Apply problem-solving techniques to solve for quantities in more complex systems of forces.
Integrate concepts from kinematics to solve problems using Newton's laws of motion.
There are many interesting applications of Newton’s laws of motion, a few more of which are presented in this section. These serve also to illustrate some further subtleties of physics and to help build problem-solving skills.
Drag force on a barge
Suppose two tugboats push on a barge at different angles, as shown in
[link] . The first tugboat exerts a force of
in the
x -direction, and the second tugboat exerts a force of
in the
y -direction.
If the mass of the barge is
and its acceleration is observed to be
in the direction shown, what is the drag force of the water on the barge resisting the motion? (Note: drag force is a frictional force exerted by fluids, such as air or water. The drag force opposes the motion of the object.)
Strategy
The directions and magnitudes of acceleration and the applied forces are given in
[link](a) . We will define the total force of the tugboats on the barge as
so that:
Since the barge is flat bottomed, the drag of the water
will be in the direction opposite to
, as shown in the free-body diagram in
[link] (b). The system of interest here is the barge, since the forces on
it
are given as well as its acceleration. Our strategy is to find the magnitude and direction of the net applied force
, and then apply Newton’s second law to solve for the drag force
.
Solution
Since
and
are perpendicular, the magnitude and direction of
are easily found. First, the resultant magnitude is given by the Pythagorean theorem:
The angle is given by
which we know, because of Newton’s first law, is the same direction as the acceleration.
is in the opposite direction of
, since it acts to slow down the acceleration. Therefore, the net external force is in the same direction as
, but its magnitude is slightly less than
. The problem is now one-dimensional. From
[link](b) , we can see that
But Newton’s second law states that
Thus,
This can be solved for the magnitude of the drag force of the water
in terms of known quantities:
Substituting known values gives
The direction of
has already been determined to be in the direction opposite to
, or at an angle of
south of west.
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
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Sekou
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Amisha
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Amisha
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Amisha
belatari
Amisha
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Amisha
nd u
Amisha
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Amisha
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Amisha
ys
Amisha
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Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.