Friction

•  CAPA homework due next Tuesday,10pm. •  Clicker scores thru Wed, Feb 15 are now

on D2L. •  Exam solutions will be available on D2L

today. •  The 14 (70%) multiple choice will be

scanned and graded today. Hope to grade everything over the weekend.

•  Will start talking about Energy + Work next week. (Chap. 7)

Web page: http://www.colorado.edu/physics/phys1110/phys1110_sp12/

Announcements:

Clickers Thru Feb 15

Extra Credit Problem Dick and Jane stand on a platform of negligible weight, as shown in the figure. Dick weighs 500 N and Jane weighs 400 N. Jane is supporting some of her weight on the end of the rope she is holding. What is the downward force she is exerting on the platform?

Force down on the platform = 500 N + 400 N –T

Force pulling up on the platform = 2T

The platform is not moving so these are equal so 900 N = 3T

So T = 300 N DownwardforceJaneexertsontheplatformis400N(down)–300N(Up)=100N

Tension is the same everywhere T T T

4

Friction Friction occurs when two materials slide past one another

On a microscopic level, molecules in one material form bonds with molecules in the other material

Friction acts parallel to the surface (perpendicular to the normal force).

Friction only acts to oppose motion

Not enough friction!

Force of kinetic friction is It depends on which depends on the materials and on the normal force N which is the force pushing the materials together.

is the coefficient of kinetic friction

Friction Experiments have found two main types of sliding friction

Static friction is the force exerted when the two objects are not in motion relative to each other (no slipping)

Kinetic friction is the force exerted when the two objects are in motion relative to each other (slipping)

m v

m

Formula for static friction is similar: .

Static friction

The static friction will oppose forces which try to slide one object across another. However, once the maximum possible static friction force is exceeded the object will “break loose” and start moving.

m m

If the block is not moving then:

is the coefficient of static friction

Static and Kinetic Friction

Applied force

Forc

e of

fric

tion

kinetic friction

Start with object at rest feeling a normal force of N Start applying a force perpendicular to N. Up to a force of µsN static friction prevents movement After movement starts, frictional force is reduced to µkN.

Clicker question 1 Set frequency to BA

A stationary block sits on an inclined plane. The coefficient of static friction is µS = 0.2. The normal, gravity, and static friction force are shown. Which set of relations applies to this situation? A. B. C.

θ

N

mg

Ff

Clicker question 2 Set frequency to BA

A stationary block sits on an inclined plane. The coefficient of static friction is µs = 0.2. If the angle of the plane increases, eventually the block begins to slide. Sliding will begin when…

A. B. C. D. None of the above

From the previous question we know &

N

mg

Ff

The maximum possible static friction force is . When the opposing force exceeds this, the block will start sliding.

Combining these 3 equations gives

so

Cornering problem A car is taking a corner with radius of 100 m at a speed of 56 mph (25 m/s). On dry pavement the rubber/asphalt coefficient of static friction is 0.8. Will the car hold the line or start skidding?

To solve this we can find the frictional force necessary to keep the car from skidding and see if this is less than

Which direction is the acceleration?

Free body diagram? Coordinate system: along acceleration direction is good

since there will no skidding

Fluid resistance Another type of force similar to friction is due to moving through a medium like air or water called fluid resistance Fluid resistance depends on the size and shape of the object and the medium being traversed The force direction is opposite the velocity with a magnitude of approximately where the proportionality constants depend on the object and medium

€

f = −kv −Dv 2

For small v, the kv term dominates when turbulence is not a factor and is called viscous drag.

For larger v, the Dv2 term (called drag) dominates and it is called quadratic drag.

Falling objects experience a constant force due to gravity and as the speed increases the drag force increases until balance is reached. This speed is the terminal velocity.

Because the resistance force is not constant, acceleration is not constant and so integral calculus is needed, but

Fluid resistance , so force increases with speed. If a constant force is trying to increase the speed, at some point the resistance will match that force and the speed will no longer increase

€

f = −kv −Dv 2

Result for terminal velocity:

-ma = -mg+ Dv2 ; when a = 0, we reached terminal velocity

Fluid resistance At high speeds the force is and it has been found that where ρ is the medium density, A is the cross sectional area, and CD is the drag coefficient (generally between 0.1 and 1)

Top submarine speed = 80 km/hr where

Top airplane speed = 3500 km/hr where

Terminal Velocity Examples Falling object Terminal velocity Skydiver 75 kg 0.7 m2 60 m/s 134 mi/hr Baseball (3.66cm radius) 33 m/s 74 mi/hr Golf ball (2.1 cm radius) 32 m/s 72 mi/hr Hail stone (0.5 cm radius) 14 m/s 31 mi/hr Raindrop (0.2 cm radius) 9 m/s 20 mi/hr

Data from Serway, Physics for Scientists and Engineers, Table 6.1. A drag coefficient C=0.5 is assumed, falling through air.

Hailstone Terminal Velocity Contributing to the danger of large hailstones is the fact that they fall faster than small ones. That is, the terminal velocity increases with the size of the hailstone. Assuming the hailstones to be spherical and using a drag coefficient of C = 0.5 gives the following : Radius (cm) v(m/s) v(mi/hr) .01 1.9 4.3 0.1 6.1 13.7 0.2 8.6 19.3 0.5 13.6 30.5 1.0 19.3 43.2 2.0 27.3 61 3.0 33.4 74.8 5.0 43.2 96.6 10.0 61 136

Dot (scalar) product One type of vector multiplication is the dot product or scalar product which produces a scalar from two vectors

Note that so

Also,

where is the angle between the two vectors

Dot (scalar) product The dot product can be thought of as the projection of one vector along another vector

x

y

But remember, the scalar product returns a scalar, not a vector