4.7 Further Applications of Newton’s Laws of Motion
3 min read•june 18, 2024
govern complex force systems, from suspension bridges to sliding blocks. By identifying all forces, determining through vector addition, and applying F=ma, we can solve for unknown quantities in various scenarios.
Accelerating reference frames introduce the concept of , affecting how forces are perceived. This is evident in elevators and situations. Understanding inertial vs. non-inertial frames helps analyze motion in these dynamic environments.
Complex Systems and Accelerating Frames
Newton's laws for complex force systems
Identify all forces acting on an object
opposes the force of the object on the surface
acts along strings, ropes, or cables (suspension bridges)
opposes the relative motion between surfaces (sliding blocks)
are external forces acting on the object (pushing a cart)
Determine the net force using vector addition
Resolve forces into horizontal and vertical components
Add force components in each direction (x and y) to find net force
Apply : Fnet=ma
Relate the net force to the object's mass and acceleration ()
Solve for unknown quantities using algebra and trigonometry
Motion in accelerating reference frames
Understand the concept of apparent weight
Apparent weight is the force felt by an object in an
In an , apparent weight is affected by the elevator's acceleration ( during freefall)
Apply Newton's second law in accelerating frames
Consider the acceleration of the frame when determining the net force
For an elevator: Fnet=m(a−g), where a is the elevator's acceleration (emergency braking)
Analyze forces in accelerating frames
Identify the forces acting on an object in the accelerating frame (tension in elevator cables)
Determine the direction and magnitude of the acceleration
Distinguish between inertial and non-inertial reference frames
Inertial reference frames are those in which Newton's laws hold without modification
Non-inertial reference frames require the consideration of fictitious forces
Circular Motion and Centripetal Force
Understand the concept of centripetal force
Centripetal force is the net force required to keep an object moving in a circular path
It is always directed toward the center of the circle
Calculate centripetal force: Fc=rmv2
Where m is mass, v is velocity, and r is radius of the circular path
Identify sources of centripetal force in various scenarios (tension in a swinging pendulum)
Integrating Kinematics and Dynamics
Kinematics and force in dynamics problems
Understand the relationship between and
Kinematics describes motion without considering forces ()
Dynamics analyzes the forces causing motion ()
Use to describe motion
v=v0+at (acceleration of a car)
x=x0+v0t+21at2 (position of a falling object)
v2=v02+2a(x−x0) (speed at the end of a ramp)
Combine kinematic equations with Newton's second law
Relate acceleration to net force and mass
Solve for unknown quantities by substituting kinematic equations into force equations
Solve multi-step problems
Identify given information and unknowns
Break the problem into smaller steps
Apply appropriate equations at each step
Use results from previous steps to solve subsequent steps (projectile launched at an angle)
Impulse, Momentum, Work, and Energy
Understand the concept of and its relation to
is the change in momentum of an object
Impulse-momentum theorem: FΔt=mΔv
Define momentum as the product of mass and velocity: p=mv
Explore the concept of as force applied over a distance: W=F⋅d