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!
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.
Planets generally move west to east in the sky. However, sometimes a planet will appear to slow down, stop its motion, and start moving in the opposite direction.Eventually the planet starts moving west to east again, but this period of east to west motion is known as retrograde planetary motion.This movement is related to Kepler’s Laws, which are:
1.The orbit of every planet is an ellipse with the Sun at one of the two foci
2.A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.
3.The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.
Kepler’s third law is the most relevant to retrograde planetary motion, since it basically states that the farther a planet is from the sun, the longer its orbital period will be. The equation below shows this relationship demonstrated in Kepler’s third law:
Even though Mercury has a much smaller gravitational force because it has a smaller mass than the Earth, which is related to the period as shown in the denominator of this equation, Mercury also has a much smaller semi-major axis (a), so it has a much smaller period. For Mercury, the orbital period is about 88 days, so for each revolution of the Earth about the Sun, Mercury makes a few revolutions.Because of this, at some points in the Earth’s revolution, Mercury will appear to be moving backwards since it will move around the same side of the Sun as us, which appears as retrograde motion, as shown in the diagram below:
When I was in middle school my friends and I decided to build our own potato cannon. It was really easy, affordable, and a lot of fun. Recently my friend brought it up and I was curious about how it actually worked. After a little bit of roaming the internet and class lectures it became pretty clear how the cannon works.
How we built or potato cannon was simple. We took two pieces of PVC piping, one piece had a twist off cap and the larger chamber was connected to the smaller chamber. A hole was drilled on the side of the PVC pipe in it we placed a grill igniter. For fuel we used hairspray, gas, ect., basically anything that would combust with a spark. So now how does the design help shoot the potato out?
First we can look at how pressure and fluid motion work together in the chamber of the cannon. We have studied that when fluids flow from larger areas to smaller areas the rate of flow increases in the smaller areas. Thus, the staggered build of the cannon; the design of the large chamber connected to the smaller chamber helps achieve an increase in flow, which pushes the potato forward. The pressure that builds up in the chamber as the gas ignites will push the potato forward out of the barrel.
Next you can look at the energy created due to the explosion of gas. This reaction releases an enormous amount of energy which is going to help propel the potato out of the barrel. At the same time the explosion of gas results in an enormous expansion in volume, which is going to greatly increase the rate of flow in the small tube. The shape of the barrel will focus the energy released by the explosion down the smaller tube. The barrel itself is going to do negative work on the potato through frictional forces of the barrel and air resistance. The greater the pressure in the large chamber the greater the difference in pressure between the two chambers. All of these concepts are going to shoot the potato out of the barrel at a tremendous rate, that’s how a potato cannon works!
Downhill skiing encompasses many of the physics concepts we have gone over this year, as well as some we have yet to see. I will briefly go over some of the more basic aspects of skiing and turning in a race setting.
What a skier does is turn gravitational potential energy (mgy) into kinetic energy (1/2mv2) by way of motion. Regardless of the trail condition, a ski slope is never frictionless, and with speeds in excess of 80mph air resistance plays a large role as well. The two forces previously mentioned, friction and air resistance, need to be minimized during a race in order for the skier to maximize their kinetic energy in the form of downhill motion.
Air resistance, or drag is minimized mostly in two ways: by a skiers form, and by choice of clothing.
First, the tight clothing that the racer wears is unfortunately not for style, but rather to create less drag (air resistance). Secondly, the body positioning of the skier is designed to decrease body area in the direction of the drag force in order to decrease its effect.
This is the equation for drag force,
C= drag coefficient
P=density of air
A= frontal area of the skier
V= velocity
As C and p are constant, the only component of this equation up to the skier to control is the frontal area. By crouching down, and keeping ones arms and legs close to the body, a skier is able to lower the frontal area exposed to the drag force.
Friction is combated by getting ones skis on edge, to avoid pushing the snow and creating friction force.
