A baseball (0.250 kg) is struck by a bat and leaves it at a 35° angle
(above the horizontal) at a speed of 40 m/s. Find the magnitude of
the net force on this projectile when it is 1.46 seconds into its flight.
10/30/15
1.
0.00 N
2.
2.45 N
3.
8.19 N
4.
10.0 N
5.
None of the above.
Oregon State University PH 211, Class #15
1
A 150,000 kg jet airliner is moving with constant velocity at an angle
of 12.7° above the horizontal, at an altitude of 10 km and a speed of
200 m/s. What is magnitude of the total force acting on the airplane?
10/30/15
1.
0.00 N
2.
1.43 x 106 N
3.
1.47 x 106 N
4.
There is not enough information.
5.
None of the above.
Oregon State University PH 211, Class #15
2
Local Gravity, Local FG
Any mass as large as a planet exerts a significant force on any other
mass—such as you. If you let that be the net force—the only force
acting on you (i.e. you step off a roof)—you know what happens:
That net force causes you to accelerate. And we have measured the
local magnitude of that acceleration here on the earth’s surface: g
But Newton’s Second Law says that every net force Fnet causes a
body to accelerate according to Fnet = ma. So the force by gravity on
you—is given by FG = mg.
Of course, on other planets, the local gravitational acceleration value
is different—depending on the characteristics of that planet. So, to
find the local gravitational force on any object, you must use its mass
and the local value of gravitational acceleration.
10/30/15
Oregon State University PH 211, Class #15
3
Weight
What is it? Weight is a force—a vector quantity—measured in
pounds (English), newtons (SI), dynes, ounces, tons, etc…
What does it measure? Your weight is the negative of the
sum of all contact forces acting on you (i.e. all forces except
gravity). Your weight can be indicated typically by a scale
upon which you stand, sit, or hang.
What factors affect any object’s weight? Its mass, its location,
and its reference frame. Weight is proportional to g and m.
Example: For a non-accelerating object near a planet:
weight = mg = FG
10/30/15
Oregon State University PH 211, Class #15
4
The local gravitational acceleration on the moon’s surface is about
1/6 that on the earth’s surface.
(a) Find the weight of a 12.0-kg block at rest on the moon’s surface.
(b) If you have a level, frictionless table on the moon, and you push
on the above block with a constant horizontal force of 60.0 N, predict
the magnitude of that block’s horizontal acceleration.
1.
(a)
2.0 N
(b)
5.00 m/s2
2.
(a)
2.0 N
(b)
0.833 m/s2
3.
(a)
19.6 N
(b)
5.00 m/s2
4.
(a)
19.6 N
(b)
30.0 m/s2
5.
None of the above.
10/30/15
Oregon State University PH 211, Class #15
5
Your weight in an elevator
An 80 kg man stands on a scale in an elevator that is
stationary. What is his weight (the reading on the scale)?
Let g = 10 m/s2.
An 80 kg man stands on a scale in an elevator that is
accelerating upward at 2 m/s2. What is his weight?
An 80 kg man stands on a scale in an elevator that is
accelerating downward at 2 m/s2. What is his weight?
An 80 kg man stands on a scale in an elevator that is
moving upward at a constant 5 m/s. What is his weight?
An 80 kg man is in an elevator with broken cables and
brakes—it’s plummeting downward in freefall.
What is his weight?
10/30/15
Oregon State University PH 211, Class #15
6
Weightlessness
A person can be weightless in a location with no
gravity. (Where would that be?) But a person in a state
of freefall is also weightless. Even if a scale is present,
it won’t push/pull on you if you’re in freefall.
But notice: For an object in freefall, gravity is clearly
still present! FG is not zero in this case.
So how/why are astronauts weightless when in orbit
around the earth?
10/30/15
Oregon State University PH 211, Class #15
7
Orbital Motion and Gravity:
Newton’s Thought Experiment
A cannon on a mountaintop
fires a shell parallel to the
ground. The shell leaves the
cannon and is thereafter pulled
toward the ground by gravity.
10/30/15
If the shell leaves the cannon
with a low velocity, it falls to
the ground near the mountain.
With a higher velocity, it falls
farther from the mountain.
Oregon State University PH 211, Class #15
8
So, what if the shell is traveling
so fast, that for every foot it
falls, the Earth also curves away
from it by one foot? The shell
will be forever falling—never
landing. It will be in orbit!
Being in orbit is being in a state of freefall.
The Moon, in orbit, is forever “falling” to the Earth.
Likewise, astronauts in orbit are in freefall, and are
thus in a state of weightlessness.
The same is true for any planet, moon, comet, asteroid,
or other satellite in orbit around any other body.
10/30/15
Oregon State University PH 211, Class #15
9
Gravity for spacecraft in orbit?
YES. There’s still strong gravity for the astronauts in
orbit. Otherwise the spacecraft wouldn’t stay in orbit. At
the altitude of the space shuttle’s orbit, for example, the
strength of gravity is about 90% of that on the earth’s
surface: gorbit ≈ 8.7 m/s2
10/30/15
Oregon State University PH 211, Class #15
10
Newton’s Laws are often misquoted, misunderstood and misapplied.
Consider the cautionary tale of Sir Edward Horse…
10/30/15
Oregon State University PH 211, Class #15
11