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In our last unit, the Balanced Force Model we only solved quantitative force questions if the forces were balanced so the motion must have been uniform. What if the motion is non-uniform and the forces are unbalanced? Our new Unbalanced Force Model will answer this question. Together the Balanced Force Model unit and the Unbalanced Force Model unit are called Dynamics - which explains why objects move as they do.
When an unbalanced force (i.e. doesn't cancel out) acts on a mass, then the mass must accelerate. Let's make this rule more specific. There are two basic patterns to note:
Net force is directly proportional to the acceleration if the mass is constant.
For a constant net force, mass and acceleration, are inversely proportional. This means that more mass implies less acceleration as long as the net force doesn't change.
The simplest way to understand Newton's 2nd Law is it's mathematical definition:
ΣF = ma
Tips to Remember:
Net force (ΣF) is the total force or the sum of the forces or the "extra" force that doesn't cancel out. Net force is NOT it's own force and it never goes on a free body diagram.
The net force and acceleration are vectors. Additionally net force and acceleration always point in the same direction since mass is a scalar.
You need to separately find the net force vertically and horizontally. In physics, what happens vertically is separate from horizontal.
We also know from Kinematics that velocity and acceleration point the same way for objects speeding up while they point opposite directions when the object slows down.
Handy Chart Summarizing directions of velocity, acceleration, and net force.
Example 1:
Two balls that have different masses are thrown with the same amount of force. How will the accelerations of the two balls compare?
The ball with less mass has a greater acceleration because Newton's Second Law states that ΣF= ma which could also be written as a = ΣF/m . Therefore, if the net force on both balls is equal, then the ball with a greater mass will have less acceleration.
Example 2:
There are two shopping carts: one with groceries and one empty. How much net force does it take to accelerate the cart with groceries vs. the empty cart with the same acceleration?
It takes more force to accelerate the cart with groceries with the same acceleration rather than the empty shopping cart because the groceries add mass. More mass requires more force to accelerate the object due to Newton's Second Law. ΣF= ma, so if the mass increases so does the net force when the acceleration is the constant.
One challenging application of Dynamics is to explain and predict what happens in elevators. Everyone knows that you feel lighter and heavier at certain points in an elevator ride. However we know that your weight (Fg) depends only on your mass and the gravitational field - neither of which are changing! However since what we feel does change, this implies that we don't feel Fg as our weight. What we actually feel is the normal force on us by the floor which changes when we are accelerating. The normal force on us by the floor is called apparent weight. If the normal force is larger then what it usually is (i.e. balancing Fg) then you feel heavy. If the normal force is less then typical you feel light.
Kinematics & Dynamics are closely connected. Dynamics tells us why objects move as they do while kinematics allows us to describe their motions. The link between Kinematics and Dynamics is acceleration since you can uses forces to find accelerations. Once you know accelerations you can find displacements, velocities etc.
In this unit we explore friction a little deeper then we did during the Balanced Force Model Unit. Friction forces do not depend on many things people expect they might like velocity (as long as you are going fairly slow), the area of contact between the objects, their shape, whether or not the object is accelerating etc. The friction force on an object does depend on the perpendicular normal force which has the same on by notation as the friction force. For example, if you increase the normal force on the box by the table the friction force on the box by table also increases. The other factor which effects the amount of friction is what the surfaces are made of. We call the coefficient of friction, the number that represents the ratio of friction to normal force between two surfaces. This can also be informally be interpreted as "slipperiness."
Newton's Laws are all around us. This includes everywhere from the football field to cars. For example, a car will continue moving with at a constant speed unless acted upon by an outside force. The outside forces that act upon the car could be friction between the tires and the road, the brakes, and perhaps a normal force from a vehicle or a wall. This is a real-world example of Newton's first law.
Balanced forces in an object result in either a stationary object or a constantly moving object with 0 acceleration. The speed of the object while moving will stay the same. On the other hand, unbalanced forces in an object results in acceleration of objects.
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