An interstellar space probe is launched from Earth. After a brief period of acceleration it moves with a constant velocity, 70.0% of the speed of light. Its nuclear-powered batteries supply the energy to keep its data transmitter active continuously. The batteries have a lifetime of 15.9 years as measured in a rest frame. (a) How long do the batteries on the space probe last as measured by mission control on Earth? yr
(b) How far is the probe from Earth when its batteries fail, as measured by mission control?
ly
(c) How far is the probe from Earth, as measured by its built-in trip odometer; when its batteries fail?
ly
Answers
Answer:
22.26 years
, 15.585 light years , 11.13 light years
Explanation:
a)
=
= 22.26 years
b)
0.7*c*22.26 years
=15.585 light years
c)
0.7*c*15.9
=11.13 light years
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Answers
Answer:
π*R²*E
Explanation:
According to the definition of electric flux, it can be calculated integrating the product E*dA, across the surface.
As the electric field E is uniform and parallel to the hemisphere axis, and no charge is enclosed within it, the net flux will be zero, so, in magnitude, the flux across the opening defining the hemisphere, must be equal to the one across the surface.
The flux across the open surface can be expressed as follows:
As E is constant, and parallel to the surface vector dA at any point, can be taken out of the integral, which is just the area of the surface, π*R².
⇒Flux = E*π*R²
Answers
(a) 7.18
The electric field within a parallel plate capacitor with dielectric is given by:
(1)
where
is the surface charge density
k is the dielectric constant
is the vacuum permittivity
The area of the plates in this capacitor is
while the charge is
So the surface charge density is
The electric field is
So we can re-arrange eq.(1) to find k:
(b)
The surface charge density induced on each dielectric surface is given by
where
is the initial charge density
k = 7.18 is the dielectric constant
Substituting,
And by multiplying by the area, we find the charge induced on each surface:
Answers
Answers
Answer:
the googles are 5.3 m from the edge
Explanation:
Given that
depth of pool , d = 3.2 m
Now, let i be the angle of incidence
a laser pointer 0.90 m above the edge of the pool and laser beam enters the water 2.2 m from the edge
⇒tan i = 2.2/0.9
solving we get
i = 67.8°
Using snell's law ,
n1 ×sin(i) = n2 ×sin(r)
n1= refractive index of 1st medium= 1
n2= refractive index of 2nd medium = 1.33
r= angle of reflection
therefore,
r = 44.1°
Now,
distance of googles = 2.2 + d×tan(r)
distance of googles = 2.2 + 3.2×tan(44.1)
distance of googles = 5.3 m
the googles are 5.3 m from the edge
Answers
Answer:
The time for final 15 cm of the jump equals 0.1423 seconds.
Explanation:
The initial velocity required by the basketball player to be able to jump 76 cm can be found using the third equation of kinematics as
where
'v' is the final velocity of the player
'u' is the initial velocity of the player
'a' is acceleration due to gravity
's' is the height the player jumps
Since the final velocity at the maximum height should be 0 thus applying the values in the above equation we get
Now the veocity of the palyer after he cover'sthe initial 61 cm of his journey can be similarly found as
Thus the time for the final 15 cm of the jump can be found by the first equation of kinematics as
where symbols have the usual meaning
Applying the given values we get
The gravitational force minus any contact forces acting on an object
The difference between the normal force and the gravitational force acting on an object
The sum of all the forces acting on an object in the same direction
Answers
The sum of all forces acting on an object in the same direction is described for the net force acting on an object.
What is a Net force?
- When the forces are acting in the same direction of movement of the object it can be said as sum of the two individual forces will be equal to the "Net Force" .
- The net force is the combined force of all individual forces acting on an object.
- If the object with the forces in the opposite direction, then the net force will not be equal to the sum of the forces.
Example : If two forces (2 kids pushing in the same direction to move the object big box) act on an object (big box) in the same direction, then the net force is equal to the sum of the two forces. If the kids pushed in the opposite direction, the net force will not occur.
Hence, Option D is the correct answer.
Learn more about Net force,
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Answer:
The sum of all the forces acting on an object in the same direction.