Find a numerical value for rhoearth, the average density of the earth in kilograms per cubic meter. Use 6378km for the radius of
1 answer:
According to the information provided to define an average density, it is necessary to use the concepts related to mass calculation based on gravitational constants and radius, as well as the calculation of the volume of a sphere.
By definition we know that the mass of a body in this case of the earth is given as a function of
Where,
g= gravitational acceleration
G = Universal gravitational constant
r = radius (earth at this case)
All of this values we have,
Replacing at this equation we have that
The Volume of a Sphere is equal to
Therefore using the relation between mass, volume and density we have that
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(a) 29.8 m/s
To solve this problem, we start by analyze the vertical motion first. This is a free fall motion, so we can use the following suvat equation:
where, taking upward as positive direction:
is the final vertical velocity
is the initial vertical velocity (zero because the pebble is launched horizontally)
is the acceleration of gravity
s = -25.0 m is the displacement
Solving for vy,
(downward, so we take the negative solution)
The pebble also have a horizontal component of the velocity, which remains constant during the whole motion, so it is
So, the final speed of the pebble as it strikes the ground is
(b) 29.8 m/s
In this case, the pebble is launched straight up, so its initial vertical velocity is
So we can find the final vertical velocity using the same suvat equation as before:
(downward, so we take the negative solution)
The horizontal speed instead is zero, since the pebble is initially launched vertically, so the final speed is just equal to the magnitude of the vertical velocity:
v = 29.8 m/s
(c) 29.8 m/s
This case is similarly to the previous one: the only difference here is that the pebble is launched straight down instead than up, therefore
Using again the same suvat equation:
(downward, so we take the negative solution)
As before, the horizontal speed instead is zero, since the pebble is initially launched vertically, so the final speed is just equal to the magnitude of the vertical velocity:
v = 29.8 m/s
We notice that the final value of the speed is always the same in all the three parts, so it does not depend on the direction of launching. This is due to the law of conservation of energy: in fact, the initial mechanical energy of the pebble (kinetic+potential) is the same in all three cases (because the height h does not change, and the speed v does not change either), and the kinetic energy gained during the fall is also the same (since the pebble falls the same distance in all 3 cases), therefore the final speed must also be the same.
Answer:
Work done = 13605.44
Explanation:
Data provided in the question:
For elongation of 2.1 cm (0.021 m) work done by the spring is 3.0 J
The relation between Energy (U) and the elongation (s) is given as:
U = ................(1)
where,
k is the spring constant
on substituting the valeus in the above equation, we get
3.0 =
or
k = 13605.44 N/m
now
for the elongation x = 2.1 + 4.1 = 6.2 cm = 0.062 m
using the equation 1, we have
U =
or
U = 26.149 J
Also,
Work done = change in energy
or
W = 26.149 - 3.0 = 23.149 J