exam, examples & friction - high energy physicsjcumalat/phys1110/lectures/lec12.pdfexam,...

Exam, Examples & Friction

•  Exam Thursday, 7:30pm – Bring a #2 pencil – Will be 2 long answer questions

in addition to 15 multiple choice – Room assignments on web page – Calculators and 1 double sided

sheet of notes allowed – No formula sheet on exam!

•  CAPA homework due next Tuesday

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

Announcements:

Pulleys on Ships, Normally known as Blocks – hence block and tackle

Exam Locations-also on web page Sec Recita)onTime RecRoom Examroom TA

Rec301 0800‐0850 G‐2B75 Hum1B50 Colussi,Victor

Rec302 0800‐0850 G‐2B77 Math100 Houlton,John

Rec303 0800‐0850 G‐2B60 Math100 Koller,Andrew

Rec304 0900‐0950 G‐2B75 Hum1B50 VonStecher,Javier


Rec306 0900‐0950 G‐2B60 Chem142 Dai,Jixia

Rec307 1000‐1050 G‐2B75 Chem140 Kravtsov,Vasily

Rec308 1000‐1050 G‐2B77 Chem140 Barbee,John

















Rec325 1100‐1150 G‐2B60 Hum1B50 VonStecher,Javier


Math, Chemistry, Humanities

-not physics

Circular motion revisited We know that a change in velocity direction is a form of acceleration even if the speed is not changing Can divide acceleration into tangential and radial

components: and

Also know a net force is required for acceleration to occur

Thus, for uniform circular motion Newton’s 2nd law becomes Note that is not a force.

There must be a net force causing the radial acceleration

What is the force?

A car going around a corner on a level surface

For each of the scenarios, what is the force which causes the radial acceleration?

Friction between tires and pavement

A car going around a banked curve Friction between tires and pavement and a component of the normal force

Satellite orbiting the Earth Earth’s gravity

Prev. Clicker question Set frequency to BA

A rider in a "Barrel O’ Fun" finds herself stuck with her back to the wall. Which diagram correctly shows the forces acting on her?

A B C D E

No acceleration in y-direction:

In the horizontal direction:

Clicker question 1 Set frequency to BA

Which tension is larger: T1 or T2 ?

A) T1 B) T2 C) Both have the same magnitude.

A mass M is supported by two threads as shown. The free-body diagram correctly shows the directions of the forces but does not correctly show their magnitudes.

T1 must be larger, since |T1x | = T2

Clicker question 2 Set frequency to BA A person sits normally in a chair on a Ferris Wheel, which rotates with constant speed. As they go around the circle, at which point is the magnitude of the net force on the person a MAXIMUM?

A: Top B: Bottom

C: Right

D: Same at all positions.

Answer: Uniform motion means constant centripetal acceleration, so Fnet is the same everywhere

Clicker question 3 Set frequency to BA A person sits normally in a chair on a Ferris Wheel, which rotates with constant speed. As they go around the circle, at which point is the magnitude of the normal force of the seat on the person a MAXIMUM?

A: Top B: Bottom

C: Right

D: Same at all positions.

N is ALWAYS up wherever you are. Calling ”up" the "positive" direction, Newton's law says TOP: Fnet = +N - mg = - mv^2/R or N = mg - mv^2/R BOTTOM: Fnet = +N - mg = +mv^2/R or N = mg + mv^2/R. So, normal force is bigger at the bottom.

It seems reasonable. If you go fast, you practically lift off your seat. At the bottom, you are squished into it...

(Note ,difference with the bucket problem. Here, faster speeds means you're more likely to fly out at the top. In the bucket question, SLOWER speeds is the situation where we might fall out at the top. )

Pulleys Revisited

200 N supporting force in rod

You supply the lifting force and put tension/stress on the rod holding the load up.

100 N Load 100 N Load

100 N Lifting

Pulleys

Double Pulley 125 N

Triple Pulley

Sail Boat Crane

How a rope/cable elevator works

Need a dead weight to balance the weight of the elevator.


A mass M is supported as shown on an incline plane. The free-body diagram correctly shows the directions of the forces but does not correctly show their magnitudes.

N – mg cos(θ) = 0

A student chooses a tilted coordinate system as shown, and then proceeds to write down Newton's 2nd Law. What is the correct equation for the y-direction ?


A mass slides down a rough inclined plane with some non-zero acceleration a1. The same mass is shoved up the same incline with a large, brief initial push. As the mass moves up the incline, its acceleration is a2. How do a1 and a2 compare?

How do a1 and a2 compare?

A: a1 > a2 B: a1 = a2 C: a1 < a2

The forces in the "down the ramp" direction (right picture) would be a component of weight, mg*sin(θ), and the frictional force. In the left picture, those are in OPPOSITE directions (gravity is pulling it DOWN the ramp, friction is pushing UP the ramp, opposite v). So, in this case, the two forces oppose each other, meaning less net force, smaller acceleration.

Ladder Discussion A ladder of weight WL leans against a wall. The ladder has rollers at the top so that the wall exerts a normal force only on the top of the ladder. A person of weight WP slowly climbs the ladder.

FWall

WL

WP

Fx

Fy

(friction)

As the person ascends the ladder, the force from the wall (Fwall) A) increases B) decreases C) stays the same.

17

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.


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


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

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 while for larger v, the Dv2 term (called drag) dominates

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

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:

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

exam, examples & friction - high energy physicsjcumalat/phys1110/lectures/lec12.pdfexam,...

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