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>> In this video,
we're going to take a closer
look at Newton's 2nd Law.
The 2nd law says that
the net force of an object
equals the object's mass
times its acceleration.
This equation is useful for
solving many types of problems
involving motion.
Let's try a few in order
to get practice working
with Newton's 2nd Law.
Walking through a warehouse,
you see a box on the floor.
You decide to give it a push
using a force of 25 Newtons
in the horizontal direction.
If the box accelerates at
0.5 meters per second squared
under this force,
what is the mass of the box?
Assuming the floor is
frictionless, your push,
which is an applied force,
is the only horizontal force
acting on the box.
By Newton's 2nd Law,
the strength of this push,
in Newtons, equals the box's
mass, in kilograms,
times its acceleration
in meters per second squared.
Dividing both sides
of the equation by
the acceleration, a,
we see that the box's mass
equals the applied force
divided by a.
We can now plug in the values
we know for f applied and a.
F applied is 25 Newtons,
and a is 0.5 meters
per second squared.
The mass of the box is
25 Newtons divided by 0.5
meters per second squared,
which is 50 kilograms.
Let's look at another example.
Two runners line up
to start a race.
The first runner has
a mass of 67 kilograms,
while the second runner's mass
is 73 kilograms.
If runner one has
an acceleration
off the starting block of
6 meters per second squared,
what force does the runner two
need to exert in order to have
the same acceleration?
We have two different runners
and we want to match
their acceleration at
the start of the race.
Written as an equation,
we say that the acceleration
of runner one equals
the acceleration of runner two.
By Newton's 2nd Law,
force equals mass
times acceleration.
The force of runner two equals
mass times her acceleration.
If we go back to our
starting equation,
that runner one's acceleration
equals the acceleration of
runner two, we can substitute
that acceleration into our
equation for runner two's force,
and find that the force
exerted by runner two equals
the acceleration of runner one
times the mass of runner two.
Plugging in the values
for a1 and m2,
we see that the force
runner two needs to exert
to accelerate just as much
as runner one equals
six meters per second squared
times 73 kilograms,
which equals 438 Newtons,
or 440 Newtons
when using significant figures.
Let's look at one more example.
An ice skater skating
in a straight line
at four meters per second
comes to a sudden stop
in half a second.
If the mass of the ice skater
is 47 kilograms,
how much force is exerted
on her in coming to a stop?
To solve this problem,
we can use Newton's 2nd Law.
The net force on the ice skater
equals her mass times
her acceleration.
We are given her mass, but,
what about her acceleration?
Remember that
acceleration is defined as
the change in velocity
divided by the change in time.
The skater's final velocity,
zero meters per second,
minus her initial velocity,
four meters per second,
divided by 0.5 seconds,
equals negative 8 meters
per second squared.
Now we can solve for
the magnitude of the force
acting on the skater
as she stops.
The force is the force
due to friction, f sub f,
and it equals the skater's mass,
47 kilograms,
times her acceleration,
negative 8 meters
per second squared,
which equals
negative 376 Newtons.
The answer becomes negative
380 Newtons when taken into
account significant figures.
This number is negative because
the force due to friction acts
opposite the positive direction
we have given as to the right
in this problem.
That's our closer look
at Newton's 2nd Law.
For more "Physics in Motion,"
go to our homepage,
where the entire series
is available to you.
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