Compare:
By getting on edge (and waxing/sharpening your skis) you reduce friction with the snow and allow you to maintain a greater velocity through a turn.
Curling is a unique sport in that not only is physics an active part of everything that takes places, but the competitors have to be aware of physics principles for every shot they take.The topics of friction, energy, conservation of momentum, and circular motion all come into play in curling.
Perhaps the most interesting example of physics at work in curling is how it explains why the stones actually curl.First, the stone only contacts the ice along a thin ring on the bottom of the stone called the “running surface,” and the ice is pebbled with frozen droplets of water that the stone actually runs on.
Above is a free-body diagram for a rotating curling stone.To ensure the rotational forces all sum to zero and maintain equilibrium, the normal force must counteract the force of friction, so the normal force is greater in the front of the stone than in the back.This means that the pressure is greater on the ice at the front of the stone, which melts the pebbling and produces less friction.With less friction in the front and a rotation already imparted on the stone, the front half of the stone will rotate more quickly than the back, producing the curl, as shown below.
Sweeping in front of the stone is done to take advantage of physics principles.By sweeping, the pebble on the ice is briefly melted, reducing the coefficient of friction.This in turn allows the stone to curl less by producing a more uniform level of friction beneath the entire stone by having melted pebble below the entire stone.This also allows the stone to travel further by reducing the force of friction acting against its motion forward.
Other instances where physics enters curling is in the delivery, where transfer of energy throughout the curler’s body allows the curler to build up enough speed to deliver the stone down the sheet.When stones collide, principles such as conservation of momentum (including angular momentum) and loss of energy allow the curlers to predict where stones will end up and assist them in their shot selection.
Nike recently filed a patent for a power-lacing system for a sneaker.Originally seen in the movie Back to the Future II, the lacing system employs machinery that takes advantage of magnetic fields.In order to create a power-lacing system, a small motor must be incorporated into the shoe.This electric motor takes advantage of magnetism and electromagnetism.The way any electric motor works is by using an electromagnet situated between the north and south poles of two permanent magnets.The electromagnet (which in simplified form is a piece of iron wrapped in a wire) is then electrified, and north and south poles are created.The electromagnet then spins about the fixed center to align with the poles of the permanent magnets.
The magnet does not stop when it is immediately aligned because it has mass and acceleration, and therefore momentum.The magnet then passes the point at which it is perfectly aligned.
In order to maintain rotation, the current in the wire is then reversed, resulting in a switching of the poles.This is continued and the electric motor then continues to spin, turning electrical energy into mechanical energy.The magnet is attached to a drive shaft, which spins.
This spinning drive shaft is part number 1232 in the patent application.The shaft is attached to gears that coil the laces as a power-lacing system. - post written by Corey Weinstein
In the movie 2001 A Space Odyssey, the acceleration caused by gravity is replaced with centripetal acceleration to simulate gravity in space. In the movie, a space ship contains a rotating wheel which rotates at a uniform speed. People and objects on the edge of this wheel experience a normal force from the edge of the wheel which is equal to the normal force they would experience from gravity.
In the picture above, we can estimate the radius of the ship to be 10 meters. We can find the tangential speed at which the circumference of the ship should be rotating by setting mass x gravity equal to velocity squared over radius times mass. We can cancel out mass, and if we know the radius and we know gravity we can then solve to find how fast the ship would need to be rotating.
Interestingly, if someone was at the center of the wheel they would be weightless since radius would be equal to zero. If they moved halfway down the ladder, the radius would be half of the total radius of the ship, and thus if we plug this into our equation (a = v^2/r) we find that artificial gravity would be half of gravity on earth.
One may ask why the current space station did not follow this design, considering that muscle loss due to weightlessness is an issue for astronauts. The answer is that the current space station had to be built in small parts, and a wheel would not be able to create artificial gravity until it was fully completed. Thus, a rotating wheel was impractical.
