For kinematics in two dimensions the kinematic equations need to be dissolved into components in the x and y directions (alternatively parallel and perpendicular to an inclined surface). This is often called projectile motion.
Average velocity is given as displacement/time, where displacement is a vector and can add negatively. Average speed is given as distance/time, where distance is a scalar and does not add negatively.
Average acceleration is given as change in velocity/time, where there is no equivalent between velocity and speed for acceleration. The acceleration in free fall is denoted as g and is given by 9.8 m/s2.
Newton’s First Law states that when an object moves at constant speed there are no outside forces acting on the object. Newton’s Second Law states that the net force acting on an object is proportional to both the mass and acceleration of the object given by . Newton’s third law states that forces are equal and opposite to each other on opposite bodies (so if a man is carrying a piano upward the piano exerts a force on the man that is equal and opposite to the force on the piano from the man).
Free-Body Diagrams are a useful problem-solving strategy that involve drawing and labelling all of the forces that act on an object. Afterwards, writing the resulting Newton’s Second Law equations for these forces is typically the second step required for solving the problem.
The force of friction is a force that retards motion given by: . Where Ff is the force of friction, the coefficient of static friction is for stationary objects and is denoted with a small s, the coefficient of dynamic or kinetic friction is for moving objects is denoted with a small d, R is the reaction force from the floor (denoted as N for normal force in this guide, sometimes called the contact force).
Spring forces have a magnitude given by kx, where k is the spring constant or Newtons required to move the spring by 1 meter, and x is the stretched distance of the spring. Larger spring constants are for stiffer springs.
Drag forces (which are largely simplified due to the nature of this course) are either best approximated as being proportional to v2 for objects with high speed that are heavy, and v being for low speeds on small objects. These are sometimes called fluid resistant forces. The drag force has a constant of proportionality k and increases in magnitude until mg = kvT, where vT is the terminal speed of the dropped object such that mg/k = vT. This constant of proportionality is often called the drag coefficient.
Energy is always conserved while Momentum is conserved when no external forces act on the system (forces that have Newton's third law pairs inside of the system like the normal force during the collision are internal forces).
Mechanical energy refers to kinetic energy (energy associated with moving) plus potential energy (stored energy like the energy in a spring or energy in a mass moved upward) and is conserved when friction is not acting on the system or no external work (effective force distance, usually denoted as Fcosx distance) is acting on the system.
Kinetic energy, potential energy from gravity, potential energy from springs are all given by: . Where m is mass, v is speed, k is a spring constant, h is a change in height, x is a change in distance, and g is the gravitational constant. Another useful formula for kinetic energy is p2/2m, this formula is not superbly useful but it might come in handy to save time (p is momentum and m is mass).
Power is defined as work per unit time (measured in W for Watts) and is therefore , where F is a force and v is a speed (this can be seen from P = W/t = Fx/t = Fv). Work is given as the area under a force displacement curve for forces that are not constant (this makes sense because for a constant force this simplifies to force * distance of the area of the rectangle generated).
Efficiency is the effective work given out from a system or effective work going in and is thus denoted as Wout/Win or Pout/Pin because the difference is only time: . Likewise mechanical advantage is useful force out over useful force in (and is often found for ideal machines where work in = work out).
Momentum is denoted as P = mass * velocity and when it is conserved Po = P can be set.
Elastic collisions are collisions where kinetic energy is conserved and momentum, inelastic collisions are where some kinetic energy is lost, and perfectly inelastic collisions is where two objects stick to each other and momentum is still conserved.
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