(1) Galileo was able to achieve the first satisfactory account of projectile motion by recognizing that the horizontal and vertical motions are independent and can be treated separately. (2) A body in uniform circular motion is accelerated toward the center of the circle, requiring a centripetal force, although its speed remains constant. (3) Directed quantities that include both magnitude and direction are represented by vectors.

1. CHAPTER 3
MOTION AND FORCES IN MORE THAN
ONE DIMENSION
By :
Ari Dewayani (12316244010)
Navis Aininah (12316244016)

2. One thing wa clear about beginning and end points the
path of a projectiles wa difficult for the acients to trace
Solved :
Fig 3-1
connon
Fig. 3-1. A cannon or a caapult must direct a procectile at an angle above
the horizontal line to hit a distant object on the same level.

3. Projectile falls verticaly as
moves horizontals
Gallileo’s
In terms of forces produce
curvacture aided the
discription of curved
motion in general

4. 3-1 Direct Quantities : Vectors
Direction for a fairly small
region of the earth’s surface
The east-west line
The North-South line The vertical
or artitude
line

5. Directed Quantity
displacement tof the point of a
pencil from one place on a notebook page to another is
called vector.
Displacement : relative position depends only on initial
and final positions and is independent of the path
beteween.
Fig 3-2
P
Two actual displacements are
made, but they result in the
1 in
single vector OP. Vector OP is the
sum of vectors OA dan OP.
E
O
1 in
1.4 in
A
Displacement from O to P

6. Fig 3-4
C
B
2 lb
A
D
Two forces acting at
the same point but in
different direction
represented in the
figure.
20 lb
A line segment whose length represents its magnitude in accord
with some predetermined scale, and whose direction is that of the
force.
The two may be added as though they were displacements and
the magnitude of the vector sum or resultant.
On the first law of motion, since equilibrium is defined as an
absence of accelertion.

7. A detailed diagram showing just how forces are distributed
in a given equilibrium in nonetheless extremely useful in
practice. (Fig 3-5)
30°
60°
R
T2
T1
100lb
W
The physical problem supporting a 100lb object by two
strings in the manner shown in (a) maybe analyzed by a
force diagram (b) The resultant sum R of the forces T1and
T2 exerted by the strings must be equal and opposite to
weight w.

8. Figure 3-6 which is velocity diagram, is applicable only to
individual instans of time, no indicationshow long those
conditions prevail.
In practice, a single velocity can be specified by giving its
magnitude (speed) and appropriate angles for describing its
direction, but diagram is invalube for determining the net
result of two simultaneous velocities.

9. 3-1 Motion of Projectiles
The correct of Galilleo disregarded fallacious views at once
in terms of Gallileo’s discoveries about falling bodies and
the most elementary ideas contained in Newton’s Law.
Law of inertia
a state either of rest or of uniform
motion in horizontal direction is then maintaned unaltered.
Work out the parabolic
path for a projectile
Gallileo
The horizontal motion
was uniform while the
simultaneous downward
motion was uniformly
accelerated

10. The important point is that the motion of the horizontally
fired ball, neglecting air resistance, is made up teo
independent but simultaneous parts, manifested in two
perpendicular direction.
1. Actual velocities different instans
Actual path
2. Other features of the motion
o
1sec
16ft
2sec
64ft
144ft
3sec
4sec
o
40ft
80ft
120ft
160ft
Position shown are those at the end of the 1st,
2nd, 3rd and 4th second of fall from a tower
256 ft high . Thr path on the left is that of a
body which is dropped and the curved
(parabolic path of a body fired horizontally at
a speed of 40 ft/sec. (Figure 3-7)

11. Uniform horizontal velocity
the ball in its flight, if
the cart also moves at steady speed it will catch the ball
when the latter returns to the horizontal level from which it
was fired.
Figure 3-8
Fig. 3-8. Ball projected upward from a cart in uniform motion keeps abreast of
the cart as it rises and falls

12. 3-3 Uniform Circular Motion
Huygens’ word
“Maintain forever a motion once
impressed upon it.”
In the absence of forces, however since the earth is curved,
the object would progressively from the earth’s surface.
(Figure 3-9).
Uniform velocity
Object fired horizontally from top of tower at various
speeds strikes earth at various distance. With unifrom
velocity it would recede from the earth surface.

13. For projectiles subject to the inescapable influence of
gravity, fired at great horizontal speeds, the effect of the
earth curvature would be to make the time of fall a little
greather than expected from Galileo’s Law of free fall.
Principle
It should be possible to fire at a bullet with a
speed so great that it falls toward the earth at
the same rate that the earth’s surface recedes
from it bcause of the earth urvature
If there were no air friction and no obstacles, it
could continue to go around earth at a
constant distance from its center

14. Figure 3-10
The distance such a projectile would travel in a time t if
there no gravity. Let y represent the distance fallen in this
same time, such that the projectile maintains its original
distance from the center of the earth.

16. Summary
• The world is three-dimensional, and changes in motion
may include change in direction as well as in speed.
• Directed quantities called vectors
• A body in uniform circular motiojn is accelerated toward
the center of the circle although its speed remains
constant.
• Cetripetal is required to produce this acceleration
• Galileo was able to achieve the first satisfactory account
of projectile motion.
• The rotation of the earth about its axis involves such
forces.