Chapter 10 Energy, Work, & Simple Machines

Energy The ability to produce change

Energy The ability to do work

Types of Energy Kinetic Potential

Kinetic Energy (K) The energy of motion

Potential Energy (U) Stored energy

Kinetic Energy v f 2 = v i 2 + 2ad v f 2 - v i 2 = 2ad

Kinetic Energy a = F/m v f 2 - v i 2 = 2Fd/m

Kinetic Energy ½ mv f 2 - ½ mv i 2 = Fd

Kinetic Energy K = ½ mv 2

Potential Energy U = mgh

Work (W) The process of changing the energy of a system

Work The product of force times displacement

Work W = Fd

Work-Energy Theorem W =  K

Calculate the work required to lift a 50.0 kg box to a height of 2.0 m:

Calculate the work done when a 250 N force is applied to move a cart 40.0 km:

Calculate the work required to push a kg box 250 m at a constant velocity.  = 0.20 between the box & the floor.

Constant force at an Angle  Direction of applied force Direction of movement

Constant force at an Angle W = F(cos  )d

Calculate the work done when mowing the lawn when a boy applied a 50.0 N force at a 37 o from horizontal for 2.0 km.

Calculate the work done when a girl pulls a 4.0 kg box with a rope at a 37 o from horizontal for 2.0 m.  = 2.5

Power The rate of doing work

Power P = W/t

A 25 Mg elevator rises 125 m in 5.0 minutes. Calculate: F, W, & P

A 10.0 Gg crate is accelerated by a cable up a 37 o incline for 50.0 m in 2.5 hrs.  = 0.20 Calculate: F T, W, & P

A 50.0 g box is accelerated up a 53 o incline for 50.0 m at 250 cm/s 2.  = 0.20 Calculate: F A, v f,W, P, K, & U at the top of the ramp

Machines Devices used to ease force one has to apply to move an object by changing the magnitude and direction of the force.

Machines Machines do not reduce the work required, but do reduce the force required.

Machines The force applied is called the effort force (F e ).

Machines The force exerted by the machine is called the resistant force (F r ).

Mechanical Advantage The ratio of resistant force to effort force

Mechanical Advantage FrFeFrFe MA =

In an Ideal Situation 100 % of the work input into a system would be transferred to output work, thus:

W o = W i or F r d r = F e d e or F r /F e = d e /d r

Ideal Mechanical Advantage dedrdedr IMA =

Efficiency The ratio of output work to input work times 100 %

Efficiency = WoWiWoWi X 100 %

Efficiency = MA IMA X 100 %

Simple Machines LeverInclined plane Wedge Wheel & Axle Screw Pulley

Lever FeFe FrFr dede drdr

FeFe FrFr dede drdr IMA = d e /d r = length d e /length d r

Inclined Plane FeFe FrFr drdr dede

FeFe FrFr drdr dede IMA = d e /d r = length hyp/hyp sin  

Wedge FeFe ½ F r

FeFe  IMA = d e /d r = cot ½ 

Screw FrFr FeFe

Pulley FeFe FrFr

FeFe FrFr IMA = the number of lines pulling up

Wheel & Axle FeFe FrFr

FeFe FrFr IMA = ratio of effort wheel radius/resistant wheel radius

A Mg trolley is pulled at 750 cm/s up a 53 o inclined railway for 5.0 km.  = 0.20 Calculate: F A,W, P, K, & U at the top of the ramp

An alien exerts 250 N on one end of a 18 m lever with the fulcrum 3 m from a 1200 N load. Calculate: IMA, MA, & efficiency

A 350 N force is applied to push a 50.0 kg box up a 20.0 m ramp at 37 o from horizontal. Calculate: IMA, MA, & efficiency

A pulley with an efficiency of 80.0 % with 5 interconnecting ropes lifts a kg load. Calculate: IMA, MA, & F A

A 1.0 m handle is connected to 5.0 cm wheel. The efficiency of this system is 90.0 %. Calculate IMA, MA, & the force required to pull a 500 kg object connected to the wheel.

A cm handle is connected to 5.0 cm wheel with teeth connecting it to another 50.0 cm wheel connected to a 2.5 cm axle. A cable is connected to the axle. The efficiency of this system is 90.0 %. Calculate IMA & MA

A sledge hammer is used to apply 25 kN drive a 2.0 cm x 10.0 cm wedge into a board. Calculate the force on the board if the efficiency is 75 %.

Design a system of simple machines that can lift at least 100,000 times the force applied by a human. Assume 90 % efficiency.

The front sprockets on a 21 speed bike are 24 cm, 18 cm, & 15 cm in diameter. The back sprockets range from 12 cm to 4.0 cm. Determine the ratio of highest to lowest gears.

On the same bike, the wheels are 80.0 cm in diameter. Calculate the speed in the lowest & highest gears if a person can pedal at 1.0 revolution per second.

A kg block (  =.20) slides from rest down a 50.0 m ramp at 37 o from horizontal. At the bottom of the ramp, it collides with a 25 kg box (  =.25) & stops. Calculate:

Answer the questions on page 175 & work Problem Section A on pages 175 & 176.

r = 5.0 cm 10.0 m 2.0 m 1.0 Mg The 1.0 m crank is turned lifting the box to a height of 50.0 cm in 5.0 minutes with an efficiency of 90 %. Calculate: IMA, MA, d i, F A, W o, W i, & P.

A 50.0 Mg elevator is raised m in 3.0 minutes at a constant speed. Calculate: F Aupward, W, & P

A kg sled (  = 0.10) slides from rest down a m incline at 37 o from horizontal. Calculate: F ,F //, F f, F net, a, t, v f, W o, P, & K max