Can Kobe Bryant jump over a moving car?

In 2008, a commercial promoting the new "Hyperdunk" line of basketball shoes went viral on the internet. The commercial involved Los Angeles Laker, Kobe Bryant, jumping over a moving Aston martin.

"If 'Rambo Part XX' can be a one-man militia, I can jump over an Aston Martin" he told the Los Angeles Times.

http://www.youtube.com/watch?v=BIWeEFV59d4

Understandably, there was a lot of speculation as to whether or not the stunt was real. Can we use physics to determine the validity of the stunt?

The "Dot Physics" blog of Wired website used physics to examine whether or not the jump was fake. They used Tracker Video Analysis to get the x,y positions of each body part in each gram and plotted center of mass values against time. They then fit a quadratic function to the center of mass and related it to the kinematics equation and found that the data fit the expected parabola very well.

Next, they examined Kobe's horizontal position during the jump using the same method. They found that the horizontal motion of his center of mass was fairly constant, which is what one would expect for a jump. There is no force in the horizontal direction while in the air, so there should be no horizontal acceleration.

Thus, by examining his vertical and horizontal positions, it seems as though the jump itself was real. However, an image overlapping two frames shows that Kobe was actually standing very near to the front right tire of the car, not in the middle of the car. This suggest that a degree of deception was involved.

"Sports Science," which is an ESPN television series that explores the science and engineering underlying athletic endeavors, also examined whether the stunt was real or fake. They, however, took a different approach: they tried to recreate the stunt that Kobe apparently performed.

The stuntman must perform the very difficult task of perfectly synchronizing the peak of his jump with the top of the car passing underneath him. In order to clear the car, a jump of at least 48 inches off the ground is required. The stuntman himself can jump 52 inches off the ground. If the Aston Martin is travelling at 55 mph it moves 1 foot every 0.01 seconds, meaning the stuntman must leave the ground when the car is exactly 24 feet away. However, it takes the brain 0.25 seconds to react to visual stimuli, meaning the stuntman must decide to jump when the car is actually 44 feet away.

After many many trials, they were ultimately unable to recreate the stunt. The stuntman was able to jump a high enough height to clear the car but the timing was impossible - 0.01s accuracy was required. The only time they were able to recreate the stunt was when the stuntman wore a harness connected to a 40 foot crane in order to give him an extra boost and to keep him safe.

Thus, the stunt was fake.

Furthermore, the earlier mentioned Dot Physics blog found that the Aston Martin that Kobe apparently jumped over was travelling at a constant velocity of about 22 mph. If Sports Science could not perform the stunt when the car was travelling at 55 mph, it is even less likely that Kobe was able to perform the stunt when the car was travelling at 22 mph since the slower velocity of the car means that Kobe had to be in the air for a longer amount of time.

In conclusion although the jump itself was real, the stunt was faked in some way.

The Physics of X-Rays

What is an X-Ray?

            X-Rays are electromagnetic waves with a wavelength of .01 to 10 nanometers. They are generated in an X-Ray tube. X–Ray tubes work by shooting a stream of electrons at a piece of metal, usually tungsten. There is a magnetic field around the tungsten, which drastically slows down the electrons. Because energy is conserved, the kinetic energy of the electrons must be converted into another form when they are slowed down. The kinetic energy is converted into X-Rays, which are a form of radiant energy (the energy of electromagnetic waves).

 How X-Ray Images are Generated

            An X-Ray sensitive film is placed below a designated area of the body, and X-rays are shot at this area. Dense materials in the body, like bone, absorb or scatter the X-rays and do not let them reach the film in that area. This causes a white shadow to appear on the film that shows the shape of the bone. Less dense materials like muscle and fat allow most of the x-ray particles to pass through and reach the film, making the film dark in these areas.  - Post written by Sammy Kay-Green.

Popping Popcorn with Cell Phones

Have you ever thought about popping popcorn with your cellphone??

http://www.youtube.com/watch?v=V94shlqPlSI

Well, sorry, you can't.

An electromagnetic wave is made up of alternating electric fields, a charge exposed to it will experience forces regularly changing in direction. For water molecules, which are dipoles, the net effect would force the molecules into rotation.. These agitated water molecules then posess heat energy to transfer into the food, thus cooking it. The key note here is that the microwave acts as a protective box, directing the waves directly at your food. Microwaves operate at a frequency of up to 300 GHz.

Cell phones cannot direct all that energy straight into a tiny popcorn kernel since it is not in a closed box like a microwave. Additionally, they do not emit enough energy (they operate at a frequency of roughly 2 gHZ) to heat up the water in the kernels to make them pop, and if they did, they would probably boil the water in your hand while you were on the phone and eventually make your hand explode!

