Answer:
a = 9.94 m/s²
Explanation:
given,
density at center= 1.6 x 10⁴ kg/m³
density at the surface = 2100 Kg/m³
volume mass density as function of distance

r is the radius of the spherical shell
dr is the thickness
volume of shell

mass of shell


now,

integrating both side



we know,




a = 9.94 m/s²
The new velocity after 4 s is 40 m/s
The height of the spaceship above the ground after 5 seconds is 1,127.5 m
The given parameters for the first question;
- initial velocity of the car, u = 76 m/s
- acceleration of the car, a = - 9 m/s²
The new velocity after 4 s is calculated as;
v = u + at
v = 76 + (-9)(4)
v = 76 - 36
v = 40 m/s
(5)
The given parameters;
- height above the ground, h = 500 m
- velocity of spaceship, u = 150 m/s
The height of the spaceship above the ground after 5 seconds is calculated as;

Learn more here: brainly.com/question/24527971
Answer:

Explanation:
We define our values according to the text,
R= Radius
Velocity
Strenght of the vortex filament
From this and in a vectorial way we express an elemental lenght of this filmaent as
. So,

Where
imply a vector acting perpendicular to both vectors.
Applying Biot-Savart law, we have,

Substituting the preoviusly equation obtained,



So we can express the velocity induced is,

To solve this exercise we need the concept of Kinetic Energy and its respective change: Initial and final kinetic energy.
Let's start considering that the angular velocity is given by,

Where,
V = linear speed
R = the radius
In the case of the initial kinetic energy:

Where I is the moment of inertia previously defined.

In the case of the final kinetic energy, we have to,


For conservation of Energy we have, that
, then (canceling the mass and the radius)





The fibers have lost electrons giving them a positive charge. The rubber gained electrons giving it a negative charge. The positively charged fibers are now attracted to the negatively charged balloon. The negatively charged balloon attracts the paper.