Download Sec 7.1ааVectors as Forces Applications of Vectors

Newton's Laws of Motion
1. First law: Every object remains in a state of constant velocity unless acted upon by an external unbalanced force. This means that in the absence of a non­zero net force, the center of mass of a body either remains at rest, or moves at a constant velocity.
2. Second law: A body of mass m subject to a net force F undergoes an acceleration a that has the same direction as the force and a magnitude that is directly proportional to the force and inversely proportional to the mass, i.e., F = ma. Alternatively, the total force applied on a body is equal to the time derivative of linear momentum of the body.
3. Third law: The mutual forces of action and reaction between two bodies are equal, opposite and collinear. This means that whenever a first body exerts a force F on a second body, the second body exerts a force −F on the first body. F and −F are equal in magnitude and opposite in direction. This law is sometimes referred to as the action­reaction law, with F called the "action" and −F the "reaction". The action and the reaction are simultaneous.
May 3­8:53 PM
Applications of Vectors
Sec 7.1 Vectors as Forces
­A force is something that either pushes or pulls an object.
­If the force is large enough, an object that is at rest will be moved by the force applied to it. ­Force is described with both direction and magnitude, so it is a vector
­Force is described by the units kg.m/s2 which is a Newton (N), or pounds (lbs)
­ 1N = 0.22lbs or 1lb = 4.4N
­Often, more than one force may act on an object, so we combine these forces using vector laws to find the resultant force.
Feb 17­2:35 PM
Resultant and composition of Forces
Since Forces can be modelled with vectors, the parallelogram and triangle laws of addition apply.
Physics Note:
When an unbalanced force acts upon an object (in a frictionless system), the object will begin to accelerate (move). F = (m)
(a) [kg m/s2 or N] (Newton's 2nd law)
IF an object is NOT moving or moving at a Constant velocity, the forces acting on the object are considered to be in equilibrium. Fnet=0
Force of Gravity (F=ma) is calculated using an acceleration on Earth of 9.8m/s2.
Feb 17­2:44 PM
What is the gravitational force acting on a 15kg jug of water resting on a table top?
What is the net force acting on the jug of water? Why?
May 3­8:48 PM
Example 1: (Parallelogram method)
Two forces of 80N and 68N are applied to an object at the same time. The angle between the forces is 230. Find the resultant force.
Feb 17­2:46 PM
Example 2:
In a tug of war, the two teams are both pulling, but neither is moving. If it is calculated that the one side is exerting a force of 120N, what force is the other team exerting?
Feb 17­2:48 PM
Forces in Equilibrium:
If two or more forces are in equilibrium, the resultant force will always be 0
Example: A 5kg weight suspended from two strings.
F1 + F2 + Fg = 0
F1
F2
F2
Fg
F1
What are the magnitudes of F1 and F2?
Fg
mg = 5(9.8)
= 49 N
Feb 17­2:49 PM
Forces in Equilibrium:
If two or more forces are in equilibrium, the resultant force will always be 0
Example: A 5kg weight suspended from two strings with an angle of 60o between the two forces.
F1 + F2 + Fg = 0
F1
F2
60o
F1
Fg
F2
Fg
What are the magnitudes of F1 and F2?
mg = 5(9.8)
= 49 N
What do you notice is different from the first example?
Feb 17­2:49 PM
Resolving a vector into its components
In many cases a vector can be described as its horizontal component and its vertical component.
Ex:
Feb 17­2:51 PM
Example:
A mass of 20 kg is suspended from a ceiling by two lengths of rope that make angles of 60o and 45o with the ceiling. Determine the tension in each of the ropes.
45o
60o
T2
T1
Fg
Feb 17­2:58 PM
Method One ­ Parallelogram/Triangle Approach
60o
The length of the rope is fixed, but the magnitude of the force vectors can extend outside the parameters of the problem.
45o
T1
Note the length of the rope can be a deception as to the magnitude of the Force Vector.
Drag and Drop
60o
T2
T1
45o
T2
Fg
Fg
Feb 17­3:02 PM
Method Two ­ Component Approach
45o
60o
T1
Horizontal Force Components
T2
Vertical Force Components
Fg
Solve the Linear System
Feb 17­3:02 PM
Homework
p362 #2, 5a, 7, 10, 11, 12 ,16
equilibrant = see glossary
Read Example 3 ­ page 367
page 368 ­ #3, 4, 5
Feb 17­3:10 PM