The Physics of Draining a Container

If you have ever bought a 2.5 gallon Poland Spring container you know that they don’t work very well as purchased. The water will flow out of the nozzle at a slow pace for a few cups of water and then come to a halt. In order to get the water to flow at an acceptable rate you must punch a hole in the top of the container. This is because when there is no hole at the top of the container a vacuum builds in the interior of the top of the container and a pressure gradient force caused by the difference between the low pressure at the top of the container and atmospheric pressure outside of the container causes air to move in through the same hole that is letting out water. This causes the water to drain from the container in a discontinuous way and at a slow pace.

Putting an additional hole at the top of the container allows the air to enter the container though a hole that is separate from the hole through which water is exiting. This allows the water to exit in a continuous stream at a much faster pace.

- Post written by John Mahon

The Physics of a Water Polo Shot

In water polo a player can shoot the ball as fast as 50 miles per hour without contact with a surface to provide force and stabilization.  I want to explain how a water polo shot works and consider a few physics concepts that are at work in scoring a goal.

Procedure:

1)    Player lifts the  ball out of water with his/her shooting arm raised above the shoulder and trunk rotated away from the goal

a.     Non-throwing arm is outstretched in the direction of the goal for aim

2)    The player raises their body as high out of the water as possible to minimize F_D

3)    Shot is initiated by rotation of front arm away from goal and trunk rotation toward goal

a.     As the trunk is rotated forward, the throwing arm is left behind for greater potential energy due to F_T in triceps and shoulder muscles

4)    The shoulder is rotated and elbow extended to release the ball

a.     Trunk lean is away from shooting arm to improve position relative to the axis of rotation (spine) and maximize velocity

5)    The wrist snaps for follow-through and fingers can be used to provide spin on the ball

Many of these procedures are similar to throwing a baseball with a few special considerations due to  the fact that the player is never in contact with the ground and does not have a stabilizing force. In water polo, the action of the legs is key for support, balance, and production of force behind the shot.  During the shot there are several key actions of the legs to aid in balance and force production.  The player starts with their non-shooting-side foot pointed to ward to goal for aim.  Force is produced during the shot by “snapping” in the shooting-side foot to initiate trunk rotation.  During the forward swing, the non-shooting-side leg is forcefully extended to achieve force balance from the upper body rotation.

The key physics concepts used in scoring a goal in water polo are buoyancy and drag force, tension of muscles, angular momentum, and distribution of forces.

Videos:

Some great water polo shots: (showed shot at 4:39 in class)

http://www.youtube.com/watch?v=3Pte0XE2oKQ&feature=related

A clip from the movie “Children of Glory” about the "Blood in the Water" match between Hungary and the USSR at the 1956 Melbourne Olympics during the Hungarian Revolution. It is a fun video to watch, but we only saw a clip of the penalty shot at 3:34.

http://www.youtube.com/watch?v=MLoA5yLZ4l4&feature=related

Post written by Kelsie Anson

The Physics of Whipped Cream

There are two physical principles involved in making the delicious white fluffs (the canned ones).

First is the liquefied gas. When the canned whipped creams are made, half the bottle is filled with cream (although these days it’s usually hydrogenated vegetable oil) and the other half of the bottle is filled with liquefied gas. To liquefy gas at high temperature, great pressure is applied to the gas and consequently the pressure inside the can is much higher than the pressure outside of the can. The liquefied gas mixes with the cream inside the bottle, and when we tweak the valve, which works to equalize the pressure inside and outside the can, the pressure inside the can decreases and some of the gas evaporates, making a gas layer on the top of the can. This layer takes up a large volume and pushes the liquefied gas + cream through the tube, out of the can. When the liquefied gas inside cream comes out of the can and experiences sudden increase in pressure, they also evaporate, making air bubbles. These air bubbles are trapped inside the cream, making the cream fluffy. (Disregard the numeric values on the graph).

Second phenomenon is the “sheer thinning.” The whipped cream when it’s coming out of the can flows out like liquid but once it sits on top of the whatever drink you have, it stays put like solid. This is because when the molecules of the cream slide or “sheer” past each other, the viscosity of the liquid decreases temporarily and the cream flows. This phenomenon was demonstrated by NASA in 2008. NASA used xenon, which is a chemically inert, sing-atom substance, in outer space because the experiment needed xenon to be at its critical point where the line between liquid and vapor states blur.  NASA demonstrated that when they stirred the xenon fluid faster, the resistance to stirring decreased, which indicated that the viscosity of the fluid has temporarily decreased. - Post written by Eunnie Jung

Physics of Internal Combustion Engine

Four-Stroke Cycle (Otto Cycle)

