Forces – Chapter 4

What are forces? A force is a push or pull exerted by one object on another object Forces are vectors; they have magnitude and direction The symbol for force is “F” The SI unit for force is a Newton (N)

Contact vs. Non-contact Forces There are two categories that forces are classified as: contact and non-contact With contact forces, the objects are touching in the interaction With non-contact forces, the objects do not touch in the interaction

Contact Forces Applied force- force applied on an object by a person or another object Friction force- force exerted by a surface as an object slides (or attempts to slide) across it Air resistance force- special type of friction Normal force- the reaction force on an object from the surface it is resting on Spring force- force exerted by a stretched or compressed spring Tension force- transmitted through a string, rope, cable or wire when it is pulled tight by forces acting from opposite ends

Non-Contact Forces Gravitational force- force of attraction between bodies of mass Electrical force- due to electric charges Magnetic force- due to magnetic dipoles

Fundamental Forces There are four fundamental forces: Strong Nuclear Force: Holds nucleus together, strongest of the fundamental forces Electromagnetic Force: Between electrically charged particles, second strongest fundamental force Weak Nuclear Force: Causes nuclear decay, second weakest fundamental force Gravity: Between bodies of mass, weakest fundamental force All contact and non-contact forces arise from the four fundamental forces.

What’s in a free-body diagram? A free body is one that is standing alone; therefore, only draw the object you are analyzing in the diagram. Represent the object (body) as a box, no matter what it actually is Only draw the forces acting on the object, do not include forces the object exerts on other objects

Force is a Vector Forces can be represented as arrows The length of the arrow represents the magnitude (size) of the force The direction of the arrow represents the direction of the force Draw the tail of the force coming out of the middle of the object

Labeling the Force After drawing the forces in the diagram, label each one Use the symbol “F” for force, and add a subscript describing the type of force Example: For an applied force use Fapp

Example

Net Force The vector sum of forces acting on an object is the net force Net force = 0

26 400 N 26 400 N 6 400 N

Many orangutans spend their entire lives among the trees and are well adapted to move in this arboreal habitat. They have long arms (about two-thirds of their body height) and powerful chest muscles. Suppose an adult orangutan is hanging by its arms from a tree branch. The angle between each of the animal’s arms and the vertical is 15° with each arm exerting a force 430 N. The gravitational force acting on it is 830 N. Draw a free-body diagram of the animal. Farm = 430 N Farm = 430 N Θ = 30o Fgravity = 830 N

Newton’s 1st Law of Motion An object at rest remains at rest, and an object in motion continues in motion with constant velocity unless the object experiences a net external force.

Force and Acceleration Forces can cause accelerations (speeding up, slowing down, changing direction) If the net force on an object is not zero, the object will accelerate If the net force on an object is zero, the object will not accelerate

Inertia Newton’s 1st Law is also called the Law of Inertia Inertia is the tendency of an object to resist changes in its motion Mass is a measure of inertia. The more mass an object has, the more inertia it has.

Newton’s Second Law of Motion If a net force is applied to an object, this causes it to accelerate. The acceleration is directly proportional to the force, and inversely proportional to the mass. Force = mass x acceleration F = ma

Units Force: Newtons Mass: kilograms Acceleration: m/s2 Because mass and acceleration are multiplied in F=ma, we would expect the units for force to be kg m/s2. A Newton is equivalent to a kg m/s2.

Newton’s Third Law All forces occur in pairs, and these two forces are equal in magnitude and opposite in direction. This is commonly paraphrased as “For every action force, there is an equal, but opposite, reaction force”.

Action-Reaction Forces Don’t Cancel Force pairs do not cancel each other because they act on different objects

Acceleration Depends on Mass Although the forces on each object are equal, the accelerations are not equal (unless the mass of both objects is the same). The object that has less mass will experience a greater acceleration than the object with more mass.

Examples of Force Pairs As Earth exerts a gravitational force on you, you exert a gravitational force on Earth.

Examples of Force Pairs When walking, your foot pushes backward against the ground, and the ground pushes forward against your foot.

Examples of Force Pairs A rifle pushes forward on a bullet, and the bullet pushes backward on the rifle (recoil).

Practice Questions Determine the reaction force. Athlete pushes bar upwards. Bowling ball pushes pin rightwards. Compressed air pushes balloon wall outwards.

Practice Questions A 60 kg woman and 80 kg man push off each other while ice skating. Compare the force experienced by each one. Compare the acceleration experienced by each one.

Friction Opposes Motion Friction acts in a direction opposite to an object’s motion. If the object is not moving when there is a force attempting to make it move, friction acts in a direction opposite to that force.

What causes friction? Friction is caused by the roughness of the two surfaces. Even though a surface may feel smooth, at the microscopic level it is actually rough. The two surfaces are in contact in just a few places.

Types of Friction Static friction: The force that resists the initiation of sliding motion between two surfaces that are in contact and at rest Kinetic friction: The force that opposes the movement of two surfaces that are in contact and are sliding over each other

Coefficients of Friction () A coefficient of friction is a ratio of the force of friction to the normal force between two surfaces Coefficients of friction depend on the material of the surfaces Coefficients of friction do not have units

Coefficients of Friction **Notice that static friction is greater than kinetic friction

Calculating the Force of Friction Ff = N Ff: Force of friction Fn: Normal force : Coefficient of friction This means the frictional force is affected by the mass of the object and the roughness of the surfaces.