Monday 14 May 2012

A 5.00-g bullet moving with an initial speed of 400 m/s is fired into and passes through a 1.00-kg block, as in Figure. The block, initially at rest on a frictionless horizontal surface, is connected to a spring with a spring constant of 900 N/m. If the block moves 5.00 cm to the right after impact, find (a) the speed at which the bullet emerges from the block and (b) the mechanical energy lost in the collision.


Pendulum

A simple pendulum is 5.00 m long. (a) What is the period of simple harmonic motion for this pendulum if it is located in an elevator accelerating upward at 5.00 m/s2? (b) What is its period if the elevator is accelerating downward at 5.00 m/s2? (c) What is the period of simple harmonic motion for the pendulum if it is placed in a truck that is accelerating horizontally at 5.00 m/s2
A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 7.50 N is applied. A 0.500-kg particle rests on a frictionless horizontal surface and is attached to the free end of the spring. The particle is pulled horizontally so that it stretches the spring 5.00 cm and is then released from rest at t = 0. (a) What is the force constant of the spring? (b) What are the angular frequency ω, the frequency, and the period of the motion? (c) What is the total energy of the system? (d) What is the amplitude of the motion? (e) What are the maximum velocity and the maximum acceleration of the particle? (f) Determine the displacement x of the particle from the equilibrium position at t = 0.500 s. 

Tires

While riding behind a car traveling at 3.00 m/s, you notice that one of the car’s tires has a small hemispherical bump on its rim, as in Figure. (a) Explain why the bump, from your viewpoint behind the car, executes simple harmonic motion. (b) If the radius of the car’s tires is 0.30 m, what is the bump’s period of oscillation?

Tuesday 8 May 2012

An ancient rangefinder (roman dodecahedron)

According to Wikipedia, "a rangefinder is a device that measures distance from the observer to a target, for the purposes of surveying, determining focus in photography, or accurately aiming a weapon. Some devices use active methods to measure (such as sonar, laser, or radar); others measure distance using trigonometry (stadiametric rangefinders and parallax, or coincidence rangefinders). These methodologies use a set of known information, usually distances or target sizes, to make the measurement, and have been in regular use since the 18th century".
It could be surprising, but probably the Roman Army had a rangefinder. This was the Roman Dodecahedron.

Image courtesy Wikipedia


Just recently, I learned about this “mistery” of archaeology: the roman dodecahedron. After preparing a copy of a specific object, I proposed a paper on arXiv, explaining that it can be used for measuring distance (as a telemeter/rangefinder). http://arxiv.org/abs/1204.6497 (In Italiano a http://porto.polito.it/2497004/ )
 For me, those dodecahedrons having a structure with holes of different sizes, are military instruments to evaluate distances for ballistics. It is simple to use. Of course, later, during the Middle Age, different instruments had been developed for surveying: the dodecahedron was of the Roman Army, and, probably, its use lost after the collpase of the Empire.

Monday 7 May 2012

Thursday 3 May 2012

Domanda di teoria - 2013 - Stevino

Discutere la legge di Stevino

Per preparare la risposta, usate il file ppt sul portale


Abbiamo visto che 
  Consideriamo il caso in cui ci sia un'energia potenziale dipendente solo da z.
Si ha che, del gradiente resta solo la derivata rispetto a z:
 

 
 Applicazioni notevoli sono i vasi comunicanti e i manometri

Domanda di teoria - 2012

Discutere la statica di fluidi, legando il gradiente della pressione alle forze di volume.

Per preparare la risposta, usate il file ppt sul portale









Wednesday 2 May 2012

Dodecahedral Sound Source

Some builders of acoustics sources produce dodecahedral loudspeakers. These sources have the characteristic to be omni-directional. This is one of important requirements for the sound source thatcan be create from various spherical polyhedrons. The paper: CHIN. PHYS. LETT. Vol. 27, No. 12 (2010) 124302, Directivity of Spherical Polyhedron Sound Source Used in Near-Field HRTF Measurements, by YU Guang-Zheng, XIE Bo-Sun, RAO Dan, is investigating  the directivities of the spherical  tetrahedron, hexahedron and dodecahedron sound sources.
See also 

Tuesday 1 May 2012

Domanda di teoria - Energia potenziale forza centrale

Discutere l'energia potenziale e il potenziale di una forza centrale.

Per rispondere alla domanda utilizzate il materiale seguente.



 Discitiamo ora l'energia di una massa m che si muova di orbita circolare attono at un corpo di massa M 
Discutiamo ora il caso della forza Coulombiana
 
 
Graficamente