General Physics I: Day 10Friction Forces & Circular Motion

Dynamics

If not equilibrium (zero acceleration), then…1. Draw a diagram. Then draw FBDs for one or

more objects in the situation.2. Choose your x & y axes.

(One axis should point in the direction of )3. Split forces into x & y components4. Apply Newton’s 2nd Law along each axis

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x xF ma

y yF ma

Sample Problem

Two blocks (2 kg and 4 kg) are pushed along a frictionless surface by a 110 N force directed 20.0° below the horizontal, as shown. What is the force exerted by the big block on the little block?

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4 kg2 kg

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Worked-Example: Realistic Cow Pull

If the tractor applies a force of 20 kN, determine the acceleration of the cow out of the ravine.

Side note:Why the weird choice of axes?

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Worked-Example: Realistic Cow Pull

1. Explain why the there is a negative sign in front of the cow’s weight.

Down is the reason.Be careful with “gravity is pushing down”Better: “the Earth is pulling down (via gravity).”

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Worked-Example: Realistic Cow Pull

2. If the tractor could only apply a 2 kN force, calculate the acceleration of the cow. Describe the motion of the cow+tractor system for this scenario.

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Worked-Example: Realistic Cow Pull

What is FApplied?

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Surface Forces

If an object touches a surface, two forces may arise:

1. The interaction always creates a force pushing on the object (and on the surface). This is the “normal force” because it is always perpendicular to the surface.

2. If the object and the surface attempt to slide against each other, friction will arise…

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Friction

BoonBane

● music ● ● material breakdown ●

● walking ● ● “lost” energy ●

● slouching ● ● rug burn ●

Imagine the interactions between the tiny “bumps” on the two surfaces… the average it all.

Our model of friction is very helpful, but of course it is much more simple than reality.

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Static & Kinetic

We assume there are two types of friction:• Static friction–Surfaces are not moving against each other!–From experience you could conclude that static

friction “adjusts” to respond to a pushing force but there is a limit to its strength.

• Kinetic friction–The surfaces move relative to each other!–Kinetic friction does not adjust! It always

resists with the same force.

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A crate is moving to the right on a conveyor belt without slipping. The conveyor belt has been running for a while and maintains a constant speed. The force of friction on the crate is

A) to the right

B) zero

C) to the left

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The Coefficient of Friction

Both kinds of friction depend how hard the two surfaces are being pressed together (i.e. FN):

Static Kinetic

is a unitless measure of the “stickiness” of two particular surfaces and is unique to those surfaces.

A thought experiment: What would happen if kinetic friction was stronger than static friction?

… we conclude that s is always larger than k.

,f s s NF F ,f k k NF F

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Difficult/Interesting

“I'm having a hard time understanding the kinetic and static friction force equations. Where do the coefficients for each come from?”

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15Static & Kinetic Friction Summary• Static friction occurs if two surfaces are trying to

slide past each other, but are not succeeding.– Static friction is adjustable, reactive

• Kinetic friction occurs if two surfaces actually slide against one another. – Always weaker than static friction– Kinetic friction does not change as long as the

sliding continues.

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Sample Problem

A 5.0 kg block is pushed up a 20.0º incline. If there is no friction present, how hard do we have to push to get the block to accelerate up the incline at 2.0 m/s2?

What changes if we add in friction?

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WarmUp: Walking Friction

People could not walk without friction. Which friction are we talking about here, kinetic friction or static friction?

~20% → Walking is almost entirely about static friction.

~31% → Walking is almost entirely about kinetic friction.

~49% → Walking involves both kinetic and static friction to a large extent.

A)

B)

C)

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The coefficient of friction between a "safe" walking surface and your shoes is supposed to be 0.6 or greater. Do a calculation to estimate the maximum acceleration you could attain under these conditions.

A) Less than 1 m/s2

B) Somewhere near 3 m/s2

C) Somewhere near 6 m/s2

D) Somewhere near 10 m/s2

E) More than 10 m/s2

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An object is held in place by friction on an inclined surface. The angle of inclination is increased until the object starts moving. If the surface is kept at this angle the object

A) slows down.

B) moves at constant speed.

C) speeds up.

D) none of the above.

Hint: How does the force of friction change when the object starts moving.

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Coming up…Tuesday (9/23) → 5.5 & Catch-up (no WarmUp)

Thursday (9/25) → Review for Exam 1

Tuesday (9/30) → Exam 1

Homework #5 due Saturday the 27th

Exam 1 is a week from Tuesday (Deal expires!)

Sample questions posted online by Monday

Extra credit (+3% on Exam 1) posted Wednesday