Newton’s 1rd law: Actio = Reactio
�12 exerted by object 1 on object 2 is equal in magnitude and
If object 1 and object 2 interact, the force F
�21 exerted by object 2 on object 1.
opposite in direction to the force F
F�21 = −F�12
Examples:
• Gravity: Earth attracts a mass on its surface, the force is the weight of the mass. But the mass also attracts
Earth with a force with the same magnitude but opposite in direction. Recall that the mass of Earth
is much higher and therefor its acceleration is much smaller.
• Attraction between two identical masses due to
- Gravity
- Electric attraction
- Magnetic attraction
both masses will accelerate toward each other with the same magnitude of acceleration
• Repulsion between two identical masses due to
- Electric repulsion
- Magnetic repulsion
both masses will accelerate away from each other with the same magnitude of acceleration
F�12
F�21 = −F�12
Wednesday, September 15, 2010
m1�a1 = m2�a2
F�21
Equal masses:
m1
a2
=
m2
a1
m1 = m2 ⇒ a1 = a2
Huge mass differential such as you vs. Earth:
m1 � m2 ⇒ a1 � a2
when you fall out of an airplane, we can safely
ignore the acceleration of Earth
Objects in equilibrium: If an object is not accelerated, we know that the net force on the object must be zero.
�a = 0 ⇒ F�net = 0
In many practical cases, the object is at rest (with respect to its environment).
Problem is then to identify and calculate all forces acting on the object.
Examples:
1-Dimensional:
Mass hanging on a single string
from ceiling
T�
F�G
Forces on mass: Gravity, Tension of the string
F�G = −T�
Obviously: The string is pulling on the anchor in the
ceiling with the same tension down.
2-Dimensional:
�
N
Mass on a slope tied to pole (No friction included yet)
Mass
Pole
Rope
�
T
No acceleration in horizontal or vertical direction:
Horizontal : maH = T cos(θ) − N sin(θ) = 0
V ertical : maV = T sin(θ) + N cos(θ) − mg = 0
F�G
Other coordinate system: x-axis parallel to slope, y-axis perpendicular
x − axis :
max = T − mg sin(θ) = 0
Wednesday, September 15, 2010
y − axis :
may = N − mg cos(θ) = 0