Chapter 4 Notes-part 2
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Transcript Chapter 4 Notes-part 2
Chapter 4 Sec
6-8
Weight, Vector
Components, and
Friction
The Force of Gravity, Weight,
and the Normal Force
•
The force causing all objects to accelerate toward
earth’s is called the force of gravity, g.
•
Applying Newton’s Second Law, F=ma, we obtain the
force of gravity on an object accelerating at 9.80m/s/s is
called Weight, Fg=mg and is measured in Newtons, N.
•
When two objects are in contact with each other a
contact force acts perpendicular to the surface of
contact and is called a Normal force, FN.
Do forces cancel?
• Newton’s third law of motion describes ‘action-
reaction’ pairs of forces. It is important to note
these forces are on DIFFERENT objects, so they
do NOT cancel. (Example: carry a ball: ball on
back force,F1, does not cancel back on ball
force,F2, because F1 is on the back and F2 is
on the ball.
• Normal force, FN on an object is not cancelled
by Earth’s Fg on the same object.
Example: Consider a box on a
table
A friend gives you a gift box with a mass of
10.0 kg. The box rests on a horizontal table.
Determine the weight of the box and the
normal force on it. If your friend pushes
down on the box with a force of 40.0 N,
determine the new normal force on the box.
Be sure to draw free body diagrams to show
the forces acting.
Solution
Given: m = 10.0 kg, g = 9.80m/s/s, FN = ?
Fg = mg = 10.0 kg * 9.80m/s/s = 98 N acting
downward. The only other force on the box
is the normal force, FN and acts upward.
F
y
FN mg 0
Since the box is at rest and the upward
direction is positive, the sum of the y forces
=0 so
FN = mg.
The normal force on the box, exerted by the
table, is 98.0N upward, and has a
magnitude equal to the box’s weight.
Solution part B
If your friend pushes down with 40.0N of
force, the normal force will change to keep
the net force = 0 (assuming the box doesn’t
move)
Now there are 3 forces on the box.
The weight is still 98.0 N (mg). The net force,
ΣFy=0, so FN-mg-40.0N = 0 and FN = 40.0N +
mg = 98.0N + 40.0 N = 138.0 N so the table
pushes back with more force than before.
Example 2 Accelerating the box
What happens when a person pulls upward
on the box in the previous problem with a
force equal to or greater than the box’s
weight, say Fp = 100.0 N?
Fy Fp mg
The net force is now
Fy 100.0N 98.0N
Fy 2.0N
With a net force larger than zero, the box
will accelerate upward.
a Fy 2.0N 0.20m /s2
y
m 10.0kg
Combining Force Vectors
The net force on an object is the vector sum
of all forces acting on the object. (Also
called the net force, Fnet or ΣF).
Forces add together like vectors according
to the rules we’ve learned previously.
We can use Pythagorean theorem and Law
of Cosines to add forces at angles.
We can find force components, Fx and Fy
using trig ratios.
Pulley Example
Muscleman is trying to lift a piano (slowly) up
to a second story apartment. He is using a
rope looped over two pulleys as shown in Fig
4-24. How much of the piano’s 2000N
weight does he have to pull on the rope?
Pulley Solution
Looking at the forces on the lower pulley,
we have 2 Tension force sections opposing
the weight of the piano. Since the piano
moves up slowly (a = 0m/s/s), then using
Newton’s second law: 2FT –mg = ma.
To move the piano requires a tension in the
cord of FT = mg/2. Muscleman exerts a
force equal to half the piano’s weight.
We say this pulley has given a mechanical
advantage of 2, since we exert 2x less force.
Example 4-13: Vector
components at angles
Look at this example on page 95 and
follow through the solution.
Your turn to Practice
Please do Chapter 4 Review pgs
104-105 #s 6, 7, 8, 10, 13, 16, 18,
and 28.