Chapter 5 Work and Energy Definition of Work

Chapter 5 Work and Energy

Definition of Work n There is a difference between the ordinary definition of work and the scientific definition of work n Ordinary Definition: To do something that takes physical or mental effort n Scientific definition: Work is equal to the magnitude of the applied force times the displacement of an object

What is necessary for work to be done? n A force that causes displacement of an object does work on the object n Therefore, work is not done on an object unless the object is moved because of the action of a force Work is being done!!!

What is necessary for work to be done? n Work is done only when components of a force are parallel to a displacement n When the force on an object and the object’s displacement are perpendicular, no work is done No Work was Done!!! Displacement Force

What about forces at an angle? n Only the component of force that is parallel to the direction of the object’s displacement does work. n Example: A person pushes a box across a frictionless floor

FBD For the Box n What part of the applied force is parallel to the displacement? FN Displacement of Box Fapp, y Fapp Fg

General Equation For Work Done Work= Component of Force that does the work x displacement x cos (angle between the force vector and the displacement)

Net Work done by a Constant Force n If there are many constant forces acting on the object, you can find the net work done by finding the net force acting on the object Net work= Net force x displacement x cos of the angle between them

Angles between vectors Vector Orientation Angle between them Cos(θ) Θ= 90 Cos(90) =0 Θ= 0 Cos(0) = 1 Θ= 180 Cos(180) = -1

Units for Work n The unit for Work is the Joule n I J= 1 Nm n One Joule = One Newton x One meter

The sign of work is important n Work is a scalar quantity, but it can be positive or negative n Work is negative when the force is in the direction opposite the displacement n For example, the work done by the frictional force is always negative because the frictional force is opposite the displacement

Sample Problem p. 193 # 10 n A flight attendant pulls her 70 N flight bag a distance of 253 m along a level airport floor at a constant velocity. The force she exerts is 40. 0 N at an angle of 52. 0° above the horizontal. Find the following: The work she does on the flight bag n The work done by the force of friction on the flight bag n The coefficient of kinetic friction between the flight bag and the floor n

FBD FN Fapp, y Ff Fapp, x Fg

Work done by flight attendant n Only the component of Fapp that is parallel to the displacement does work. n n Fapp, x is parallel to the displacement Fapp, x = 40 cos 52 = 24. 63 N n Remember that in the W=Fdcosθ equation, θ represents the angle between the force vector and the displacement vector Fapp, x d n W= (24. 63 N)(253 m) cos(0)= 6230 J Θ = 0°

Work done by friction n The bag is moving at constant velocity, so what is Ff? n Ff = Fapp, x= 40 cos(52)= 24. 62 N Ff n d Θ =180° W= Fdcosθ= (24. 62 N)(253 m)(cos 180) = -6230 J

Find μk n What is FN? n Fn + Fapp, y = Fg n Fn = Fg - Fapp, y= 70 N- 40 sin(52)= 38. 48 N

Energy- Section 5. 2 p. 172 n Kinetic Energy- The energy of an object due to its motion I Have Kinetic Energy I don’t Have Kinetic Energy

Kinetic Energy Depends on Speed and Mass n Kinetic energy = ½ x mass x speed 2 n The unit for KE is Joules (J)

Sample Problem p. 173 n A 7. 00 kg bowling ball moves at 3. 0 m/s. How much kinetic energy does the bowling ball have? How fast must a 2. 45 g tennis ball move in order to have the same kinetic energy as the bowling ball?

Solve the Problem n KE= ½ mv^2= ½ (7 kg)(3 m/s)^2= 31. 5 J n How fast must 2. 45 g ball move to have the same KE? n n Convert g to kg 2. 45 g =. 00245 kg Solve for v

Work-Kinetic Energy Theorem n The net work done by a net force acting on an object is equal to the change in kinetic energy of the object n You must include all the forces acting on the object for this to work!

Sample problem p. 176 #2 n A 2000 kg car accelerates from rest under the actions of two forces. One is a forward force of 1140 N provided by the traction between the wheels and the road. The other is a 950 N resistive force due to various frictional forces. Use the work-KE theorem to determine how far the car must travel for its speed to reach 2. 0 m/s.

What information do we have? n M= 2000 kg n Vi= 0 m/s n Vf= 2 m/s Ffriction= 950 N Fforward= 1140 N

What is the Work-Ke Theorem? n Remember that: n So Expand the equation to this:

n Solve for Fnet n Fnet= Fforward- Ffriction= 190 N forward n Rearrange the equation for d and plug in values n Why is θ= 0 in the denominator? Because the net force is in the same direction as the displacement.

Potential Energy Section 5. 2 n Potential Energy is stored energy n There are two types of PE n Gravitational PE n Elastic PE

Gravitational Potential Energy n Gravitational Potential Energy (PEg) is the energy associated with an object’s position relative to the Earth or some other gravitational source n

Elastic Potential Energy n Elastic Potential Energy (PEelastic) is the potential energy in a stretched or compressed elastic object. n k= spring (force) constant n X= displacement of spring

Displacement of Spring

Sample Problem p. 180 #2 n The staples inside a stapler are kept in place by a spring with a relaxed length of 0. 115 m. If the spring constant is 51. 0 N/m, how much elastic potential energy is stored in the spring when its length is 0. 150 m?

What do we know? n K = 51. 0 N/m n We need to get x, in order to use the equation for elastic PE n X is the distance the spring is stretched or compressed n Relaxed length is 0. 115 m, stretched length is 0. 150. How much was it stretched? n 0. 150 - 0. 115 m= 0. 035 m= x

Solve the problem

Conservation of Energy – 5. 3 n The total amount of energy in the universe is a constant n So we say that energy is conserved n From IPC: The Law of Conservation of Energy: Energy can neither be created nor destroyed

Mechanical Energy n There are many types of energy (KE, PE, Thermal, etc) n We are concerned with Mechanical Energy n Mechanical Energy is the sum of kinetic energy and all forms of potential energy n ME= KE + PE

Conservation of ME n In the absence of friction, mechanical energy is conserved n When friction is present, ME can be converted to other forms of energy (i. e. thermal energy) so it is not conserved.

Expanded Form of Conservation of ME n Without elastic PE n With elastic PE

Practice Problem p. 185 #2 n A 755 N diver drops from a board 10. 0 m above the water’s surface. Find the diver’s speed 5. 00 m above the water’s surface. Find the diver’s speed just before striking the water.

What do we know? n W= 755 N n Initial height = 10 m n Vi= 0 m/s n There is no elastic PE involved.

Solve part a. n What is the diver’s speed 5. 0 m above the water’s surface? n M= Weight/g=76. 96 kg n Vi= 0 m/s n Initial height = 10 m n Final Height = 5 m

Rearrange equation and solve for vf Vi = 0 m/s

Second Part n What is the diver’s speed just before striking the water? n M= Weight/g=76. 96 kg n Vi= 0 m/s n Initial height = 10 m n Final Height = 0 m

Finish the Problem Vi = 0 m/s hf = 0

Power- Section 5. 4 n Power: The rate at which work is done n The unit for power is Watts n 1 Watt = 1 J 1 s

Alternate Form for Power

Sample Problem (Not in book) n At what rate is a 60 kg boy using energy when he runs up a flight of stairs 10 m high in 8. 0 s? n Time = 8 s n What is work done? n W=Fdcos(θ)

Solve the Problem n What force does the boy apply to get himself up the stairs? F= Weight= mg= 588. 6 N n d= 10 m n n W= Fdcos(θ)=588. 6 N(10 m)(cos(0)) n W=5886 J n P=W/t = 5886 J/ 8 s= 735. 8 Watts