AP Physics Chapter 8 Review

What is a conservative force?

A force is a conservative force if the net work it does on a particle moving across any closed path, from an initial point and then back to that point, is zero.

Equivalently, a force is a conservative force if the net work it does on a particle moving between two points does not depend on the path taken by the particle

What are examples of conservative forces?

gravitational force and spring force

What are examples of nonconservative forces

kinetic frictional force

What is potential energy?

Energy that is associated with the configuration of a system in which a conservative force acts.

When conservative force does work W on a particle in the system is △U = -W

If the particle moves from x_i to x_f, the change in potential energy of the system is △U=-∫F(x)dx where F is force

What is gravitational potential energy?

Potential energy associated with a system consisting of Earth and a nearby particle. If the particle moves from height y_i to y_f, then the change in gravitational potential energy of the particle-Earth system is △U = mg(y_f-y_i) = mg△y

If the reference point of the particle is set as y_i = 0, and the corresponding potential energy of the system is set as U_i = 0, then the gravitational potential energy U when the particle is at any point is U(y)= mgy

What is a reference point?

The reference point is where you define potential energy to be zero, regardless of the type of conservative force.

Elastic potential energy

Energy associated with the state of compression or extension of an elastic object

For a spring that exerts a spring force F = -kx when its free end has a displacement x, the elastic potential energy is U(x) = 0.5kx² (can derive using the U = -W integral)

What is the reference configuration for a spring?

where the spring is at its relaxed length, at which x = 0 and U = 0

physical, original, undeformed state of the system (corresponds to the natural, unstressed shape of the object)

What is mechanical energy?

The mechanical energy E_mec of a system is the sum of its kinetic energy K and potential energy U as seen through the formula: E_mec = K + U

What is an isolated system?

a system in which no external forces cause energy changes

If only conservative forces do work within an isolated system, then the mechanical energy E_mec of the system _______ change

cannot

Principle of conservation of mechanical energy

K₂ + U₂ = K₁ + U₁

or….

△E_mec = △K + △U = 0 (both energies acting in different directions)

Potential energy curves

If we know the potential energy function U(x) for a system in which a one-dimensional force acts on a particle, we can find the force as F(x)=-dU/dx

If U(x) is given on a graph, then at any value of x, the force F is the negative of the slope of the curve and the kinetic energy is K = E_mec - U(x)

What is a turning point?

a point x at which particle reverses its motion (v = 0 so K = 0)

Emec is just equal to U so where U intersects with Emec

What is equilibrium?

points where the slope of the U(x) curve is 0 (F(x) = 0))

Work done on a system by an external force

Work is energy transferred to or from a system by means of an external force acting on the system. When more than one force acts on a system, their net work is the transferred energy

When friction is not involved, the work done on the system and the change Emec in the mechanical energy of the system are equal: W = ΔE_mec=ΔK+ΔU

When a kinetic frictional force acts within a system, then the thermal energy E_th of the system changes (energy associated with random motion of atoms and molecules in a system). The work done on the system is done W = ΔE_mec+ΔE_th

Change in thermal energy

The change in E_th is related to the magnitude f_k of the frictional force and the magnitude d of the displacement caused by the external force by

ΔE_th = f_kd

What is the total energy E of a system?

the sum of its mechanical energy and its internal energies including thermal energy

Law of conservation of energy

The total energy E of a system can change only by amounts of energies that are transferred to or from the system

If work W is done on a system, then W = ΔE = ΔE_mec + ΔE_th + ΔE_int

If system is isolated, this gives ΔE_mec + ΔE_th + ΔE_int = 0 and E_mec2 = E_mec1-ΔE_th - ΔE_int

Power

The power due to a force is the rate at which that force transfers energy. If an amount of energy ΔE is transferred by a force in an amount of time ΔT, the average power of the force is P_{avg =} ΔE/ΔT

Instantaneous power due to a force is P = dE/dt

Isolated system

system that is free from the influence of a net external force that alters the momentum of the system

(No work)

Different types of equilibrium?

neutral equilibrium

• a state where an object remains in its new position after being displaced, with no force to either return it to its original location or move it further away

stable equilibrium:

• a state where a system, if slightly disturbed, will return to its original position once the disturbance is removed

unstable equilibrium: 

• a state of balance where a system, if slightly disturbed, will move further away from its original position instead of returning to it