Forces and Motion

• Forces can cause something to happen, and is defined as a push or a pull exerted by one object on another.
• It is measured in Newtons (N)
• 1 N = 1 kg・m/s²
• Force is a vector with direction and magnitude.

Identifying Forces

• Weight is the gravitational force on an object
• Mass is the measure of the amount of matter
• Mass is not a force
• Weight can be measured with spring scales
• These work due to the weight is balanced by another force.
• Normal force is the supporting force perpendicular to a surface.

Types of forces

• Air Resistance
• Air exerts a force against the moving box in a way that increases with the box's speed.
• Friction
• Two sliding surfaces produce a force that acts opposite to the direction of the relative motion of the surfaces.
• Gravitational Force
• Earth exerts a force of attraction on the box.
• Normal Force
• An object exerts a force on the box in a direction perpendicular to the surfaces in contact

Exploring Friction

• Friction is a force opposing motion between two surfaces
• Static friction resists force that would cause an object to slide when the two surfaces are not sliding
• Kinetic friction is the resistance when the object slides along a surface
• Always less than the maximum value of static friction.
• Static and kinetic friction doesn't typically depend on speed or the area of contact
• Proportional to the force pushing the surfaces together (normal force) which is perpendicular to the surface.

Using Diagrams to Analyze Force

• Normal force and static friction oppose other forces
• Forces acting in the same direction produce a greater force.
• Forces combine as vectors the same way velocities and accelerations combine.

Free-Body Diagram

• A way to model a situation showing only one object and the forces acting on it
• Each force on an object is represented by a vector arrow.
• Forces act at a single point, called the center of mass of the object.

Determining Net Force

• The net force on an object is the vector sum of all external forces acting on it.
• ΣF is net force (capital sigma, ∑, indicates a summation).
• When forces are balanced the net force is zero.

Net Force

• Represented as positive and negative numbers when forces act in one dimension.
• E.g. A force of 10 N down and a force 8 N up equals -2 N
• When forces are in two dimensions, analyze forces in perpendicular directions
• Frictional forces are parallel to surfaces in contact and normal forces are perpendicular to them.
• Normal force can be determined by analyzing the other forces.
• The normal force equals the weight of the object supported by the surface when gravitational force is the only one acting on it at rest.

Atwood's Machine

• Shows how net force affects motion.
• The forces of the string have the same magnitude but opposite direction.
• If the masses are equal and unmoving, the net force on each object must be zero.
• If the objects are at rest, they stay at rest but if the system is initially moving, it continues moving steadily until one object reaches the stop and one moves at contant velocity.

Effect of Balanced Forces on Motion

• Moving objects tend to slow down/stop unless kept moving
• Frictional force acts on an object representing a force in the direction opposite to the object's velocity
• Objects can move at constant velocity for a long time without being pushed on nearly frictionless surfaces.
• An object can move at a constant velocity when the net force is equal to zero (Fnet = 0)
• If the net force is zero, an object remains at rest and an object in motion continues in motion with constant velocity, according to Newton's First Law
• Newton's First law of motion states that when the net force is zero, an object will remain at constant velocity and doesn't accelerate.

Effect of Unbalanced Forces on Motion

• An object's velocity changes when the net force on it is not zero.
• Force causes an object to slow down, speed up, or turn.

Net force statements

• The points lie along a straight line, so the relationship between acceleration and force is linear.
• a is directly proportional to the magnitude of the force F.
• The overall slope represents the rate of change in acceleration.

Net Force, Velocity, and Acceleration

• If you push on an object at rest, static friction may keep it in place (net force is zero).
• If you push hard enough, the object starts moving/accelerating in the direction of the net force.
• Direction of net force can be different from the direction of an object's motion E.g., kinetic friction is opposite to the velocity.

An object acted upon by a nonzero net force

• The direction of acceleration is the same as the direction of net force.
• A force in the direction of motion causes an object to speed up.
• A force opposite the direction of motion causes an object to slow down.
• A force at a 90° angle to the direction of motion causes an object to turn.

Relating Force, Mass, and Acceleration

• A more massive object acted on by the same net force as a less massive object has a smaller acceleration.
• Relationship between the mass of an object and its acceleration is an inverse one.
• Acceleration is proportional to 1/m

Newton's Second Law of Motion

• a = Fnet/m
• Constant acceleration happens with a constant net force on an object (e.g., a falling object near Earth).
• Total mass is the mass being accelerated
• On a frictionless surface/in space, an object accelerates as soon any force is applied.
• Heavy object on a high-friction surface will move when the applied force becomes great enough as static friction has been exceeded/kinetic friction begins.
• Greater force required in frictionless surface/space to speed up/turn/stop a more massive object b/c its mass resists change in velocity.
• A more massive object requires a greater force because mass resists acceleration and an objects weight produces greater friction in situations with friction dependent on weight.

Analyzing Paired Forces

• Free-body diagrams model forces on a single object/system treated as a point and require other models to analyze forces between objects.
• Motion of a car slowing as it hits a wall
• exerts a forward force (action force). It’s speed decreases (wall pushes backward = reaction force)
• Action and reaction forces act on different objects.
• For every action force, there’s a reaction force equal in magnitude/opposite in direction (Newton's 3rd law of motion).
• Forces cannot balance one another since each force acts on a different object.
• Forces are equal even when one/both objects accelerate.

Newton's Laws of Motion

• First law
• An object remains at rest/in uniform straight-line motion unless a net external force acts on it
• Second law
• An object acted on by a net external force accelerates in the direction of the force. (Fnet=ma).
• Third law
• Every action force has an equal/opposite reaction force.

Analyzing Internal Forces

• Cardboard Tube Example
• Normal force from table balances the weight of the tube and the tube doesn’t accelerate. If you press down on the tube with your hand, then the tube presses down on the table.
• Increased upward normal force occurs as downward forces increase, the cardboard tube remains balanced b/c the forces remain balanced.

Forces on a Tube

• Can cause deformation so the cross-section becomes oval and a dent forms in the side
• As forces from your hand and the table are transferred, they produce internal forces.
• Internal forces are called stress = Action-reaction force pairs between adjacent particles. (denoted by the variable σ)
• Stress is classified into three types: compression, tension, and shear stress dependending on whether the forces push an object inward, pull an object outward, or push/pull unevenly.

Forces

• For a structure to stay stable/move as intended it must withstand expected forces E.g. Umbrella resists weight of precipitation.
• Designer looks at external forces (free-body diagram).
• When wind blows on house, designer identifies source of reaction force (structure, ground); structure must transfer force from one side to the other.
• Designer uses equations for balanced forces and action-reaction force pairs to break problems and come up with an overall solution.
• Possible outcomes includes choosing lighter parts, widening a support, or adding more supports