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An introduction to the concept of forces, acceleration, and newton's laws of motion. It explains how forces cause acceleration, the relationship between force, mass, and acceleration, and the difference between net and total forces. It also covers the concept of inertia and the units of measurement for force.
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***** You MUST apply a force *****
If there is no force being applied on an object, it cannot accelerate. That is, it must have: acceleration = 0
Can you think of a counter-example (where an object accelerates without a force being applied to it)?
Since a = ∆v/∆t, a = 0 Ë ∆v=0 … So velocity cannot change unless a force acts on an object.
Force is simply:
A PUSH or A PULL
Forces are vectors Ë they have both magnitude and direction
q Experimentally, we find that if we apply a force to an object, it accelerates.
q That is, we find that: acceleration (a) is directly proportional to the applied force (F) , and acceleration (a) is inversely proportional to the mass (m).
Isaac Newton (1642-1727)
q In fact, it is experimentally found that:
This is Newton’s Second Law, and it is often written:
Here, F is the total force, Ftot.
Mass is the way we quantify “inertia”.
Inertia: Tendency for a body to maintain its state of motion, whether moving or at rest.
A common unit of mass is kilograms [kg]
Large inertia Ë it’s “hard” to accelerate the object Small inertia Ë it’s “easy” to accelerate the object
If m is large Ë a is small
If m is small Ë a is large
What are the units?
[F] = [mass][acceleration] = [kg][m/s^2 ] = [kg m/s^2 ]
Since this unit is rather cumbersome, it has been given a single name, called the Newton, [N].
1 [N] = 1 [kg m/s^2 ]
M = 2kg
In F 1 is the only force acting on the mass M, we expect the block to accelerate to the right with an acceleration a = F 1 /M = 10 N / 2 kg = 5 m/s^2
If we now add a 2nd^ force, F 2 , pushing to the left, what happens? We have to consider both forces.. That is, the total force acting on the object.
+x
a = Ftot/M = -10 N / 2 kg = -5 m/s^2
Total force = Ftot = 10 N – 20 N = -10 N
The minus sign tells us the direction!
-x
Ch4#8: An object moves with unchanging velocity. Does it then have no forces acting on it? A) YES B)NO Does it then have no net force acting on it? A) YES B)NO
Ch4#12: Car A starts from rest, and starts to accelerate at 1 m/s2. Car B comes racing past at car A at a steady 120 km/hr. Which vehicle has the larger net force acting on it? A) Car A B) Car B
Everyone knows that when you drop an object from, say 2 [m], it speeds up, and eventually hits the ground.
That is, …it accelerates..
According to Newton’s Second Law, if the object accelerates, the re MUST BE A NET FORCE ACTING ON THE OBJECT.
The force which gets the credit for this is called the gravitational force.
But, if forces have to occur between 2 objects…
What is the “other” object? (^) The earth!
due to the gravitational force which the earth exerts on you.
q The acceleration near the surface of the earth is equal to 9.8 m/s^2 downward
It is given the special letter “g” (for gravity)
q I don’t mind if you use 10 m/s^2 for convenience…
q All objects which are allowed to fall near the surface of the earth will experience this same acceleration (neglecting air resistance)
Weight is defined to be the force on an object due to gravity.
w = weight in Newtons [N] m = mass in [kg] g = acceleration due to gravity = 9.8 [m/s^2 ]
q Notice that weight is NOT the same as mass.
q Mass has to do with the amount of matter inside the object
q Weight depends on the mass, and also the value of “g”
q On the moon, the value of “g” is only about 1/6th^ of the value on earth! Therefore, objects “weigh” about 1/6th^ as much!
(F = ma)
When you stand on the floor, does the floor exert a force on you? A) YES B) NO
Would you rather have a hunk of gold whose mass is measured to 1 kg on the earth or 1 kg on the moon? A) Earth B) Moon C) They’re the same, so it doesn’t matter
Would you rather have a hunk of gold whose mass is measured to 10 N on the earth or 10 N on the moon? A) Earth B) Moon C) They’re the same, so it doesn’t matter
