The diagram below shows a 10,000 kg motorcoach traveling on a straight road which rises and falls. The horizontal dimension has been foreshortened. The speed of the coach at point A is 26.82 chiliad/s (lx mph). The engine has been disengaged and the jitney is coasting. Friction and air resistance are assumed negligible. The numbers on the left show the distance above bounding main level in meters. The letters A–F correspond to points on the route at these altitudes.
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Notice the speed of the omnibus at bespeak B.
An extortionist has planted a flop on the motorcoach. If the speed of the passenger vehicle falls below 22.35 k/s (50 mph) the bomb will explode. Will the speed of the bus fall below this value and explode? If you feel the motorcoach volition explode, place the interval in which this occurs.
Derive an equation to determine the speed of the bus at whatever altitude.
Two 64 kg stick figures are performing an extreme blob jump as shown in the diagram beneath. (Alarm: These are professional stunt stick figures. Don't try this at home.)
One stick effigy stands atop a 7.0 m high platform with a 256 kg bedrock. A second stick figure stands a partially inflated air bag known as a blob (or water trampoline). The offset stick figure rolls the bedrock off the edge of the platform. It falls onto the blob, catapulting the second stick figure into the air. What is the maximum acme to which the second stick figure tin can rise? Assume that stick figures, boulders, and blobs obey the police of conservation of energy.
The illustration below shows a vertical loop segment of a roller coaster. The path of the rail is highlighted in xanthous.
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Segments of roller coaster track are rarely circular. The transition between a direct segment and a circular segment, or two circular segments of different radii, would subject field the rider to abrupt changes in acceleration, called jerk, that would be uncomfortable, especially at loftier speeds. Thrill rides should exist thrilling, not jarring, jerking, or jostling. Curves with a gradually changing radius of curvature are more than common.
The illustration below shows the same vertical loop with circles added to represent the instantaneous curvature at three locations. (For those of you who like technical language, these are called osculating circles.) The analogy also includes the radius of curvature and tiptop above the lowest betoken on the track for these locations.
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Summary of data given for this problem
segment
h (g)
r (m)
a. top of loop
25.8
07.one
b. bottom of arroyo
00.0
23.2
c. vertical descending side
14.0
13.4
Assume minimal energy losses due to air resistance, rolling resistance, or other forms of friction and answer the following questions.
Decide the speed of the coaster at the top of the loop if the normal force of the track on the wheels is half the weight of the coaster (that is, if the frame of reference acceleration is ½grand).
Determine the speed of the coaster at its lowest bespeak before information technology entered the loop. How does the normal forcefulness on the wheels compare to the weight of the coaster at present (that is, what is the new frame of reference dispatch)?
Make up one's mind the speed of the coaster on the side of the loop when it is instantaneously moving straight down. How does the normal strength on the wheels compare to the weight of the coaster at this location (that is, what is the frame of reference dispatch hither)?
Write something completely different.
conceptual
Four identical assurance are thrown from the top of a cliff, each with the same speed. The first is thrown directly up, the second is thrown at 30° above the horizontal, the third at 30° below he horizontal, and the fourth straight down. How do the speeds and kinetic energies of the balls compare as they strike the basis…
when air resistance is negligible?
when air resistance is meaning?
A brawl is dropped from the top of a tall building and reaches concluding velocity as information technology falls. (At last velocity drag equals weight and a falling object stops accelerating.) Will the potential energy of the ball upon release equal the kinetic energy it has when striking the ground? Explicate your reasoning.
numerical
A 55 kg human missive is shot out the oral cavity of a iv.five m cannon with a speed of 18 m/s at an angle of threescore°. (Friction and air resistance are negligible in this problem. Yous may not use Newton's laws or the equations of motion to solve these issues. Call up conservation of free energy.) Determine the following quantities for the human cannonball she exits the mouth of the cannon…
the horizontal and vertical components of her velocity
her kinetic free energy
Determine the following quantities for the human cannonball at the acme of her trajectory.
the horizontal and vertical components of her velocity
her kinetic energy
her potential energy relative to the oral cavity of the cannon
her height above the mouth of the cannon
Watch the video below before showtime this trouble. The tiptop of the building Spider-Man (a.thousand.a. Peter Parker, a.k.a. Tobey McGuire) starts off on is half dozen stories, or 18 meters high (assuming one story is 3 meters). The peak of the building he wants to swing to is 1 story, or iii meters high. The crane onto which he shoots his web is 7 stories, or 21 meters high. Tobey McGuire is 1.75 m tall and approximately 72 kg in mass. (Do not use the equations of movement to solve whatever part of this problem.) Determine…
Spider-Man's speed when his feet touch the roof the 2d edifice
the maximum tension in Spider-Man's web during this video prune
the approximate kinetic energy dissipated when Spider-Human struck the wall
A laboratory cart (g1 = 500 1000) is pulled horizontally across a level track by a atomic number 82 weight (g2 = 25 g) suspended vertically off the end of a pulley as shown in the diagram below. (Presume the cord and pulley contribute negligible mass to the system and that friction is kept low plenty to be ignored.)
If the lead weight falls 85 cm, decide…
the final speed of the system
the acceleration of the organisation
the tension in the cord
A laboratory cart (thousandane = 500 g) rests on an inclined track (θ = 9°). It is connected to a lead weight (m2 = 100 thousand) suspended vertically off the end of a pulley as shown in the diagram below. (Assume the cord and caster contribute negligible mass to the organisation and that friction is kept low enough to be ignored.)
If the lead weight falls 85 cm, determine…
the last speed of the organisation
the acceleration of the organisation
the tension in the string
A 45 kg box is pushed upward a 21 chiliad ramp at a uniform speed. The top of the ramp is 3.0 m higher than the bottom.
