I would like to ask a couple of questions and clear up a few things about the course work. Until this past Friday I have been busy working on my other two summer classes as well as working with a high school football team as part of my minor, so I have not dedicated the expected amount of time to the course yet. I am currently a senior at JMU majoring in Exercise Science interning at Virginia Tech Athletic Training for the past semester and summer, this is actually the last class I have to complete to satisfy my major. I am not sure how to state this without sounding arrogant, but a lot of the material covered in this class has already been covered - either in high school where I took AP through AP physics, and in my major in classes such as calculus and biomechanics, which is physics with sport related word problems. I have noticed that a lot of the material asked seems to be aimed at people with little to no experience in either of these fields, and I am finding it difficult to proceed with the work because of this as I become very bored and frustrated quickly with the work. I feel confident in my abilities to pass this first test that I am taking this coming week with ease, even with only a few days to review the material. I am asking for your opinion on what I should do in this situation. While finishing the class is something that I believe I can do easily and with good grades, I do not want to continue with the possibility of becoming frustrated with the work and having the quality or tone of the work suffer. Dropping the course and picking up an in-class physics is an option, or if there is an high level online physics going on this summer that is an option also. I am free for the rest of the summer to complete the course work so regardless of the situation I am confident that I have the time and resources to finish. Again I am sorry for the late inquiry, I have had a full first two summer sessions so far and this class was put on the backburner. Please get back to me at your first convenience, either as my vccs email or at scott.wyatt.d@gmail.com.
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To gauge the level of the course you should look at Test 1, Test 2 and the Final Exam (see the link to 'Testing'), and not at the unfortunately necessary remedial work at the beginning. You should also look at the problem assignments from the text.
Your work looks very good so far but you've barely scratched the surface of this course. It does start slowly because students typically come to this course ill-prepared despite having had prerequisite courses, at least on paper.
The first real task of the course is to apply the definition of rates to the analysis of uniformly accelerated motion. This is as opposed to using the four equations of uniformly acceleration motion, which can be used to get answers without understanding much of anything about the physics or the type of thinking necessary to do physics. Most situations can be reasoned out from the definitions, which are equivalent to the first two equations of motion. The last two are derived from the first two.
I believe you have a calculus background and it might be interesting for you to then explore the calculus derivation and its implications, and how this derivation is related to the preceding.
In this course the use of 'canned formulas' is actively discouraged. Everything is to be based on and connected to a few basic principles and definitions, which are amplified by the problem sets and labs. No formula sheets are permitted for tests, and all details of reasoning are required.
Here's a suggestion: Work through all of the 'seed' questions you can, as quickly as you can, which will allow us to better gauge what you know and to come up with a plan tailored to the state of your current knowledge.
When working through the q_a_ exercises you're welcome to simply enter 'ok' on any you're completely sure of, with the exception of the exercises that don't include solutions, which you are expected to solve in detail. I have engineering students from Tech and UVA, enrolled in higher-level courses, who are unable to solve all of those problems (though the better students do easily get most).
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Here's an interesting problem from q_a_13, I believe. I'm including a partial solution given by an average University Physics student, who did not address the University Physics question (most of which is accessible to a Physics 201 student, though the challenge question requires the calculus assumed for that course, and even with that background it's a stretch), along with my notes.
A 1500 kg automobile is moving at 10 m/s.
If its kinetic energy increases by 100 000 Joules, how fast will it be moving?
Suppose the automobile accelerated uniformly as it gained the 100 000 Joules of kinetic energy, which it gained in 10 seconds. What can be determined from this information? Indicate all the answers you can to this question, and how these quantities can be determined.
(University Physics students): If the energy is added at a constant rate of 10 000 Joules / second, will the distance traveled by the automobile be the same as, greater than or less than the distance calculated previously. Consider the fact that a constant force will not add energy at a constant rate to an object whose velocity is changing.
Challenging question: If the distance is different how far will the automobile travel during that time?
Your solution:
`dke=.5 m vf^2 - 5 m v0^2
100000==.5 1500kg vf^2 - .5 1500kg (10m/s)^2
175000=.5 1500kg vf^2
Vf=15.2m/s
We now have 3 values vf vo dt
`ds = (10 + 15.2 )/ 2 * 10
`ds=126m
`dke= fnet `ds
100000=fnet * 126m
Fnet= 793.6561N
From this we can determine acceleration
Fnet=ma
A=0.53m/s^2
We can then find everything else
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A constant force will not add energy at a constant rate so if energy is added at a constant rate, it follows that the force is not constant.
