BesslerWheel.com

[Kirk]

It is an observable fact that momentum is changed by the force/time product on a mass.
Gravity on earth produces an acceleration of 32.2 feet per second per second. This is called g or the gravitational constant. The period of a pendulum is:
T = 2 pi times the square root of L over g
where L is the length of the pendulum and g is the local acceleration of gravity.

For small swings, the period of swing is approximately the same for different size swings: that is, the period is independent of amplitude. This property, called isochronism, is the reason pendulums are so useful for timekeeping. Successive swings of the pendulum, even if changing in amplitude, take the same amount of time.

For larger amplitudes, the period increases gradually with amplitude so it is longer than given by the equation . For example, at an amplitude of θ0 = 23° it is 1% larger than that given by the formula.
For this discussion we will assume the velocity of a pendulum is equivalent to the velocity imparted to a mass dropped the height of the pendulum. In other words a 1 foot drop is 8 feet per second, a 4 foot drop is 16 feet per second.

The farther any object falls, the faster it falls. The amount of kinetic energy that an object could have if it fell is called its gravitational potential energy. It does not matter how far it moves horizontally while it is falling, its kinetic energy at the bottom only depends on the height it fell.

A pendulum is a weight on the end of a tether. As it falls, the tether pulls it horizontally so that it swings back and forth. The kinetic energy of a pendulum when it reaches the bottom of its arc is the same as its gravitational potential energy at the height of its arc. Knowing the height a pendulum started at can tell you how fast it will be moving when it reaches the bottom.

Normally we think in terms of force per unit distance, ie a foot pound or a Newton meter. We define work in these units. Notice, however, we speak in terms of force per unit time when describing acceleration, ie foot per second per second. Since our pendulum is constantly exchanging velocity and potential energy as it travels its arc we see it describes a sine wave if we graph velocity versus time.

If we use the velocity of the pendulum when it is travelling fastest to compress a spring the force distance product (length of the spring) will be obtained using the shortest force time product. The momentum of the pendulum is affected directly proportional to force time.

If we use the force of the spring to affect the momentum of the pendulum the greatest force time product is when the pendulum is slowest, ie at the top of its arc. The difference in the force time products of compressing and expanding the spring is available useful product for this technique.

Momentum or mv is the product of a force accelerating a mass for a period of time. Impulse = force x time. An impulse is a change of momentum.

_________________
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[Kirk]

assume a 4 foot pendulum so 16 feet per second at bottom of swing.
A 2 foot long spring is compressed in 1/8 second at 16fps.
At the top of the swing and pendulum is accelerated by gravity and the spring 2 feet will takeabout 0.3 seconds. So we decelerate for .125 second and accelerate for .3 seconds
.175 second force to the good right?

[Shawn7363]

Kirk

If the spring is unloading at .3 on the way down, compressing the spring on the way up should take longer than .125, most likely more than .3 ..
Even compressing a weak spring will take energy out of the pendulum and slow it down.

Shawn

[Kirk]

the length of the spring is fixed so the compression time is directly a function of velocity. V is max at the bottom of the swing so T will be the distance to be compressed and how fast that distance is traveled.
At the top of the swing you start at zero velocity and accelerate. You are traveling slower than at the bottom, thus it takes longer.
If your spring force is 5% of the mass of the pedulum you will slow at 5% of a g for 1/8 second. wont slow you a lot. most of the v is still there.
once stopped and reversing you have 1 g of accel plus the spring for over twice the time.

[Mark]

Hi, Kirk. Because the tone of conversation that would normally be obvious in a face to face exchange is somewhat lost in this medium, would you please clarify something for me?

Are you proposing a thought experiment, for others to work out with you and determine the feasibility of a possible mechanism...

or, are you explaining what you have observed from hands-on experimentation of a physical model?

Thanks

[Kirk]

model in progress but had a realization as I lay in bed. Even though the time- force mechanism is valid you cant recover all the energy because at the bottom of the swing the V you lose is kinetic energy, ie proportional to v squared so although small is small squared.
What a dissapointment. I have been struggling with sciatica for the past 3 weeks, only last 3 days have I gotten more than 2 hours sleep. Finally found a method of relief, a gravity inversion board whereby you hang from your feet and stretch spine until sciatic nerve isnt pinched.
Actually thought I was onto something and might be useful somewhere else. Have to think about it if that is possible.
I have been thinking about building an electric 3 wheel bicycle (a tricycle) as I fear my 2 wheel days are over. Thats how I injured myself and got the pinched nerve, trying to ride a bicycle. The simple delights of youth how we take them for granted.
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