Answer:
Explanation:
An object is at rest along a slope if the net force acting on it is zero. The equation of the forces along the direction parallel to the slope is:
(1)
where
is the component of the weight parallel to the slope, with m being the mass of the object, g the acceleration of gravity, 
the angle of the slope
is the frictional force, with 
being the coefficient of friction and R the normal reaction of the incline
The equation of the forces along the direction perpendicular to the slope is
where
R is the normal reaction
is the component of the weight perpendicular to the slope
Solving for R,
And substituting into (1)
Re-arranging the equation,
This the condition at which the equilibrium holds: when the tangent of the angle becomes larger than the value of , the force of friction is no longer able to balance the component of the weight parallel to the slope, and so the object starts sliding down.
If the rod is in rotational equilibrium, then the net torques acting on it is zero:
∑ τ = 0
Let's give the system a counterclockwise orientation, so that forces that would cause the rod to rotate counterclockwise act in the positive direction. Compute the magnitudes of each torque:
• at the left end,
τ = + (50 N) (2.0 m) = 100 N•m
• at the right end,
τ = - (200 N) (5.0 m) = - 1000 N•m
• at a point a distance d to the right of the pivot point,
τ = + (300 N) d
Then
∑ τ = 100 N•m - 1000 N•m + (300 N) d = 0
⇒ (300 N) d = 1100 N•m
⇒ d ≈ 3.7 m
Probably for kind of the same reason that speed is expressed as a
relationship between two units. You know, like miles per hour .
I guess the only reason is because no single unit has been invented
to describe density.
The rate of doing work or using energy would always be expressed
as a relationship between two units ... we would say that the rate of
work is "(so many) joules per second". But the "watt" was invented,
so we can say "(so many) watts" instead.
So I guess you're right. Density could be simpler to describe
if we only had a unit for it. Then we wouldn't have to say "(so many)
grams per cubic centimeter". We would just say "(so many) (new unit)".
Let's try it out:
"Uhhh, pardon me Professor . . . I've been working late in the lab,
and I believe I've identified a new substance, hitherto unknown to
the scientific community, and totally unexpected. In its pure form,
the substance appears to be pink, it smells like butterscotch, and
its density is approximately 27.4 Brianas. I think it's time we published
these findings ... with your name as lead investigator, of course."
I like it !
Answer:
Given that refractive index of the material is √2. i.e. n = √2. Hence, critical angle for the material is 45°