What is the potential energy of the box at the peak of the ramp relative to the bottom of the ramp?
What piece of work was done pushing the box up the ramp if friction were negligible?
What work was washed pushing the box upwards the ramp if the forcefulness of friction betwixt the box and the ramp was 100. N?
A 1200 kg automobile driving downhill goes from an altitude of 70 1000 to 40 g above sea level and accelerates from 11 yard/s to 23 m/s.
How much potential free energy did the automobile lose?
How much kinetic energy did it gain?
How much energy is unaccounted for?
Where did this energy become?
An 82 kg skydiver jumps from a height of 95 m and strikes the ground with a speed of vi.0 thou/s.
Calculate the piece of work done by air resistance on the skydiver.
What was the average air resistance on the skydiver during this bound?
How does the magnitude of the average air resistance compare to the weight of the skydiver?
Top pole vaulters have a mass of nearly 80 kg and tin clear a bar 6.0 one thousand above the footing. Top sprinters also have a mass of about 80 kg and can cover 100 m in 10 south. Given these numbers, evidence that world record pole vaults would not exist possible without the pole contributing some rubberband potential free energy.
A two.0 kg rock initially at rest loses 400 J of potential energy as information technology falls freely to the basis.
Calculate the kinetic energy that the stone gains while falling.
What is the rock's speed just before information technology strikes the ground?
A batter hits a pop fly in baseball. It travels direct up at 26.six m/s.
Using the appropriate equation of motion, determine…
the maximum height of the ball in a higher place the bat.
the time it takes for the ball to reach its highest bespeak.
Given that a baseball has a mass of 145 grand, determine…
the kinetic energy of the ball when it left the bat.
the potential energy of the brawl at its highest signal.
algebraic
A mass m slides downward a loop-the-loop track with the dimensions shown in the diagram below. If the mass is released from residual at the bespeak labeled "a" and the rails is effectively frictionless, decide the speed of the mass at each of the other five lettered points in terms of m, r, and g.
A lab cart of mass m is pulled by a cake of mass m in a lab experiment like the one shown in the diagram to the right. Initially, the cart is a distance twoh from the edge of the tabular array and the block is a distance h above the floor. The system starts from rest and is released. Exercise not use Newton's Second law to solve any part of this problem. Land your answers in terms of m, g, and h. Assume that friction is negligible.
Determine the speed of the cart when the block lands on the floor
Determine the speed of the cart when the cart reaches the edge of the table.
statistical
A rough physical model of the pole vault assumes that all the vaulter's kinetic energy on approach is converted to gravitational potential energy at the top of the vault. As we all know, existent world situations are never this elementary. If we compare the kinetic energy of an Olympic sprinter to the gravitational potential free energy of an Olympic pole vaulter, we find that the two numbers are non equal. In the earlier years of the modern Olympics, the potential energy of a vaulter was e'er less than the kinetic energy of a sprinter. (No surprise there. Lost energy is inevitable.) Somewhere in the middle of the 20th century, even so, the situation reversed. The potential free energy of globe class pole vaulters at present routinely exceeds the kinetic energy of world class sprinters. It would appear that vaulters have discovered a way to "violate" the police force of conservation of energy.
Using 1 of the data sets provided below, produce a graph that tin be used to identify the year in which the maximum gravitational potential free energy of Olympic pole vaulters exceeded the average kinetic energy of Olympic sprinters. (Choose an appropriate mass for an athlete and exist sure to identify the year of the transition.)
What changed nearly the sport that enabled pole vaulters to "violate" the police force of conservation of energy? (Was information technology the shoes? Free energy confined? Performance enhancing drugs? Plainly, it has something to practise with energy, but y'all need to be a chip more specific.) Where is the extra energy coming from?
Pick a data set for your analysis.
olympic-dash-vault.txt Combined gold medal results from the men's hundred meter nuance and pole vault for every one of the modern Olympiads.
olympic-decathlon.txt Hundred meter dash and pole vault results of the decathlon gold medalists for every Olympiad in which this event was held.
pile-commuter.txt A group of students performed an experiment driving nails into a wooden block. They used a pile driver of mass m = i.1091 kg released at rest from a height h above the cake. Before the pile driver cruel, the acme of the nail was a tiptop southwardane higher up the block. After the pile driver fell, the height of the smash was a height stwo above the block. They repeated the experiment eight times — four times driving the nail with the grain of the woods and iv times driving the blast across the grain. For each trial determine…
the displacement of the nail when hitting by the pile commuter
the work done past the falling pile driver
the average force exerted past the pile driver on the nail
the boilerplate acceleration of the pile driver while in contact with the nail
the speed of the pile driver on impact
the duration of each impact (in milliseconds), and
the power of each impact (in kilowatts)
Compile your results in tables like those beneath.
Nailing with the grain
h (m)
s1 (m)
sii (m)
∆s (m)
W (J)
F (Due north)
a (m/due south2)
5 (1000/s)
∆t (ms)
P (kW)
0.3060
0.07160
0.06600
0.6115
0.06600
0.05675
0.9180
0.05675
0.04435
1.2220
0.04435
0.03060
Nailing across the grain
h (m)
s1 (m)
southward2 (m)
∆due south (g)
W (J)
F (N)
a (one thousand/s2)
v (thou/s)
∆t (ms)
P (kW)
0.3060
0.06935
0.06670
0.6115
0.06670
0.06095
0.9180
0.06095
0.05370
1.2220
0.05370
0.04640
Lastly, construct a graph of penetration depth vs. average force and…
make up one's mind the effect that force has on the distance a nail moves for this type of wood.
Source: The hammer falls: A fresh look at the pile commuter. Kyle Hathcox and David Ward. The Physics Instructor. Vol. 43 No. 7 (October 2005): 428–431.
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