Demonstration DesignLight Sensor

Truck

Light

As the truck passes the light, the light sensor turns off the power to the truck, ensuring that the truck begins stopping at the same point on each run.

Zero Line

What do we need to know?

• Velocity of the truck on low speed:d=t=v=

• Velocity of the truck on high speed:d=t=v=

Derivation of Stopping Distance

• Equations you are familiar with:

F=ma

W=Fd

W=ΔK

K=mv2/2

Derivation of Stopping Distance

Fd=ΔK

mad=mvf2/2 – mvo

2/2

We see that the stopping distance is mass independent.

ad=vf2/2 – vo

2/2

In our case, vf=0. The equation becomes:

d= -vo2/2a

Can you explain the negative sign?

d = -vo2/2a

• Remember we are working with vector values.

d

a v

While the value of v is positive, the value of a is negative. Negative signs will cancel to give a positive distance.

d= -vo2/2a = cvo

2 where c is a constant

volow=

volow2=

dlow=

c=

Now predict stopping distance on high speed

vohigh2=

dhigh=

A Note About Error• Data varies over a range depending on the

equipment and the person making the measurements. This is not uncommon.

• The more measurements used to find an average value, the more accurate that value will be.

• If the experimental value is equal to the expected value within error, the experimental value is correct.

• What are some sources of error in the demonstration?

So what does this mean?

• When cars hit objects, the car is compressed, not the object. The faster the car is going, the more it will compress, and the greater the likelihood of injury.

Review of FrictionSliding friction:• Acts between two surfaces• Opposes the direction of

motion.• Is proportional to the normal

force. • Varies with the slipperiness

of the surfaces.

F = μN

Friction• The friction between the

road and a car’s wheels is called traction.

• Traction allows cars to accelerate and to change direction.

• What happens when the surface the wheels contact changes (the coefficient of friction is changed)?

velocity

acceleration

friction

Normal force

weight

Accelerating rolling object

How does friction act?

Applied force

(a) (b)

(c) No friction is acting

velocity

acceleration

friction

Normal force

weight

Force diagram of a accelerating rolling object

Applied force

The answer is (b)

Why does rolling friction act this way?

• Imagine that no friction exists between the tires and the road. When the wheels are rotated, they will simply spin in place (think of peeling out)

• In order to make the tire travel forward, the tire must “bite into” the road at the point of contact - i.e., friction must exist in the direction opposite the motion.

• Imagine the spinning wheel again. The motion at the point of contact is towards the left.

• The friction must act to the right in order to make the wheel roll!

• Hence, the road pushes the tire.

velocityacceleration

friction

Normal force

weight

Decelerating rolling object

How does friction act in?

Applied force

(a) (b)

(c) There is no friction force acting

velocityacceleration

friction

Normal force

weight

Force diagram of a decelerating rolling object

Applied force

The answer is (a)

Why does friction act this way?• Imagine a tire rolling along. Now imagine

that the rotation of this tire is slowed by some internal force (e.g. brakes).

• Remember Newton’s first law: an object in motion will stay in motion unless an external force acts upon it.

• The tire’s inertia will carry it on at the same velocity (though slipping) unless rolling friction slows the speed of the tire.

• This is what happens when your car skids.

• Applied force speeds up or slows down rotation; friction force is what actually accelerates or decelerates the object.

• Friction force varies with amount of applied force.

• The maximum friction force is determined by the coefficient of friction between the wheel and surface. If the applied force exceeds the maximum friction force, slipping occurs.

Friction

What force is stopping the truck?

FRICTIONInternal friction acting on the wheel axis is slowing

the rotation of the wheels.

However, according to Newton’s first law, an external force must act upon an object to change its inertia.

Rolling friction is what slows the moving body.

ABS

• Anti-lock breaks work by keeping the breaking force on the tires equal to or less than the friction force.

• The rotation then slows at the same rate the car decelerates, so the car does not skid.