Lecture 10: Work & Energy

Questions of Yesterday 1) A student pushes her physics book across a flat table. Another student pushes his physics book up a 30o inclined plane. Assuming the coefficient of kinetic friction is the same in both cases, in which case is the force of friction acting on the book greater? a) the book on the flat table b) the book on the inclined plane c) the force of friction is the same in both cases 2) If you hold your physics book up against the chalkboard, in what direction is the force of friction directed? a) upwards b) downwards c) away from the chalkboard d) into the chalkboard

Work W = FDx F Dx We often apply FORCE to an object because we want to move it from one point to another WORK is done on an object when… a FORCE is applied to the object while moving that object through a certain DISPLACEMENT F Dx W = FDx

Work W = FDx F Dx ONLY valid if F and Dx are in the SAME DIRECTION!! Units = N*m = Joule Magnitude of F * Magnitude of Dx Work is a SCALAR - NO direction! F Dx What about the directions of F and Dx ??

Will the same work be done if F is applied in different directions? q F Dx Will the same work be done if F is applied in different directions? Only the component of force in the same direction as the displacement does work on the object!! W = (Fcosq)Dx

Work W = (Fcosq)Dx What force is needed to raise the box to the table at a constant velocity? How much work do you do when you lift it to the table? 10 kg F 2 m 10 kg

What force is needed to lower Work W = (Fcosq)Dx What force is needed to lower the box from the table to the ground at a constant velocity? How much work do you do when you lower it to the ground? 10 kg 2 m 10 kg

the opposite direction Work W = (Fcosq)Dx Negative work is done on an object when the force is in the opposite direction to the displacement 10 kg 2 m 10 kg

carrying it to the table? Work W = (Fcosq)Dx 10 kg 10 kg 10 m What force is needed to carry the box horizontally to the table at constant velocity? How much work do you carrying it to the table?

NO component of force is in direction of displacement Work W = (Fcosq)Dx 10 kg 10 kg 10 m NO WORK is done on the object if the applied force is perpendicular to the displacement! NO component of force is in direction of displacement

Work-Energy Theorem Wnet = FnetDx = (ma)Dx v2 = v02 + 2aDx Newton’s 2nd Law (∑F = ma) can be difficult to solve when many forces are acting on an object in many different directions…. The scalar quantity WORK can tell us information about the net force acting on an object and its induced motion Wnet = FnetDx = (ma)Dx v2 = v02 + 2aDx Wnet = (1/2)mv2 - (1/2)mv02

Work-Energy Theorem Wnet = (1/2)mv2 - (1/2)mv02 KE = (1/2)mv2 Kinetic Energy KE of an object with mass m moving with a speed v KE = (1/2)mv2 KINETIC ENERGY the energy of an object associated with its motion Units = kg*m2/s2 = Joules (J) Wnet = KEf - KEi = DKE WORK-ENERGY THEOREM The total work done on an object is equal to the change in the object’s kinetic energy

Conservative Forces v0 Wnet = KEf - KEi = DKE 2 h 1 3 What work does gravity do on the ball (mass = m) from 1-2? v0 1 3 From 2-3? From 1-3? Gravity caused NO change in energy over entire trip! The energy lost from 1-2 is regained in 2-3 The work done against gravity from 1-2 is recovered in 2-3

Conservative Forces v0 Wnet = KEf - KEi = DKE 2 h 1 3 Gravity is a Gravity caused NO change in energy over entire trip! The energy lost from 1-2 is regained in 2-3 The work done against gravity from 1-2 is recovered in 2-3

Would the work done from 1-3 be different in this case? Conservative Forces Wnet = KEf - KEi = DKE h 2 v0 Would the work done from 1-3 be different in this case? What about 1-2? 2-3? 1 3 A force is conservative if the work it does moving an object between two points is the same no matter what path taken

Nonconservative Forces The coefficient of kinetic friction between the box and table is mk What work does friction do on the box from 1-4? What about over the path 1-2-3-4? What about 1-2-3-4-1? Wnet = KEf - KEi = DKE 4 3 m m 1 m m 2 x Friction is a Nonconservative Force Energy lost from friction is NOT recovered

Work done by Friction Wnet = KEf - KEi = DKE 4 3 m m 1 m m 2 x Friction always acts in a direction opposite an object’s motion. Work done by friction is always Negative Wnet = KEf - KEi = DKE 4 3 m m 1 m m 2 x Friction causes an object to lose energy in the form of heat and noise

Work done by Friction Wnc + Wc = KEf - KEi = DKE A block slides down the inclined plane at a constant velocity. What forces are acting on the block along the incline? What is the work done by each of the forces? What is the net work Wnet done on the block over the distance d? M d M q Wnc + Wc = KEf - KEi = DKE

How much kinetic energy is lost due to friction acting on the runner? Practice Problem A 70-kg runner begins his slide into second base when he is moving at a speed of 4.0 m/s. The coefficient of friction between his clothes and Earth is 0.70. He slides so that his speed is zero just as he reaches the base. How much kinetic energy is lost due to friction acting on the runner? How far does he slide?

Questions of the Day You slam on your brakes in a panic and skid a certain distance d down a straight and level road before coming to a stop. If you had been traveling twice as fast, what would the skidding distance be? a) 2d b) d/2 c) 4d d) d/4 2) As a pendulum swings back and forth, the forces acting on the pendulum are the force of gravity and tension in the supporting cord. Which of these forces does no work on the pendulum? a) Gravity b) Tension c) neither one does work on the pendulum d) they both do work on the pendulum