Math 1210-007
Forces
Fall 2010
Forces
Definition:
Force is an entity that can influence the motion of a massive object.
Force is commonly measured in units known as Newtons (N), where 1 N is the amount of force
required to accelerate a 1 kg object at a rate of 1 m/s2.
When considering vertical motion, a force is considered positive if it acts in the upward
direction, and negative if it acts in the downward direction. For example, a 30 N force acting
downward has a value of -30 N.
When considering horizontal motion, a force is considered positive if it acts in the right
direction, and negative if it acts in the left direction. For example, a 20 N force acting to the left
has a value of -20 N.
Addition of Forces: Forces can be added and subtracted in much the same way as regular
numbers. The sum of all forces acting on an object is known as the net force.
Examples:
1.
An object experiences a 20 N force to the right and a 15 N force from to left. What is the
net force acting on this object?
2.
An airplane experiences a 100 N force in the downward direction due to gravity, and an
80 N force in the upward direction due to lift. What is the net force acting on the plane?
Question: How can we use our knowledge about the forces acting on an object to better
understand the motion of the object?
Answer:
Newton's Second Law of Motion explains how to do this!
Newton's Second Law of Motion: The net for exerted on an object can be measured as the
product of its mass and acceleration. In other words
.
In the above notation,
is the net force acting on the object, m is the mass of the object, and a
is the acceleration of the object.
Math 1210-007
Forces
Fall 2010
Using Newton's second law, we can calculate an object's acceleration given its mass and the net
force acting on the object. Once we know the object's acceleration, we can then use calculus to
understand its motion over time.
Examples:
1.
A 30 kg object experiences a force of 50 N to the left and 35 N to the right. What is the
objects acceleration?
, therefore
Solving for a gives
2.
m/s2
A 5,000,000 kg space shuttle experiences a force of 100,000,000 N in the upward
direction due to thrust, and a 49,000,000 N force in the downward direction due to
gravity. What is the acceleration of the shuttle??
, therefore
Solving for a gives
m/s2