Mechanics | Relativity Answers

A dipole is consisting of an electron and proton, 4e-10 m apart. compute the electric field at a distance of 2e-8 m on a line making perpendicular with the dipole exist from the centre of the dipole?
Answer this question please
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Suppose you want to design an airbag system that can protect the driver at a speed of 100km/h if the car hits a brick wall. How fast the airbag must inflate to protect the driver?

a weight is suspended from a steel wire of length 1.0m and cross sectional area 1.0mm². The ultimate strength of the steel is 400.0 x 10^6 N.m². What is the maximum mass that the weight can have without breaking the wire?

Theoretically, and according to Newton's second law, a car of mass m driven under a constant force of traction F should acquire a constant acceleration a=F/m. in practice, however, the car does not necessarily acquire the expected constant value of a. In fact, its acceleration is found to be a’< a, or it could move with a constant speed! Explain

a body is resting on top of a hemispherical mound of ice of radius r if ice is frictionless then what minimum horizontal velocity must must be imparted to the body so that it leaves the mould without sliding over it

Suppose that Alice is moving to your right at speed c/2 (relative to you)
and Bob is moving to Alice’s right at speed c/2 relative to her.
(a) What is the boost parameter between you and Alice?
(b) Between Alice and Bob?
(c) Between you and Bob? Use this to calculate the relative velocity
between you and Bob. [Hint: Your calculator almost certainly
7 has
a built-in function called tanh−1
or arctanh. The relation between θ
and v can be written as θ = tanh−1
(v/c) = arctanh(v/c).]

Try evaluating the numerator and denominator separately.]
(c) Sketch a graph of cosh θ vs. θ, letting θ range from large negative
values to large positive values. [Hint: Note that for large positive θ,
e
−θ
is very small (e
−θ ≈ 0).]
(d) Sketch a graph of sinh θ vs. θ, letting θ range from large negative
values to large positive values. [Hint: Note that for large positive θ,
e
−θ
is very small (e
−θ ≈ 0).]
(e) Sketch a graph of v/c vs. θ for v/c = tanh θ, letting θ range from
large negative values to large positive values. [Hint: Note that for
large positive θ, e
−θ
is very small (e
−θ ≈ 0).]
(f) Let τ = 1sec and let θ range from large negative values to large
positive values. Sketch the curve in spacetime described by:
t = τ cosh θ,
x = (cτ) sinh θ.
(g) Let d = 1Ls and let θ range from large negative values to large
positive values. Sketch the curve in spacetime described by:
t = (d/c) sinh θ,
x = d cosh θ.

How about some practice working with hyperbolic trig functions? Recall
that
sinh θ =
e
θ − e
−θ
2
,
cosh θ =
e
θ + e
−θ
2
,
and
tanh θ =
sinh θ
cosh θ
.
(a) Verify that cosh2
θ − sinh2
θ = 1.
(b) Verify that
tanh θ1 + tanh θ2
1 + tanh θ1 tanh θ2
= tanh(θ1 + θ2),
so that the law of composition of velocities from last week just means
that “boost parameters add.”

In relativity, it is always nice to look at things from several different ref-
erence frames. Let’s look at the same trip of Gaston to Alpha Centauri
and back, with Alphonse staying at home. This time, though, draw the
spacetime diagram using the inertial reference frame that Gaston had on
his outward trip. Using this frame of reference, calculate the total proper
time that elapses for both Alphonse and Gaston between the event where
Gaston leaves Alphonse and the event where they rejoin.

Let’s get one more perspective on the twin paradox. It is always interesting
to ask what each twin sees during the trip. Now, note that what you
actually see has to do with light rays, and with when a bit of light happens
to reach your eye. So, to study this question, we should study light rays
sent from one twin to the other. We will again have Gaston go off to
Alpha Centauri (4 light-years away) and back at .8c while Alphonse stays
at home.Now let’s figure out what Alphonse sees. Draw another spacetime
diagram for the trip in some inertial frame (again, Alphonse’s frame
is the easiest one to use), but this time suppose that Gaston emits
one light ray every year (according to his own proper time – you may
have to calculate this). What does this diagram tell you about what
Alphonse sees if he watches Gaston through a telescope during the