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1. Maximum elastic energy in rope

The dynamic kernmantle rope used for fall protection by climbers is specifically designed to absorb quite a lot of energy. To complicate things further, the climber has a whole lot of choices as to which rope to buy, each with different energy absorption characteristics. That is why the rope...
2. How to find the weight of an object given the force

PhanthomJay is right. It would help to draw a free body diagram. You will also have to either know where the CG of the door is, or assume it to be in the center of the door. If that be so, the weight will work out to twice that required to open it. (Drawing the FBD and working the equations...
3. Tire pressure problem

Back when I used to work heavy equipment, civil engineers would often ask me how much pressure a piece of equipment applied to the ground, so that they could design a concrete slab to park it on. I've seen all sorts of schemes to measure contact area to divide the axle weight by. But that...
4. Number of bolts required for a flanged coupling?

You already have much good help in finding the simple solution, but it should be noted that in my experience shaft imbalance often becomes the dominant factor in real rotating flange design. Either because of a manufacturing error or because of a potential mechanical failure.
5. Siphoning problem

From what you have here, you can calculate only the pressure difference from one end of the hose to the other. You need to go back into your book and see how to get water flow rate given pressure and tube diameter.

7. Apparent Weightlessness

I don't think it was a part of anybody's design constraints to achieve apparent weightlessness on the Shuttle. That was just a consequence of achieving a stable orbit.
8. Power generated by water flowing over a dam

The simple answer to your question is that water flowing over a dam generates no power at all. But to figure potential power generation, figure power flowing into the turbine from head height and mass flow rate going into the turbine. Then figure power of water flowing out by the flow rate...
9. The Physics Behind a Bullet Hitting The Human Body

The momentum imparted to the victim will be less than that imparted to the shooter by the recoil of the gun. Did that knock him down? I saw a training vidio once where they shot a guy wearing heavy body armor in the chest with several different high powered rifles, and a 12 ga deer slug...
10. How fast can an object spin!

The light string still has some mass and stiffness, and it has a mass hanging from it. All this means that it has a natural frequency. If the mass spins at that frequency long enough to approach equilibrium, the the string will break at a much lower speed than you calculated here. But if the...
11. Torque on a pulley with a mass

I see no pulley in your picture. It looks to me like a simple hoist drum lifting a load. If you add a frictionless Lilly to the rigging then the torque on it is zero. That is the whole point of putting good bearings in a pulley.
12. Hurricane Evacuation, how l long will it take to evacuate100 000 people?

That's what I got.
13. Hurricane Evacuation, how l long will it take to evacuate100 000 people?

That would have two advantages that are commonly observed in places where they do that. Under nominal conditions, it doubles the flow rate. But even more important traffic continues to flow when one lane is blocked by an accident or breakdown, or more likely you can expect people to start...
14. Hurricane Evacuation, how l long will it take to evacuate100 000 people?

As for how I worked your problem, that was quick and easy because the numbers selected eliminated the need for a calculator. Speed works out to 8000 m per hr. If each car needs 10 m of space, then that is 800 cars per hr. Can you take it from there?
15. Hurricane Evacuation, how l long will it take to evacuate100 000 people?

Chrisman: I base what I say on five decades of living with hurricanes in Florida. I stay put for most of them, even when ordered to evacuate. My house has survived all of them in the last 40 years, always with little or no wind damage. So I look more at the storm surge forecast. If it is...
16. Hurricane Evacuation, how l long will it take to evacuate100 000 people?

I get a little less than two days. But we need to understand that this is an academic exercise only with little relationship to reality. I've done many hurricane evacuations. The only way to make sure you get out safely is to leave about two days before the official order. That is when the...
17. Designing a buoy teather

I remember getting this same question in 9th grade in 1971, but it was a steel buoy. I answered it "not enough information." I went on to explain that I needed the river current. This would obviously be at flood stage, where the component of line tension caused by the current may dominate over...
18. Simple Gear Ratio Problem

It is common in the bike industry to express the ratio as the chain ring size divided by the cluster sprocket size and multiplied by the wheel diameter. If you multiply that by pi, then you have distance traveled per turn of the crank. That is a more meaningful metric.
19. Simple Gear Ratio Problem

No complicated math required. The wheel turns 2.5 times for every one turn of the crank.
20. How many people needed to excite the lift cable to the 15th harmonic?

I'm sorry, but I don't seem to understand the physics under discussion here. It does not seem to match my real world experience, in which I've excited many structures to find many modes, but usually not beyond the tenth. By then the natural frequencies are so high that nobody cares what they...
21. How many people needed to excite the lift cable to the 15th harmonic?

That is not the natural frequency of the human body. So if he is to maintain 100 Hz, then he needs some sort of feedback to know he is doing that. If the amplitude of motion of the lift was great enough, then that would provide sufficient feed back. But the 15th harmomic motion will be too...
22. How many people needed to excite the lift cable to the 15th harmonic?

One person is all you need, if that person has some instrumentation feedback and an understanding of what he is doing. But this is a very simplified mode of an elevator. In real life he would have much damping in the system so that excitation would be small enough to require the...
23. Hip Fracture fall

My mother broke her hip by turning in an akward manner, then she fell. Old bones break easily. Her doctor says this is common in the elderly. They break bones first, doing what for younger people is ordinary activity, and then they fall. Padding would not help.
24. Calculating the force during a collision.

If this were a real problem then how the vehicles crushed would be very important. You would use that to estimate the accelerations. But since the accelerations are given, then you can use the F=ma to find forces on the drivers.
25. How can i find breaking strength of steel, if it's possible at all?

So much so good for a rod. For the rope, let's select a very common rope used in the rigging industry. 6 x 37 IWRC XIPS, one inch diameter. It has a very convenient generic breaking strength of 100,000 pounds and a weight of 1.85 pounds per foot. So how long does it have to be to weigh...
26. How can i find breaking strength of steel, if it's possible at all?

Are we assuming a constant gravity, or are we doing the math to figure out what it really is, knowing that for part of the way the moon's gravity will be stronger. Also, with a wire rope the calculations are entirely different than for a steel rod. E means nothing in a rope because its...
27. The Physics of Fishing and Rotational Motion

It is not a simple question of pole length. One the one hand we must figure the length, spring rate, and lure mass. One the other hand we must match all that to the skill and casting style of the fisherman, which is not purely rotational. The idea is to apply the greatest possible force over...
28. Elevator physics

An elevator normally has a counterweight, that travels in the opposite direction as the car. The counterweight in all the elevators that I've worked on is heavier than an empty car, but a loaded car might be different. So the car would have an effective weight of whatever the difference...
29. Mechanical advantage of a crane

This is just like when i rig a bosun's chair. If I hoist myself it takes less force to pull the rope than if my buddy on the ground pulls me up. While all parts of line in a block system see the same load, my effective weight is reduced by an amount equal to the line load if I'm pulling on the...
30. Force made by a mass falling on the floor

The man has become an engine, and you make the same error often made by people talking about how much torque or power the engine produces. It produces none at all. The load produces power/torque and the drive train transmits it back to the engine shaft. Look at this problem in the opposite...