Physics 1200: Midterm 2

if the net work on an object by nonconservative forces is zero, then its energy _____

does not change

angular displacement

the angle through which the object rotates

work-energy theorem

when a net external force does work on an object, the kinetic energy of the object changes according to... W=KEfinal - KEinitial (also valid for curved paths and non-constant accelerations)

impulse-momentum theorem

when a net force acts on an object, the impulse of this force is equal to the change in the momentum of the object

nonconservative forces

- examples: static and kinetic frictional forces, air resistance, tension, normal force, propulsion force of a rocket - the concept of potential energy is not defined for nonconservative forces

vertical circular motion

- gravitational force must always be considered - there is a minimum speed the rider must have in order to stay in the loop - this speed can be found by setting normal force equal to 0 at the top of the circle

Hooke's Law

- restoring force of an ideal spring - k= spring constant - x= displacement from unstrained length

equilibrium of a rigid body

- zero translational acceleration - zero angular acceleration - the sum of the externally applied forces is zero, and the sum of the externally applied torques is zero

applying the principle of conservation of linear momentum

1. decide which objects are included in the system 2. relative to the system, identify the internal and external forces 3. verify that the system is isolated 4. set the final momentum of the system equal to its initial momentum (remember that momentum is a vector)

external forces

forces exerted on objects by agents external to the system

internal forces

forces that objects within the system exert on each other

How are work and PE related?

- Wgravity = -ΔPEgravity - positive work results from a negative change in PE - nonzero work can only be done on the ball by gravity if the PE changes

average angular velocity

- angular displacement / elapsed time - units: radian/second

average angular acceleration

- change in angular velocity / elapsed time - units: radian/second^2

average power

- the rate at which work is done, and it is obtained by dividing the work by the time required to perform the work - units: Watts (W) - from the work-energy theorem, power is also equal to change in energy / time - when moving at an average speed, power is also equal to F*v

principle of conservation of linear momentum

- the total linear momentum of an isolated system is constant (conserved) - an isolated system is one for which the sum of the average external forces acting on the system is zero

work

- involves force and displacement - scalar

uniform circular motion

- the motion of an object traveling at a constant speed on a circular path - speed is constant, but the direction of the velocity vector is not constant

in normal situations, both conservative and nonconservative forces act simultaneously on an object, so the work done by the net external force can be written as...

W = Wconserved + Wnonconserved W= ΔKE Wconserved = -ΔPE ΔKE = -ΔPE + Wnonconserved (different version of work-energy theorem)

Can PE be converted to KE?

Yes! W = ΔKE W = -ΔPE

centripetal acceleration (uniform circular motion)

direction is towards the center of the circle (in the same direction as the change in velocity)

the total linear momentum is conserved when two objects collide, provided they constitute an _____ system

isolated

elastic collision

one in which the total kinetic energy of the system after the collision is equal to the total kinetic energy before the collision

when a car is driving around a curve, _____ provides the centripetal force

static frictional force

instantaneous angular velocity

the angular velocity at an instant in time (t), can be defined in an analogous way as was done with linear velocity

conservation of mechanical energy

the total mechanical energy (E = KE + PE) of an object remains constant as the object moves, provided that the net work done by nonconservative forces is zero

period of the circular motion (t)

time it takes for the object to travel once around the circle

particle

a piece of matter, small enough in size to be regarded as a mathematical point

on a frictionless banked curve, the centripetal force is the _____ component of the normal force

horizontal

conservative force

- *version 1*: a force is conservative when the work it does on a moving object is independent of the path between the object's initial and final positions - *version 2*: a force is conservative when it does no work on an object moving around a closed path, starting and finishing at the same point - examples: gravitational force, elastic spring force, electric force

Newton's Law of Universal Gravitation

- every particle in the universe exerts an attractive force on every other particle - the force that each exerts on the other is directed along the line joining the particles

centripetal force (Fc)

- force required to keep an object moving on a circular path - net force needed to produce the centripetal acceleration in uniform circular motion - direction is always pointing towards the center of the circle and continually changes direction as the object moves - sometimes there can be several forces acting and different forces can contribute - any force pointing towards the center is positive

net external torque

- moment of inertia * angular acceleration - units: radians/s^2

inelastic collision

- one in which the total kinetic energy of the system after the collision is not equal to the total kinetic energy before the collision - if the objects stick together after colliding, the collision is said to be completely inelastic

impulse

- product of the average force and the time interval during which the force acts - a vector quantity and has the same direction as the average force - describes the direction and "severity" of the collision - units: J (newton*seconds)

elastic potential energy

- the energy that a spring has by virtue of being stretched or compressed - unit: joule (J)

center of gravity of a rigid body

- the point at which its weight can be considered to act when the torque due to the weight is being calculated - is at the geometrical center when an object has a symmetrical shape and its weight is distributed uniformly

linear momentum

- the product of the object's mass times its velocity - a vector quantity and has the same direction as the velocity - units: kilogram*meter/seconds)

general principle of conservation of energy

- the total energy is neither increased nor decreased in any process - energy can be transformed from one form to another, and transferred from one object to another, but the total amount remains constant

torque

- what causes an object to have an angular acceleration - tells you how effective a given force is at rotating something about some axis - the amount of torque depends on where in and what direction the force is applied, as well as the location of the axis of rotation - units: newton x meter (N*m)