Further Topics: Work & Energy

Section 8.1

Reminders

• Weekly Reflection #8 due on Tuesday evening.• Online reading quiz due prior to the start of

class on Thursday.• LAB this week A7-CE: Conservation of Energy

due in lab by Friday at 4 p.m.• Quiz #4 on Thursday, October 23rd, addressing

Chapter 8 (Work and Energy) and Chapter 9 (Gravitation).

Work

• Work is done only when energy is expended.• Physical work not same as physiological work.• Work is defined as force times distance, FΔd• Work causes a change in the energy of a body:– FΔd = ΔE (work-energy principle)

• Impulse causes a change in momentum:– FΔt = mΔv (impulse-momentum principle)

Mechanical Energy

• Kinetic Energy = (½)mv2

• Gravitational potential energy = mgh• Elastic potential energy = (½)kx2 where k is the

spring constant that has units of F/Δx• The unit of work or energy is the Nm or Joule, J• Like momentum, mechanical energy is always

conserved. That is, Ei = Ef

• It is “meaningfully” conserved only in “isolated” systems and in perfectly elastic collisions.

Power

• Power is the rate at which energy is produced or consumed.

• P = energy transferred/unit time = E/t• The unit of power, Nm/s = J/s = Watt, W.

An now some examples

• Conservation of energy, Ei = Ef

– A ball is tossed up into the air…– An amusement park cart collides with a spring…– A moving roller coaster reaches bottom…

• Work FΔd = ΔE (work-energy principle)– A block slides under frictional force, f = μN = -μmg

• Power = ΔE/t = W/t– How much power required to lift an elevator…

Sample Problems #1 & #2

• A bullet is shot upward from with an initial speed of 55m/s. How high does it go?

• #1: Use kinematics (equations of accelerated motion) to solve the problem.

• #2: Use conservation of energy to solve the problem.

Sample Problems #3 & #4

• A 0.005kg bullet moving horizontally with a speed of 330m/s hits a wooden block with a mass of 2.3kg that is suspended like a pendulum but with two V-strings. The bullet become imbedded in the wood.

• #3: What is the speed of the block immediately after the bullet is embedded?

• #4: How high do the block and bullet go?