Answer:
θ = 21.8º
Explanation:
We can solve this exercise using Newton's conditions for equilibrium, in the attached we can see a diagram of the forces.
The most used coordinate system is an axis parallel to the plane (x axis) and an axis perpendicular to the plane (y axis), let's write Newton's equations on this axes
Y Axis
N- 
= 0
N =
X axis
fr - Wₓ = 0 (1)
Let's use trigonometry to find the normal ones
sin θ = Wₓ / W
cos θ = / W
Wx = W sin θ
= W cos θ
The friction force has the formula
fr = μ N
fr = μ (W cos θ)
We substitute in 1
μ mg cosθ = mg sin θ
μ cos θ = sin θ
tan θ = μ
θ = tan⁻¹ μ
calculate
θ = tan⁻¹ 0.40
θ = 21.8º
Answer:
3.6m
Explanation:
if you are at a building that is 46m above the ground, and the professor is 1.80m, the egg must fall:
46m - 1.80m = 44.2m
the egg must fall for 44.2m to land on the head of the professor.
Now, how many time this takes?
we have to use the following free fall equation:
where 
is the height, 
is the initial velocity, in this case 
. 
is the acceleration of gravity: 
and 
is time, thus:
clearing for time:
we know that the egg has to fall for 44.2m, so 
, and , so we the time is:
Finally, if the professor has a speed of 
, it has to be at a distance:
and t=3.002s:
so the answer is the professor has to be 3.6m far from the building when you release the egg
Continental
drift. This Theory was invented by Alfred Wegener.
<span>His
hypothesis was that the continents move relative to each other on the tectonic
plate and so they drift. The drifting and folding of the continents results in pushing
up huge mountains.</span>
Answer:
w = 0.55 rad / s
Explanation:
For this exercise let's use the conservation of angular momentum, let's write the moment in two moments
Initial
L₀ = r p + 0
L₀ = r mv
The first term is the angular momentum of the mass
Final
Lf = (I + m r²) w
Where I is the moment of inertia of the stool and the other term is the moment of inertia of the mass
L₀ = Lf
r mv = (I + m r²) w
w = m r v / (I + m r²)
Let's calculate
w = 2.0 0.45 3.0 / (4.5 + 2.0 0.45²)
w = 2.7 / 4.9
w = 0.55 rad / s
