Wile E. Coyote vs. Roadrunner

(Projecticus Physicus)

When you were a child, did you ever wonder how tall the cliffs were from which Wile E. Coyote would always plummet?

Has the question of "Just how much force did that crazy Coyote exert when he smacked into that wall?" ever kept you up at night?

Have you ever agonized over the required coefficient of friction for Wile E. to go around a treacherous corner without going flying off an adjacent cliff?

Are you experiencing mild to severe hair loss due to the stressful issue of "Can that catapult really throw the boulder far and fast enough to squash that pesky bird?"

If you answered "yes" to one or more of these questions, then this site is for you!

Let's take a look at a typical day in the life of Wile E. Coyote Click here to hear Wile E. Coyote introduce himself

and his insanely relentless pursuit for the scrawny yet tantalizing Roadrunner.

Click here to hear the Roadrunner introduce himself

Early in the morning, we find Wile E. already hard at work, hoping to catch his prey for a lean, nurtitious breakfast. Having painted a roadway scene on a large steel sheet that stretches the width of the road, he hopes to make the Roadrunner run into the steel slab, stunning him long enough for the Coyote to capture him. Unfortunately, the bird is able to run right through the painted scene and around the corner. Frustrated, Wile E. takes a running start and attempts to do the same, but he smashes into the steel slab.

Let's calculate the amount of force the poor Coyote exerted on the steel door.

The Coyote weighs about 40 kg. When he hit the wall, he was traveling at a velocity of 60mph, and he then came to rest after 1.0 seconds. Therefore:

Vi = 60 miles/1 hour x 1 hour/3600 seconds x 1609 meters/1 mile = 26.8 m/s; Vf = 0

F = (mvchange)/tchange

F = (40 x (26.8 - 0))/1.0

F = 1072 N

It is amazing how the metal is so distorted by such a relatively small force! Acme must have sold him something other than steel!

Undaunted by this initial failure, we next find this predator back in the drawing room with a new plan: use a catapult to fling a large boulder that will squash the pest. After all, everyone knows that a Roadrunner tastes just as good when it is flattened.

Using his favorite cliff to watch for the Roadrunner, Wile E. spots him coming on the exact road at which he aimed his catapult. What luck!

Let's see how much force the catapult has to exert to fling the boulder far enough and fast enough to crush the bird when both the Roadrunner and the boulder are traveling in the same direction. The boulder weighs about 2000 lbs, and the Roadrunner is running at about 125mph.

125 miles/1 hour x 1 hour/3600 seconds x 1609 meters/1 mile = 55.88 m/s

2000 lbs x 1 lb/2.2 kg = 909.1 kg

When it is released from the catapult, the boulder will be 50 meters off the valley floor. Thus:

y = 1/2 at²

50 m = 1/2 (9.8 m/s²)t²

t = 3.19 s

Using this time of 3.19 seconds and assuming that the boulder travels at an average horizontal velocity equal to that of the Roadrunner, the distance traveled by the boulder is:

Dx = vxt

Dx = (55.88 m/s)(3.19s)

Dx = 178.24m

Finally, we will calculate the force that must be exerted by the catapult in order to fling the boulder and squash the Roadrunner.

va = (vi + vf)/2

55.88 = (0 + vf)/2

vf = 111.76 m/s

F = ma

F = (909kg)(111.76m/s / 3.19s)

F = 31843 N

The catapult would need to exert a force of 31843 N on the boulder to throw it far enough and fast enough to kill the Roadrunner. Unfortunately, due to a glitch in the manufacturing of the catapult, the boulder is hurled straight up in the air, and it comes right back down on top of our friend the Coyote. He described this experience to us as "one of my flatter ideas."

Deciding to make one last attempt at catching his prey, Wile E. suddenly has a colossal idea: strap on an Acme rocket jet pack with wheels!

After igniting the rocket Wile E. takes off and soon reaches a maximum speed of about 125 miles per hour. Just as he is about to catch up to roadrunner he sees a turn ahead. The turn radius, he estimates, is about 75 meters and does not seem to be banked. All Wile E. can do is hope that his wheels hold on. (Fat chance!!)

The weight of Wile E. and his rocket are toward the ground, opposed by a normal force in the opposite direction. The force of friction is perpendicular to these, going in the opposite direction of the rocket's travel.

The frictional force of the skates must be equal to the centripetal force caused by the turn. So:

F = ma_c = mv_t²/r

Because there is equilibrium in the vertical direction the Normal force is equal to the force of Wile E. Coyote’s weight.

 N = mg

Also,

Ff = m_s N

so

Ff = m_s mg

m_s mg = m v_t²/r

The mass crosses out and the final equation becomes:

 m_s =v_t²/rg

(55.875 m/s) ²/ (75m)(9.8 m/s²) = 4.25

Therefore the minimum coefficient of static friction that Wile E. Coyote must have between his skates and the asphalt is at least 4.25. Obviously this is not possible (even in the cartoon world!), so instead of making the turn Wile E. Coyote goes flying off the curve at a velocity of 125 mils per hour.

As it always seems to go with our much-maligned friend, the rocket runs out of fuel in mid-air and comes to a complete stop. Wile E. then proceeds to plummet to the bottom of the canyon, hitting the canyon's floor 4 seconds later.

Click here to hear Wile E. Coyote fall to the ground.

Assuming that he traveled in a horizontal path off the road and off the cliff, let's determine how high the cliff was using the length of time it took for him to hit the ground.

t = 4.0 seconds

Therefore:

y = 1/2 at²

y = 1/2(9.8 m/s²)(4.0s)²

y = 78.4m

Frustrated, hungry, and (most importantly) injured, our friend the Coyote calls it quits for the day.

Although his desire to eat the Roadrunner will never end, for the time being, Wile E. must resign himself to simply dreaming about the culinary possibilities...

THE END

A few possibly helpful links:

World Freefall Convention - A bit more explanation of the ins and outs of freefall.

How Stuff Works - Catapults - More explanation about catapults.

How Stuff Works - Rockets - More explanation concerning rockets.

Wile E. Coyote Theater - A place to download Wile E. Coyote cartoons. (Excellent for finding scenarios to use for physics projects!!)

All characters depicted are © Warner Bros. Inc. Looney Tunes, all character names, and related slogans are Trademarks of Warner Bros. Inc.