A photon has an energy of 5.53 à 10¯17 j. what is its frequency in s¯1?
1 answer:
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Answer:
1.dr/dt=0.0096cm/s
2. dA/dt=2.19cm^2/s
Explanation:
A spherical balloon is deflating at 10 cm3/s. At what rate is the radius changing when the volume is 1000π cm3 ? What is the rate of change of surface area at this moment?
for this question, we need to analyze the parameters we know
V=volume of the spherical balloon 1000π cm3
volume of the sphere=
1000π=4/3πr^3
dividing both sides by 4
250*3=r^3
r=9.08cm, the radius of the balloon
dv/dt=dv/dr*dr/dt...................................1
dv/dr ,means
V=
dv/dr=4*pi*r^2
dv/dt=10 cm3/s
from equ 1
10=4*pi*9.08^2*dr/dt
10=1036 dr/dt
dr/dt=10/1036
dr/dt=0.0096cm/s
2. to find the rate at which the area is changing we have,
dA/dt=dA/dr*dr/dt
area of a sphere is 4πr^2
differentiate a with respect to r, radius
dA/dr=8πr
dA/dt=8πr*0.0096
dA/dt=8*pi*9.08*0.0096
dA/dt=2.19cm^2/s
is the rate of change of the surface area
(a) Because the tension in the rope would be larger than the maximum value allowed
When you are sliding down the slope, there are two forces acting on you:
- Your weight, , acting downward, where
m = 70 kg is your mass
g = 9.8 m/s^2 is the acceleration of gravity
- The tension in the rope, T, acting upward
Therefore, the equation of motion is
where a is the acceleration.
If you want to slide at constant speed, then the acceleration must be zero:
And so the equation becomes
This means that the tension in the rope must be:
Which is larger than the maximum tension allowed in the rope (500 N), so the rope will break.
(b) downward
Again, we must refer to the equation of the forces:
In this case, we want the tension in the rope to be the maximum allowed value,
T = 500 N
the other data are
m = 70 kg is your mass
g = 9.8 m/s^2 is the acceleration of gravity
Substituting into the equation, we can find the corresponding value of acceleration:
where the negative sign means the acceleration is downward.