If the force is not constant, neither is the acceleration.
So the v vs. t graph will not be linear.
The same total amount of energy is added, so the initial and final velocities will be the same as before, but the nonlinearity of the graph will tend to change the area under the curve and hence the displacement. If the graph is concave up or concave down on this interval, the displacement will certainly change.
So:
Must the force increase or decrease in order to work at a constant rate while the automobile is speeding up, and why?
What are the implications for the acceleration, and hence for the velocity function?
Does the graph of v vs. t therefore have constant concavity?
If so, is the result an increase or a decrease in the distance traveled compared to the constant-acceleration result?
In addition:
Can you find the velocity function for this situation?
Can you find the actual distance traveled?
These last two questions would be considered pretty challenging.
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Another interesting question relevant to your field, which is not included in any of the course materials but which can be answered in terms of the content of this course:
How does the rate of energy dissipation change with speed and with time when a swimmer pushes off the wall and glides, assuming the glide is well executed (which would make it very close to maximally efficient) and assuming a typical composite body shape.
If the above information was known, how might it be related to the power required vs. speed for a freestyler and for a breaststroker?
What would be the implications for strategy in a 2-minute race, during which it is not possible to sustain maximal power output (i.e., nobody can do an all-out sprint for 2 minutes)?
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Finally, to give you a better picture of the level of the coruse, here are the problems from the current version of Test 2 and the final exam (tests are expire every 5 mintes, at which point they are randomly regenerated):
Problem Number 1
A disk of negligible mass and radius 10 cm is constrained to rotate on a frictionless axis about its center. The disk remains in a vertical plane with its axis horizontal. On the disk are mounted masses of 11 grams at a distance of 8.7 cm from the center, 24 grams data distance of 5.2 cm from the center and 49 grams at a distance of 4 cm from the center. A force is applied at the rim of the disk by a mass of 7.125 grams attached to by a light string around the rim.
As the mass descends 134 cm, with the disk originally at rest, by how much does the potential energy of the system change?
What therefore will be the angular velocity attained by the disk and the velocity attained by the descending mass?
Problem Number 2
A white dwarf star might have about the mass of our Sun, around 2 * 10^30 kg, packed into a very nearly perfect sphere of radius roughly 1600 km (the radius of the Moon). If you suddenly appeared at the surface of a dwarf star you would vaporize-they're hot, even if they are small.
Suppose you somehow managed to retain your mass and some form of structural integrity and began walking across the surface of the star.
If there was a long incline on the star, with the far end of the incline 1 meter higher than the near end, how long would it take you to climb the incline? Assume that you can sustain a production of 92 Joules of useful energy per kg of body mass for 8 hours each day.
Problem Number 3
If a mass of 1.33 kg is spun in a circular arc on a string 38.99 cm long, moving at 171 meters / sec, then what is its angular velocity around the center of the circle and what is the tension in the string?
Problem Number 4
A cart of mass 1.3 kg coasts 95 cm down an incline at 8 degrees with horizontal. Assume that the frictional force is .02 times the normal force, and that other nongravitational forces parallel to the incline are negligible.
What is the component of the cart's weight parallel to the incline?
How much work does this force do as the cart rolls down the incline?
How much work does the net force do as the cart rolls down the incline?
Using the definition of kinetic energy determine the velocity of the cart after coasting the 95 cm, assuming its initial velocity to be zero.
Problem Number 5
A simple pendululm of length 2.8 meters and mass .47 kg is pulled back a distance of .283 meters in the horizontal direction from its equilibrium position, which also raises it slightly. How much force tends to pull the pendulum back to its equilibrium position at this point?
Problem Number 6
A mass of .62 kg rests on a frictionless tabletop, attached by a string running horizontally to and then over a pulley to a mass of .1488 kg.
When the system is released what will be its acceleration?
What is the tension in the strings?
Problem Number 1
A gun fires a bullet of mass 30 grams out of a barrel 21 cm long. The gun is attached to a spring. From the recoil of the spring and the masses of the gun and the spring we determine that the gun recoiled with a total momentum of 13.8 kg m/s.
With what velocity did the bullet exit the barrel?
Assuming that the bullet accelerated uniformly from rest along the length of the barrel, how long did it take the bullet to accelerate from rest down the length of the barrel?
What was the average force exerted on the bullet as it accelerated along the length of the barrel?
