The most important barriers to diffusion today are physical features of Earth's surface.
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Answer:
The velocity of the collar will be 3.076 ft/s
Explanation:
Given data
weight of the disk, Wa = 20lb
weight of rod BC, Wbc = 4lb
weight of collar, Wc = 1lb
Considering the equation of equilibrium
Vb = 1.5Wbc
Wa = 1.875 Wbc
to calculate the velocity of the collar using energy conservation equation
T1 + V1 = T2 + V2
=>
=>
=>
Wbc = 1.18rad/sec
i.e.
= 3.076 ft/ s
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) the initial kinetic energy of the projectile is equal to:
The projectile is fired straight up, so at the top of its trajectory, its velocity is zero; this means that it has no kinetic energy left, so for the law of conservation of energy, all its energy has converted into potential energy, which is equal to
b) If the projectile is fired with an angle of
, its velocity has 2 components, one in the x-direction and one in the y-direction:
This means that at the top of its trajectory, only the vertical velocity will be zero (because the horizontal velocity is constant, since the motion on the x-axis is a uniform motion). Therefore, at the top of the trajectory, the projectile will have some kinetic energy left:
For the conservation of energy, the initial energy mechanical energy must be equal to the mechanical energy at the highest point:
the initial kinetic energy is the same as point a), so we can re-arrange this equation to find the new potential energy at the top of the trajectory:
The projectile is fired straight up, so at the top of its trajectory, its velocity is zero; this means that it has no kinetic energy left, so for the law of conservation of energy, all its energy has converted into potential energy, which is equal to
b) If the projectile is fired with an angle of
This means that at the top of its trajectory, only the vertical velocity will be zero (because the horizontal velocity is constant, since the motion on the x-axis is a uniform motion). Therefore, at the top of the trajectory, the projectile will have some kinetic energy left:
For the conservation of energy, the initial energy mechanical energy must be equal to the mechanical energy at the highest point:
the initial kinetic energy is the same as point a), so we can re-arrange this equation to find the new potential energy at the top of the trajectory: