![Page 1: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/1.jpg)
PH-211 Andres La Rosa
CHAPTER 6: Friction Force ____________________________________________________________________
View of the contact surface at a microscopic scale
Surfaces are rough at microscopic levels
![Page 2: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/2.jpg)
Stationary surface
Then, it turns out, to keep the mass M moving at constant
Here we describe an experimental fact:
velocity, we need to apply a force Fk somewhat smaller than Fs, max
![Page 3: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/3.jpg)
Interpretation of the experimental fact described above:
Stationary surface
Static friction forces
Then, it turns out, to keep the mass M moving at constant
velocity moving at constant, we need to apply a force Fk somewhat lower than Fs, max
![Page 4: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/4.jpg)
![Page 5: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/5.jpg)
![Page 6: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/6.jpg)
2N
Example
Exercise
If m = 1 Kg then,
N"
m = 1 Kg
mg
N'
N'
![Page 7: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/7.jpg)
STATIC CASE
KINETIC CASE
Quantifying the friction force
![Page 8: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/8.jpg)
Exercise μs = 0.15
![Page 9: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/9.jpg)
![Page 10: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/10.jpg)
![Page 11: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/11.jpg)
CH-6, Problem #25
B
A
What is the maximum weight of block-A, for which the system will remain stationary?
No horizontal motion implies
Maximum static friction force
No motion along the vertical direction implies,
![Page 12: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/12.jpg)
![Page 13: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/13.jpg)
Warm up, for problems involving inclined planes 1)
Resolving the force mg into components parallel and perpendicular to the ramp
2)
3)
![Page 14: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/14.jpg)
4)
5)
Ff
Ff
![Page 15: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/15.jpg)
Ch-6 Problem 79. Block A in Fig. 6-56 has mass mA 4.0 kg, and
block B has mass mB 2.0 kg. The coefficient of kinetic friction
between block B and the horizontal plane is �k 0.50. The inclined
plane is frictionless and at angle � 30°. The pulley serves only to change the direction of the cord connecting the blocks. The cord has negligible mass. Find (a) the tension in the cord and (b) the magnitude of the acceleration of the blocks.
![Page 16: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/16.jpg)
Problem #79
![Page 17: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/17.jpg)
![Page 18: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/18.jpg)
![Page 19: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/19.jpg)
![Page 20: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/20.jpg)
![Page 21: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/21.jpg)
![Page 22: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/22.jpg)
v = 0 v � 0
2. Usually μs > μk
0.1 < μ <1 for many pair of materials
v = 0 v
However: μ depends very much on surface conditions (cleanliness)
This rule is true only if the objects in contact do not deform appreciable.
1. The friction force is proportional to the normal force at the surface: f = μs N
N1
N2
f1 f2
General rules for dry sliding friction
![Page 23: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/23.jpg)
3. For a given object, the friction force is independent of the apparent area in contact with the supporting surface
In both cases the same force F is needed to drag the block.
![Page 24: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/24.jpg)
Increasing the load increases the normal force N, and increases the actual contact area
fs, max α actual contact area Actual contact area α N Hence fs, max α N More quantitatively, fs, max = μ N
Key aspects in friction: - The actual contact area is proportional to the normal force - When two objects are forced together, the high peaks of their surface will crumble, bringing more and more area into intimate contact.
![Page 25: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/25.jpg)
Metal-metal friction
![Page 26: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/26.jpg)
![Page 27: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/27.jpg)
![Page 28: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/28.jpg)
![Page 29: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/29.jpg)
![Page 30: CHAPTER 6: Friction Force · Block A in Fig. 6-56 has mass mA 4.0 kg, and block B has mass mB 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane](https://reader030.vdocuments.net/reader030/viewer/2022033121/5eba28cd41905f0ee16affa9/html5/thumbnails/30.jpg)