What average force would be felt by the individual holding the gun for the time the bullet accelerates along the length of the barrel?
Problem Number 2
A uniform rod of mass 2.3 kg and length 93 cm is constrained to rotate on an axis about its center. A mass of .529 kg is attached to the rod at a distance of 35.34 cm from the axis of rotation. An unknown uniform torque is applied to the rod as it rotates through .16 radians from rest, which requires 1.3 seconds. The applied torque is then removed and, coasting only under the influence of friction, the rod comes to rest after rotating through 2.2 radians, which requires 11 seconds.
Find the net torque for each of the two phases of the motion.
If the applied torque is the result of a force applied at one end of the rod, and perpendicular to the rod, then what is this force?
What is the maximum KE of the system? How much of this KE resides in the .529 kg mass?
Problem Number 3
An Atwood machine consists of masses of .5 Kg and .53 Kg hanging from opposite sides of a pulley.
As the system accelerates 3.3 meters from rest, how much work is done by gravity on the system?
Assuming no friction or other dissipative forces, use the definition of KE to determine the velocity of the system after having moved through the 3.3 meters, assuming that the system was released from rest.
Problem Number 4
A disk of negligible mass and radius 10 cm is constrained to rotate on a frictionless axis about its center. The disk remains in a vertical plane with its axis horizontal. On the disk are mounted masses of 7 grams at a distance of 8.5 cm from the center, 12 grams data distance of 5.3 cm from the center and 45 grams at a distance of 3.6 cm from the center. A force is applied at the rim of the disk by a mass of .9162 grams attached to by a light string around the rim.
As the mass descends 187 cm, with the disk originally at rest, by how much does the potential energy of the system change?
What therefore will be the angular velocity attained by the disk and the velocity attained by the descending mass?
Problem Number 5
An automobile starting from rest can reach the legal speed of 15 m/s in the first 2.678 meters. What is its average acceleration? code `t
Problem Number 6
A white dwarf star might have about the mass of our Sun, around 2 * 10^30 kg, packed into a very nearly perfect sphere of radius roughly 1600 km (the radius of the Moon). If you suddenly appeared at the surface of a dwarf star you would vaporize-they're hot, even if they are small.
Suppose you decided to orbit the white dwarf in a heat-resistant craft at a radius of 1900 km from the center. At what rate would you orbit?
Problem Number 7
A simple harmonic oscillator with mass 1.19 kg and with restoring force constant 250 N/m is released from rest at a displacement of .2 meters from its equilibrium position. What will be its velocity when it is halfway to its equilibrium point, and what will be its velocity at equilibrium?
Problem Number 8
A pendulum is released from rest at a displacement of .38 meters from its equilibrium position. It is stopped abruptly and uniformly at its equilibrium position and it is observed that a loose bit of metal slides without resistance off the top of the pendulum and falls to the floor .95 meters below.
If the projectile started off with a velocity in just its horizontal direction, and if travels .21 meters in the horizontal direction during its fall, what was the velocity of the pendulum at equilibrium?
What would be the velocity of the pendulum at a point .1634 meters from its equilibrium position?
Problem Number 9
An average force of 410 Newtons acts on a mass of 3.1 Kg for .05 seconds. Use the Impulse-Momentum Theorem to determine the change in the object's velocity.
Problem Number 10
What will be the tension in the string holding a ball which is being swung in a circle of radius 1.2 meters, if the ball is making a complete revolution every .6 seconds? Assume that the system is in free fall (e.g., in a freely falling elevator, in orbit, etc.)?
What would be the tension in the string if the system was on and stationary with respect to the surface of the Earth, with the ball being swung in a vertical circle, when the ball is at the top of its arc?
What if the ball is at the bottom of its arc?
What if the ball is at its halfway height?
Problem Number 11
A simple harmonic oscillator has a restoring force of 30 N/m and a mass of .27 kg. It is given a KE of .2485 Joules at a point .1 meters from equilibrium.
What will be its maximum displacement from equilibrium?
What will be its equation of motion?
According to the corresponding acceleration function what will be the acceleration of the oscillator at clock time t = 1.194 sec?
What will be its position at this clock time?
What is the force on the oscillator at this position?
Does this force result in the acceleration you just calculated?
Problem Number 12
A simple harmonic oscillator is observed to undergo simple harmonic motion with a frequency of .3 cycles / second.
What are the maximum magnitudes of its acceleration and velocity?
At what displacements from equilibrium can each maximum occur?
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