Questions on Fluids, Gravity, Inertia, and Friction

[ritwik06]

My doubts:
1. Why doesn't the time period of a simple pendulum depend either on mass or on the magnitude of amplitude?

2.Why is pressure regardeed as a scalar quantity?

I can't say anything about the first question. But about the second I'll share my views. Pressure = Force/ Area : Force is vector and 1/Area is scalar. So their product should be a vector. There was one more question regarding this in my book, A very thin foil of a metal is placed at a certan depth in water. My book states that it will remain in that position (it will niether rise up nor will sink down) because pressure acts on both sides is equal in magnitude but opp. in direction. If pressure has a direction, then why is it scalar? This is really confusing.

3. For fluids the magnitude of pressure is given by hdg. Why isn't it applicable for solids?

For solids as well: A*h*d*g/A =Pressure.

 

[Pyrrhus]

For the first question, do you know how period is defined? and what is the angular frequency of a simple pendulum?

For the 2nd question, in short pressure is a scalar because of having no direction unlike its twin by units stress (a tensor). This has to deal mostly with how we define pressure. If you have a body and you have a normal vector to its surface, which magnitude is the area of finitessimal segment of the body, and you apply a force on the segment, pressure can be defined as:

$$P = \frac{\vec{F} \cdot \vec{A}}{A^2}$$

 

[ritwik06]

For the first question, do you know how period is defined? and what is the angular frequency of a simple pendulum?

For the 2nd question, in short pressure is a scalar because of having no direction unlike its twin by units stress (a tensor). This has to deal mostly with how we define pressure. If you have a body and you have a normal vector to its surface, which magnitude is the area of finitessimal segment of the body, and you apply a force on the segment, pressure can be defined as:

$$P = \frac{\vec{F} \cdot \vec{A}}{A^2}$$

Time period(T) is the time taken by a simple pendulum to complete one oscillation.

Angular frequency =(2*pi)/T

Well, what's the definition of pressure according to you?

If you have a body and you have a normal vector to its surface, which magnitude is the area of finitessimal segment of the body, and you apply a force on the segment, pressure can be defined as:

$$P = \frac{\vec{F} \cdot \vec{A}}{A^2}$$

I can't understand. Please use some simple words so that I can grasp easily.

 

[ritwik06]

More questions...
1. Which is more accurate stop watch or a stop clock?
My view: Stop watch, becoz it has a lower L.C.
2. Quote from my textbook:

A one dimensional motion can be represented parallel to the x-axis if x-axis is taken in the direction of motion. Then only the x coordinate of the moving particle will vary with time.

My correction: Then only the y coordinate of the moving particle will vary with time!
3. Example of my book:

For example rain drops reach on Earth's surface falling with uniform velocity.

My correction: uniform acceleration! am i right?

 

[AlephZero]

A one dimensional motion can be represented parallel to the x-axis if x-axis is taken in the direction of motion. Then only the x coordinate of the moving particle will vary with time.

My correction: Then only the y coordinate of the moving particle will vary with time!

Wrong. If the motion is parallel to the x-axis then the y coordinate is constant, by definition.

For example rain drops reach on Earth's surface falling with uniform velocity

My correction: uniform acceleration! am i right?

Wrong. (Well OK, if you are being pedantic, the accleration is zero, which is "uniform"). You forgot about the drag force caused by the viscosity of the air.

 

[AlephZero]

My doubts:
1. Why doesn't the time period of a simple pendulum depend either on mass or on the magnitude of amplitude?

It doesn't depend on the mass, because the force of gravity on the pendulum is proportional to the mass, so the accleration of the pendulum = force/mass is independent of the mass.

The period does depend on the amplitude for large amplitudes. for small amplitudes it is approximately constant.

2.Why is pressure regardeed as a scalar quantity?

I can't say anything about the first question. But about the second I'll share my views. Pressure = Force/ Area : Force is vector and 1/Area is scalar. So their product should be a vector.

No, in the context area is also a vector. The force caused by a pressure is always normal to the area you are considering. (People who know about tensors are free to nit-pick about that statement if they want, but from the questions I guess the OP doesn't know about tensors).

Force = Pressure * Area, Force and Area are vectors, therefore Pressure is a scalar.

A very thin foil of a metal is placed at a certan depth in water. My book states that it will remain in that position (it will niether rise up nor will sink down) because pressure acts on both sides is equal in magnitude but opp. in direction. If pressure has a direction, then why is it scalar?

See above - but the statement that the foil will neither rise up nor sink down is complete nonsense, and if what the book says implies this only works at one particular depth, it's very misleading nonsense. Maybe you should burn the book.

3. For fluids the magnitude of pressure is given by hdg. Why isn't it applicable for solids?

It is applicable to solids. Why do you think it doesn't apply to solids?

However, often the pressure in a solid caused by its own weight is small compared with the other forces acting on it, so the pressure effects can be ignored.

 

[xnick]

I can't understand. Please use some simple words so that I can grasp easily.

That formula says that the force that counts for the pressure is only the normal (perpendicular) part of the vector, and that only its modulus if of interest.

Side commentary, IMO, the given definition of pressure at a point in most textbooks lacks an explanation of why the orientation of the surface whose area if infinitesimally small doesn't affects the defined pressure.

 

[ritwik06]

Thanks a lot...

 

[ritwik06]

For a freely falling body under gravity:
1.Why does the slope of S vs. t^2 gives g/2? Why not g itself?
2.Does the graph exhibit linear relationship?

I have studied that the slope of a velocity time graphy gives the acceleration directly. Now when we make a graph for S vs. t^2 from a graph of velocity-time for a freely falling body. So why does the slope of the graph obtained gives g/2?

Why is inertia called an inherent property?

According to third law of motion, specify the action and reaction while hammering a nail.

Action is hammering but what's the reaction?

Why is the force of friction independent of the area of the 2 surfaces in contact? Name a subtance used for coating to reduce friction. Is it paint?

What is meant by uniform magnetic field?

These were some other questions which came to my mind while reading my textbook. Please help!