university physics: mechanics ch6. friction and centripetal force lecture 8 dr.-ing. erwin sitompul

University Physics: Mechanics

Ch6. Friction and Centripetal Force

Lecture 8

Dr.-Ing. Erwin Sitompulhttp://zitompul.wordpress.com

8/2Erwin Sitompul University Physics: Mechanics

A traffic light weighing 122 N hangs from a cable tied to two other cables fastened to a support, as in the figure below. The upper cables make angles of 37° and 53° with the horizontal. These upper cables are not as strong as the vertical cable and will break if the tension in them exceeds 100N. Will the traffic light remain hanging in this situation, or will one of the cables break?

Homework 6: The Traffic Light


Free-Body Diagram for the Traffic Light

Free-Body Diagram for the Knot

3T mg

Solution of Homework 6: The Traffic Light


Both values of T1 and T2 are less than 100 N. So, the cables will not break.

net 0F ma

• Why zero?

net, 1 2cos37 cos53 0xF T T

1 2cos37 cos53T T

1 2

cos53

cos37T T

net, 1 2 3sin 37 sin 53 0yF T T T

2 2(0.7536 )sin 37 sin 53 122 NT T

20.7536T

2 20.4535 0.7986 122 NT T

21.2521 122 NT 2 97.4363 NT

1 0.7536 97.4363 N T 1 73.4280 NT

Forces along the x axis:

Forces along the y axis:• Why zero?

Solution of Homework 6: The Traffic Light


Friction Frictional forces are unavoidable in our daily lives. If we were not able to counteract them, they would stop every

moving object and bring every rotating shaft to a halt. About 20% of the gasoline used in a car is needed to counteract friction.

On the other hand, if friction were totally absent, we could not get an automobile to go anywhere, and we could not walk or ride a bicycle. Nobody can hold a pencil and it would not write.

Here we deal with the frictional forces that exist between dry solid surfaces, either stationary relative to each other (static) or moving across each other at slow speeds (kinetic).

The friction is a passive force. When a force is applied to an object, the friction force arises against it.

fs : static frictional force

fk : kinetic frictional force

→

→


Friction

Nomotion

• A block rests on a tabletop with the gravitational force balanced by a normal force.

• There is no friction force,

sF f

N gF F

• An increasing force is applied to the block, attempting to pull it to the left.

• The block does not move. An equal and opposite static frictional force arises between the object and the surface, exactly balancing the applied force.

(a)

(b) (c) (d)

sF f

N gF F


Friction

Acceleration

Constant velocity

kF f ma

(e)

(f)

• Eventually the object will be accelerated when the applied force reaches a certain magnitude.

• The frictional force that oppose the motion is now the kinetic frictional force,

• The magnitude of the kinetic frictional force, which acts when there is motion, is less than the maximum magnitude of the static frictional force, which acts when there is no motion.

• To move the block across the surface with a constant speed, the magnitude of the applied force must be decreased once the block begins to move,

kF f

kF f ma

kF f


(a) (b) (c) (d) (e) (f)

Friction


Two surfacesIn Contact

When two ordinary surfaces are placed together, only the high points touch each other.

Some contact points do cold-welt together. These welds produce static friction when an applied force attempts to slide the surface relative to each other.

If the applied force is great enough to pull one surface across the other, there is first a tearing of welds (at breakaway) and then a continuous re-forming and tearing of welds as movement occurs.

If the two surfaces are pressed together harder, many more points cold-weld. Sliding the surfaces relative to each other requires a greater applied force.

Friction


Experiment shows that when a body presses against a surface and a force F attempts to slide the body along the surface, the resulting frictional force has three properties.

Property 1If the body does not move, then the static frictional force fs and the component of F that is parallel to the surface balance each other. They are equal in magnitude, and oppose in direction.

Property 2The magnitude of fs has a maximum value fs,max that is given by

Property 3If he body begins to slide along the surface, the magnitude of the frictional force rapidly decreases to a value fk given by

s,max s Nf F

→

→

→

→

k k Nf F

μs : coefficient of static friction

μk : coefficient of kinetic friction

Properties of Friction


Friction depends on how strongly the surfaces are pressed together. This pressing strength is represented by the normal force FN.

It is easier to keep an object sliding than to get it starts sliding. The coefficients μs and μk are dimensionless and must be

determined experimentally.

→

The value of μs and μk depends on certain properties of both the body and the surface. Therefore, they are usually referred to with the preposition “between.”



A block lies on a floor.(a) What is the magnitude of the frictional force on it from the

floor?(b) If a horizontal force of 5 N is now applied to the block, but

the block does not move, what is the magnitude of the frictional force on it?

(c) If the maximum value of fs,max of the static fictional force on the block is 10 N, will the block move if the magnitude of the horizontally applied force is 8 N?

(d) What about if it is 12 N?(e) What is the magnitude of the frictional force in part (c)?

Zero

5 N

No Yes

8 N



If a car’s wheels are “locked” (kept from rolling) during emergency braking, the car slides along the road. Ripped-off bits of tire and small melted sections of road form the “skid marks.” The record for the longest skid marks on a public road was reportedly set in 1960 by a Jaguar on the M1 highway in England –the marks were 290 m long.

Assuming that μk = 0.6 and the car’s acceleration was constant during the braking, how fast was the car going when the wheels became locked?

Example: Jaguar


net,x xF ma

kf ma

2 20 02 ( )v v a x x

2 20 0(0) ( ) 2 ( )v a x x

kmg ma ka g

0 02 ( )v a x x

0 k 02 ( )v g x x

2(0.6)(9.8)(290)58.40 m s210.24 km h

Example: Jaguar


F1= 10 N is applied to a box on a floor, but the box does not slide. Then, F2 is increased from zero. Before the box begins to slide, do the following quantities increase, decrease, or stay the same?(a) The magnitude of the frictional force on the box.(b) The magnitude of the normal force on the box

from the floor.(c) The maximum value fs,max of the static frictional

force on the box.

→

→

The same, 10 N

Decrease

Decrease

Checkpoint


A 2.5 kg block is initially at rest on a horizontal surface. A horizontal force F of magnitude 6 N and a vertical force P are then applied to the block (see below). The coefficients of friction for the block and surface are μs = 0.4 and μk = 0.25.Determine the magnitude of the frictional force acting on the block if the magnitude of P is (a) 8 N (b) 10 N (c) 12 N

→ →

→

Example: Amber Block


FN

→

Fg

→

f→

s 0.4 k 0.25

N g 0F P F

N gF F P

s,max s Nf F

On the verge of sliding, the maximum static frictional force is:

Forces along the y axis:

mg P

s,max 0.4 (2.5)(9.8) 8f 6.6 F

F

The box does not move

s ( )mg P

8 NP

s,max 0.4 (2.5)(9.8) 10f 5.8 F

The box moves

10 NP

s 6 Nf f F

kf f k NF 0.25 (2.5)(9.8) 10

3.625 N

12 NP The box moves

kf f k NF 0.25 (2.5)(9.8) 12

3.125 N

Example: Amber Block


The figure below shows a coin of mass m at rest on a book that has been tilted at an angle θ with the horizontal. By experimenting, you find that when θ is increased to 13°, the coin is on the verge of sliding down the book, which means that even a slight increase beyond 13° produces sliding.

What is the coefficient of static friction μs between the coin and the book?Hint: Draw the free-body diagram of the coin first.

Final Homework 7: Coin On A Book

university physics: mechanics ch6. friction and centripetal force lecture 8 dr.-ing. erwin sitompul

Documents

friction force

kinetic frictional force

horizontal force

gravitational force

increasing force

passive force

resulting frictional

force f attempts