A spherical marble that has a mass of 45.0 g and a radius of 0.500 cm rolls without slipping down a loop-the-loop track that has a radius of 30.0 cm. The marble starts from rest and just barely clears the loop to emerge on the other side of the track.
1)
What is the minimum height that the marble must start from to make it around the loop? (Express your answer to three significant figures and in cm.)
In: Physics
A geosynchronous satellite is one that stays above the same point on the equator of the earth. Determine the height above the Earth's surface such a satellite must orbit and find it's speed. (Note that the radius in equation is measured from the center of the earth, not the surface.) You may use the following constants:
The universal gravitational constant G is 6.67 x 10-11 N m2 / kg2 .
The mass of the earth is 5.98 x 1024 kg.
The radius of the earth is 6.38 x 106 m.
Hint: In order for the satellite to remain in orbit, the gravitational force must equal the centripetal force:
In: Physics
1.) A 5.99?C and a -2.04?C charge are placed 16.2cm apart.
Where can a third charge be placed so that it experiences no net force? [Hint: Assume that the negative charge is 16.2cm to the right of the positive charge.
2.) A downward force of 3.0 N is exerted on a -8.4?C
charge.
a.) What is the magnitude of the electric field at this point?
b.)What
is the direction of the electric field at this
point?
In: Physics
A thin uniform pole of length 30 m is pivoted at the bottom end. Calculate the most probable point of rupture on the pole as the pole falls.
In: Physics
In: Physics
A sound wave from a police siren has an intensity of 103.1 W/m2 at a certain point; a second sound wave from a nearby ambulance has an intensity level that is 14 dB greater than the police siren's sound wave at the same point. What is the intensity level of the sound wave due to the ambulance?
In: Physics
I'm teaching a conceptual introduction to physics for American 13-15 year old students this summer.
One of the main ideas I want to hit on is the relationship between energy conservation, equilibrium, and dissipative forces. (e.g. When a box sliding over the floor comes to rest, its kinetic energy mostly goes into heating the floor. We expect this because there there are many degrees of freedom in the floor, while the bulk motion of the box is at most six degrees of freedom.)
I'm looking for experiments and demonstrations of this effect. We can look at examples of turning mechanical work into heat (rub your hands together, hammer a nail, start a fire with friction), but this doesn't quite get across the idea of what thermal energy is. We might be able to observe Brownian motion, but since molecules are too small to see this has limited intuitive appeal for this age range.
Ideally, I'd like to find systems where you can actually see the "microscopic" degrees of freedom alongside the "macroscopic" degrees of freedom. This could be actual physics demonstrations, or artificial scenarios in the form of games the students play out on a field (perhaps following certain rules about the field's layout as individual decision makers, but inevitably creating a certain distribution of students in different "zones" on the field) or simulations on a computer.
All suggestions welcome, and if I implement it in the course next month, I'll report back on how it went.
(Mods, could you please mark this community wiki?)
In: Physics
1) The radioactive isotope 57Co has a half-life of 272
days.
(a) Find its decay constant.
(b) If your source has an activity of 2.00 mCi, how many
radioactive nuclei does it contain?
(c) What is the activity of your source after one year?
In: Physics
In: Physics
A square uniform raft, 18.1m by 18.1m, of mass 6229kg, is used as a ferryboat. If three cars, each of mass 1176kg, occupy the NE, SE, and SW corners, determine the CM of the loaded ferryboat. Use east as the positive x-axis, north as the positive y-axis and the centre of the raft as the origin.
Y coordinate?
X Coordinate
In: Physics
A 2.15-kg object hangs in equilibrium at the end of a rope (taken as massless) while a wind pushes the object with a 18.5-N horizontal force. Find the magnitude of the tension in the rope, and the rope\'s angle from the vertical. The acceleration due to gravity is 9.81 m/s2.
In: Physics
A 6 kg sled is initially at rest on a horizontal road. The sled is pulled a distance of 2.8 m by a force of 36 N applied to the sled at an angle of 30o to the horizontal. Find the change in the kinetic energy of the sled.
In: Physics
Question 1
Which of the following are true statements about the electric field?
|
Equipotential lines imply magnitude and direction of the electric field. |
||
|
The electric field inside a spherical conducting shell in 3D is zero. |
||
|
If the electric field inside a conductor is nonzero, charges must not be moving; that is, there is a zero current. |
||
|
The direction of the electric field is the direction of acceleration of a positive test charge. |
||
|
The electric lines of force indicate the vector force experienced by a positive test charge released at a particular point. |
||
|
The electric field is a vector field that is found by taking the gradient of the negative potential. |
||
|
No electric field exists between the plates of a charged capacitor. |
||
|
The electric field is a charge-specific force field independent of any test charge. |
||
|
The electric field points towards a negative charge and away from a positive charge. |
||
|
A moving charge produces a magnet anomaly. |
10 points
Question 2
Which of the following are true statements about how magnetism is like electricity?
|
Single magnetic poles exist, just like single electric charges. |
||
|
Magnetic circuits can be created, just like electric circuits. |
||
|
The magnetic field lines around a magnet are just like the electric field lines around an electric dipole. |
||
|
Opposites attract and likes repel; poles for magnetism, charges for electricity. |
||
|
Cutting a magnet in half always produces two smaller magnets, just like cutting a charge in half always creates two smaller charges. |
5 points
Question 3
What is Faraday’s Law?
|
It gives the direction of the induced current going through a coil when the magnetic field going through it changes. |
||
|
The sum of all the voltage drops going around any loop in a circuit has to equal zero. |
||
|
The sum of all the current going into a junction has to equal the sum of all the currents coming out. |
||
|
The potential difference across a resistor is proportional to both the resistance and the current going through it |
||
|
It defines the induced voltage across a coil when the magnetic field going through it changes. |
5 points
Question 4
How does the magnetic field in the center of a solenoid change when the number of turns of the single wire is tripled?
|
It doesn’t change because the field is always zero in the center. |
||
|
The magnetic field decreases to one third of the original. |
||
|
It doesn’t change because it’s still only one wire. |
||
|
It depends on the number of turns of the secondary. |
||
|
Edge effects and self-induction keep the magnetic field to double the original. |
||
|
The magnetic field triples. |
In: Physics
shopper in a supermarket pushes a loaded cart with a horizontal force of 8 N. The cart has a mass of 26 kg.
(a) How far will it move in 2.0 s, starting from rest? (Ignore
friction.)
1 m
(b) How far will it move in 2.0 s if the shopper places his 30 N
child in the cart before he begins to push it?
2 m
In: Physics
Prove Carnot’s Theorem: No real heat engine operating between two energy reservoirs can be more efficient than a Carnot engine operating between the same two reservoirs.
In: Physics