Answer:
k = 6.72
Explanation:
K of paper = 3.7
k of air = 1
Given that charge Q on the capacitor is constant because cell is disconnected from the circuit. So
V = Q / C = 2.5
Capacity becomes C / 3.7 in air .
capacity becomes C/3.7 when paper is replaced by air .
V₁ = Q / (C/3.7)
= 3.7 Q/C
3.7 x 2.5
= 9.25 V
In the second case ,
capacitance due to new unknown dielectric k
= C/3.7 x k
= kC / 3.7 ( Capacitance in air is C/3.7 )
V ( new ) = Q / ( kC/3.7 )
= 3.7 Q/kC
.55 x 2.5 = 3.7 x( 2.5 / k )
k = 3.7 / .55
= 6.72
Answer:
vi = 4.77 ft/s
Explanation:
Given:
- The radius of the surface R = 1.45 ft
- The Angle at which the the sphere leaves
- Initial velocity vi
- Final velocity vf
Find:
Determine the sphere's initial speed.
Solution:
- Newton's second law of motion in centripetal direction is given as:
m*g*cos(θ) - N = m*v^2 / R
Where, m: mass of sphere
g: Gravitational Acceleration
θ: Angle with the vertical
N: Normal contact force.
- The sphere leaves surface at θ = 34°. The Normal contact is N = 0. Then we have:
m*g*cos(θ) - 0 = m*vf^2 / R
g*cos(θ) = vf^2 / R
vf^2 = R*g*cos(θ)
vf^2 = 1.45*32.2*cos(34)
vf^2 = 38.708 ft/s
- Using conservation of energy for initial release point and point where sphere leaves cylinder:
ΔK.E = ΔP.E
0.5*m* ( vf^2 - vi^2 ) = m*g*(R - R*cos(θ))
( vf^2 - vi^2 ) = 2*g*R*( 1 - cos(θ))
vi^2 = vf^2 - 2*g*R*( 1 - cos(θ))
vi^2 = 38.708 - 2*32.2*1.45*(1-cos(34))
vi^2 = 22.744
vi = 4.77 ft/s
Answers:
a) 
b) 
c) 
Explanation:
<h3>a) Mass of the continent</h3>
Density 
is defined as a relation between mass 
and volume 
:
(1)
Where:
is the average density of the continent
is the mass of the continent
is the volume of the continent, which can be estimated is we assume it as a a slab of rock 5300 km on a side and 37 km deep:
Finding the mass:
(2)
(3)
(4) This is the mass of the continent
<h3>b) Kinetic energy of the continent</h3>
Kinetic energy 
is given by the following equation:
(5)
Where:
is the mass of the continent
is the velocity of the continent
(6)
(7) This is the kinetic energy of the continent
<h3>c) Speed of the jogger</h3>
If we have a jogger with mass 
and the same kinetic energy as that of the continent 
, we can find its velocity by isolating 
from (5):
(6)
Finally:
This is the speed of the jogger
Answer:
<em>Force of gravity may not affect a pendulum during its equilibrium state</em>. But the gravity can affect the pendulum when a force occurs in any direction of the bob connected to the cord that makes a swing sideways. The gravity of pendulum never stops, it always accelerates. So the gravity affects the pendulum acceleration and speed.
<em>Similarly the tension in the cord will not affect the pendulum</em><em> </em>but if change in the length of the pendulum while keeping other factors constant changes the length of the period of pendulum. longer pendulum swings with lower frequency than shorter pendulums.
