Question 4.1a:
the block shown in the figure is sliding along a frictionless horizontal surface the block's mass is
m = 4.95 kg,
the magnitude of the applied force is
f = 24.0 n,
and the angle of the applied force
f
from the horizontal is
θ = 33.0°.

three forces act on a block labeled m that is on a horizontal surface. the three forces acting on the block are as follows.
an arrow labeled vector f starts on the right side of the block and points up to the right at an angle θ above the horizontal.
an arrow labeled vector n starts at the top of the block and points up.
an arrow labeled vector fg extends from the bottom of the block and points down.
determine the magnitude n of the normal force acting on the block.
n

question 4.1b:
the block shown in the figure is sliding along a frictionless horizontal surface. the block's mass is
m = 4.90 kg,
the magnitude of the applied force is
f = 21.5 n,
and the angle of the applied force
f
below the horizontal is
θ = 29.5°.

three forces act on a block labeled m that is on a horizontal surface. the three forces acting on the block are as follows.
an arrow labeled vector f starts on the right side of the block and points down to the right at an angle θ below the horizontal.
an arrow labeled vector n starts at the top of the block and points up.
an arrow labeled vector fg extends from the bottom of the block and points down.
determine the magnitude n of the normal force acting on the block.
n

question 4.1c:
the block shown in the figure is sliding down a frictionless surface inclined at an angle
θ = 29.9°
above the horizontal. the block's mass is
m = 5.20 kg.

a block labeled m is positioned upon the incline of a right-triangular wedge that makes an acute angle θ with a horizontal surface. two arrows extend from the block.
a diagonal arrow labeled vector n starts on the block and points in a direction perpendicular to the incline and upward.
a vertical arrow labeled vector fg starts on the block and points downward.
determine the magnitude of the normal force n acting on the block.

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.

bacteria that live on the ocean floor are sustained by phytoplankton. phytoplankton, microscopic marine photosynthetic organisms, have a vastly significant role to play not only in the marine food web of which they’re part of, but also on a more global scale. despite their infinitely small size in comparison to other marine organisms, these tiny creatures occupy an immensely important ecological niche: they are the foundation of the marine food web, and as primary producers, play key roles in supporting all other organisms in the marine environment, as well as in the regulation of the earth’s climate through the sequestration of carbon, oxygen production, and other related processes. phytoplankton account for roughly half of all global primary productivity; therefore, their significance extends far beyond the marine environment alone. there is an intriguing sense of irony in the realization that these tiny living beings that often live out their existence unnoticed and undetected by the rest of the world, have such a far-reaching impact on the lives of virtually all other living organisms on the planet, particularly on those in the marine environment. the world that we have become accustomed to has been and is continuously shaped by the workings of these miniscule yet vital “plants of the sea”.

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