1. Intake Stroke: piston moves to max volume and sucks in vaporized fuel mixture

2. Compression Stroke: piston moves to min volume, compressing the fuel mixture (increase in pressure, temp, density of fuel)

3. Power Stroke: spark plug ignites the fuel mixture; piston moves to max volume; power transmitted to crank shaft

4. Exhaust Stroke: piston moves back to min volume, exhaust valve opens to let exhaust out

Chemical PE, Translational & Rotational KE

High temperature and pressure converted to work

Thermodynamic Limit (Efficiency): 37%

Most engines: average efficiency of 18-20%

NOT Frictionless, Ideal Gases, Perfect Insulator

Direct Injection

—Direct Injection: better dispersion of air/fuel mixture, cylinder and piston cooler

—Better Fuel/Air Ratio (Increase Fuel Efficiency) Higher Compression Ratio (Extract more mechanical energy), Higher Power Output

Supercharging/Turbocharging

—Forced Induction (“Direct Injection” for Air) : compresses air and allows more fuel/air to enter the cylinder

—Turbocharger: uses exhaust gases to power a turbine to spin the compressor (no parasitic effect)

—Supercharger: uses a belt/chain connected to the engine’s crankshaft to power compressor (no lag)

—Increases mass flow-rate and burns more fuel; extract more useful energy per unit of fuel

—Increase Power and Efficiency

The Physics of the Bullet Drop Problem

A typical physics problem combines two identical bullets, one shot from a gun at a given height and the other dropped from the same height. Analyzing when they hit the ground suggests that, ideally, they hit the ground at the same time. MythBusters actually tested this problem and looked at the reality of obtaining these results.

When the bullets are both fired and dropped there are forces acting on them, the force of gravity acting in the downward direction and the force of air resistance acting in the direction opposing the motion of the bullet.

If we were to look at this problem in a vacuum the air resistance could be ignored and it would be very clear that the force due to gravity would be the same on both bullets. The force that the gun applies to the fired bullet is only acting horizontally and thus determines how far in the x-direction the bullet will move, not how long it will take. Since the height the bullets are dropped from is the same and the force causing their downward motion is the same both bullets would hit the ground at the same time.

However, as the MythBusters found out this is not exactly true. Because of air resistance acting on the bullets there is a slight difference in the time it takes for them to reach the ground, though very, very small. As discussed in class air resistance (or the drag force) is expressed as

But in order to determine this force on the fired bullet as it relates to the time that it takes for the bullet to fall we must break this force into components. Because of this breakdown into components it can be determined that the air resistance on the fired bullet actually causes it to take longer to hit the ground than the dropped bullet, also experiencing air resistance.

The MythBusters demonstration made it clear that, though the bullets won’t hit at exactly the same time the difference in the time is so small it has to be measured with a high-speed camera and using the images can be calculated to be about 39.6 milliseconds, a time that is smaller than the human eye can detect.

http://www.youtube.com/watch?v=D9wQVIEdKh8 (start at around 2:10)

Physics of Skydiving

Skydiving is a great example of many of the physics concepts that we have discussed thus far in our class. First we can examine the forces acting on a skydiver as he is falls. Initially as the diver jumps out of the plane the main force acting on him is a gravitational force. There is also a really small buoyant force which can largely be neglected since it is based on the density of the 'fluid,' in this case air, surrounding the skydiver. As the skydiver accelerates downwards due to gravity his velocity increases, which subsequently increases the drag force acting on him due to air resistance which is dependent on the skydiver's velocity. He will eventually reach his terminal velocity, the speed at which he is no longer accelerating because the force due to gravity is exactly balanced by the drag force. However this terminal velocity is still really large and it would be a bad idea for a skydiver to hit the ground going at this speed, so the use of a parachute comes into play. A parachute increases the skydiver's area, another variable of the drag force. So as soon as the skydiver deploys his chute he is still going pretty fast but now greatly increased his area and thus his drag force. This causes a rapid net force upwards, the force of drag is much greater than the force of gravity, which causes him to rapidly decelerate and slow down. As his velocity slows his drag force also decreases and eventually he once again comes to a new terminal velocity where the forces are balanced, however this second terminal velocity is much lower than the first so he won't injure himself upon impact with the ground.


This is a fun animation which shows all the forces acting on a skydiver, check it out in motion at this site!

Here is a link to an extreme skydiver

If you wanted to calculate this terminal velocity all you would need to do is set the drag force equal to the force of gravity and solve for v.


Fun facts:

Because air density increases with decreasing altitude, this causes an increased buoyant force near the surface of the earth. The buoyant force causes the terminal velocity to decrease by 1% every 525ft.

The world record for skydiving speed of 614 mph was obtained at high altitude where the less dense air reduces drag and buoyant effects.