velocity of a car before it skids to a stop.
The car begins it's stop right as it is going up a road that is 20 degrees above the horizontal. The car makes a 15.2 m skid mark before it stops. The coefficient of kinetic friction is 0.60, and static friction is 0.80. The mass of the car and its driver is 1630kg.
Now this is my assumption, that since the car left a skid mark, that would mean the wheels aren't turning. Which I don't think matters, since it would still be kinetic even if the wheels were turning (?) Since I am stopping, there is no other positive force working against the force of friction. My final velocity is 0 since I stop.

First thing I should do is find the force of friction.
Force of friction = (coef) (normal force)
The normal force is the force parallel to the plane, so it is m*g*cos20
F(k) = (0.60) (1630kg*9.8m/s^2) = 9010 N

Next:
F = ma; 9010N = 1630kg(a) = 5.53 m/s^2
I think I can use kinematics now, and:
vf^2 - vi^2 = 2a(x)
vi^2 = 2(5.53 m/s^2)(15.2m)
vi = 13.0 m/s

Does that seem about right? Or am I suppose to use the static friction in there somehow?
 
Physics news on Phys.org
  • #2
PascalPanther said:
I am suppose to find the initial velocity of a car before it skids to a stop.
The car begins it's stop right as it is going up a road that is 20 degrees above the horizontal. The car makes a 15.2 m skid mark before it stops. The coefficient of kinetic friction is 0.60, and static friction is 0.80. The mass of the car and its driver is 1630kg.
Now this is my assumption, that since the car left a skid mark, that would mean the wheels aren't turning. Which I don't think matters, since it would still be kinetic even if the wheels were turning (?)
No, if the weels were turning you should use static friction. A weel turns because at each instant one of it´s points is static relative to the ground.
This is why you break more fast if you don´t block your weels, since static friction is greater than the kinectic.
Since I am stopping, there is no other positive force working against the force of friction. My final velocity is 0 since I stop.

First thing I should do is find the force of friction.
Force of friction = (coef) (normal force)
The normal force is the force parallel to the plane, so it is m*g*cos20
No, normal is a synonim to perpendicular. The normal force is orthogonal to the plane. It is mg sin(20).
F(k) = (0.60) (1630kg*9.8m/s^2) = 9010 N

Next:
F = ma; 9010N = 1630kg(a) = 5.53 m/s^2
I think I can use kinematics now, and:
vf^2 - vi^2 = 2a(x)
vi^2 = 2(5.53 m/s^2)(15.2m)
vi = 13.0 m/s

Does that seem about right? Or am I suppose to use the static friction in there somehow?
Redo your calculations with the correct normal force.
 
  • #3
SGT said:
It is mg sin(20).
No, it's not (at least not when the x-axis is oriented parrallel to the incline :smile: ).
 
Last edited:
  • #4
PascalPanther said:
First thing I should do is find the force of friction.
Force of friction = (coef) (normal force)
The normal force is the force parallel to the plane, so it is m*g*cos20
F(k) = (0.60) (1630kg*9.8m/s^2) = 9010 N
The normal force is perpendicular to the plane, but m*g*cos20 is correct. What happened to the cos20?

Next:
F = ma; 9010N = 1630kg(a) = 5.53 m/s^2
Friction is not the only force acting on the car.

Or am I suppose to use the static friction in there somehow?
Kinetic friction applies here. See my comments: https://www.physicsforums.com/showpost.php?p=1093726&postcount=6
 
  • #5
Doc Al said:
The normal force is perpendicular to the plane, but m*g*cos20 is correct. What happened to the cos20?


Friction is not the only force acting on the car.


Kinetic friction applies here. See my comments: https://www.physicsforums.com/showpost.php?p=1093726&postcount=6
oops, forgot to put it in the equation. But I did solve with it.
F(k) = (0.60) (1630kg*9.8m/s^2)*cos20 = 9010 N

Okay, I think I understand why it is kinetic friction for locked wheels now, and static for unlocked. Seemed odd at first, but it makes sense now.

I believe I am missing the weight of the car on the incline? Now this force should be parallel, not the other, and is F= m*g*sin20.
F(w) = (1620kg * 9.8m/s^2 * sin20)= 5430N.

Both forces are against the car, so 5430N + 9010N = 14440N
F=ma
14440N = 1630kg * (a)
a= 8.86 m/s^2
vf^2 - vi^2 = 2a(x)
vi^2 = 2(8.86 m/s^2)(15.2m)
vi = 16.4 m/s

Does that look better?
 
  • #6
PascalPanther said:
I believe I am missing the weight of the car on the incline? Now this force should be parallel, not the other, and is F= m*g*sin20.
Exactly.
F(w) = (1620kg * 9.8m/s^2 * sin20)= 5430N.
Isn't the mass 1630 kg?

Both forces are against the car, so 5430N + 9010N = 14440N
F=ma
14440N = 1630kg * (a)
a= 8.86 m/s^2
vf^2 - vi^2 = 2a(x)
vi^2 = 2(8.86 m/s^2)(15.2m)
vi = 16.4 m/s
Much better. (Just check your calculations for errors. Don't round off until the last step.)
 

1. What is friction on an inclined plane?

Friction on an inclined plane is a force that acts in the opposite direction of an object's motion as it slides down an inclined surface.

2. How does the angle of the inclined plane affect friction?

The steeper the angle of the inclined plane, the greater the force of friction will be. This is because the weight of the object is distributed more vertically, increasing the normal force and therefore the friction force.

3. How does the mass of the object affect friction on an inclined plane?

The mass of the object does not directly affect the force of friction on an inclined plane. However, a heavier object will have a greater force of gravity pulling it down the incline, which can increase the normal force and therefore the friction force.

4. What factors can affect the coefficient of friction on an inclined plane?

The coefficient of friction, which is a measure of the roughness of the surfaces in contact, can be affected by factors such as the material of the surfaces, the smoothness of those surfaces, and the presence of any lubricants. Other factors, such as temperature and humidity, can also affect the coefficient of friction.

5. How does friction on an inclined plane affect an object's speed?

The force of friction acts in the opposite direction of an object's motion, so it will slow down the object as it slides down the inclined plane. The steeper the angle of the incline or the greater the coefficient of friction, the more the object's speed will be affected.

Similar threads

  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
18
Views
1K
  • Introductory Physics Homework Help
2
Replies
57
Views
572
  • Introductory Physics Homework Help
Replies
6
Views
474
Replies
24
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
640
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
14
Views
1K
Back
Top