Answer:
From the question we are told that
The length of the rod is
The speed is v
The angle made by the rod is
Generally the x-component of the rod's length is
Generally the length of the rod along the x-axis as seen by the observer, is mathematically defined by the theory of relativity as
=>
Generally the y-component of the rods length is mathematically represented as
Generally the length of the rod along the y-axis as seen by the observer, is also equivalent to the actual length of the rod along the y-axis i.e
Generally the resultant length of the rod as seen by the observer is mathematically represented as
=>
=>
=>
=>
=>
=>
Hence the length of the rod as measured by a stationary observer is
Generally the angle made is mathematically represented
=>
=>
Explanation:
The temperature of an object is dependant on its heat capacity and the rate at which heat can be removed from its surface. Heat conduction depends on the structure and capability of the atoms to move within the material and pass on their energy to other atoms. Some materials are better conductors then others that is why two objects can be in the same room but feel two different temperatures. It is also true if two object are at different temperatures and are in contact with one another they will reach the same temperature.
Answer:
a) r eq = -a/(2b)
b) k = a/r eq = -2b
Explanation:
since
U(r) = ar + br²
a) the equilibrium position dU/dr = 0
U(r) = a + 2br = 0 → r eq= -a/2b
b) the Taylor expansion around the equilibrium position is
U(r) = U(r eq) + ∑ Un(r eq) (r- r eq)^n / n!
,where Un(a) is the nth derivative of U respect with r , evaluated in a
Since the 3rd and higher order derivatives are =0 , we can expand until the second derivative
U(r) = U(r eq) + dU/dr(r eq) (r- r eq) + d²U/dr²(r eq) (r- r eq)² /2
since dU/dr(r eq)=0
U(r) = U(r eq) + d²U/dr²(r eq) (r- r eq)² /2
comparing with an energy balance of a spring around its equilibrium position
U(r) - U(r eq) = 1/2 k (r-r eq)² → U(r) = U(r eq) + 1/2 k (r-r eq)²
therefore we can conclude
k = d²U/dr²(r eq) = -2b , and since r eq = -a/2b → -2b=a/r eq
thus
k= a/r eq
Answer:
A) 200 j
B) 0 J
C) -100 J
D) -300 J
Explanation:
We know that change in potential energy is given as
where, mg is weight
yf and yi final and initial position
mg = 10 N
yf = 0 m
yi = 20 m
B) mg = 10 N
yf = 20 m
yi = 20 m
c) before fall from the drone
U = mgh
h = yf - yi = 20 - 30 = -10 m
D) point has 0 potential energy
mg = 10 N
h = yf -yi = 0 -30 = - 30 m