Chapter 10 Energy Work Simple Machines Energy The

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 2 2 • vf = vi + 2 ad • vf - vi = 2 ad 2 2

Kinetic Energy • a = F/m 2 2 • vf - vi = 2 Fd/m

Kinetic Energy ½ mvf - ½ mvi 2 = Fd 2

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 = DK

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 500. 0 kg box 250 m at a constant velocity. m = 0. 20 between the box & the floor.

Constant force at an Angle Dire ctio n of app lied forc Direction of movement e a

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

Calculate the work done when mowing the lawn when a boy applied a o 50. 0 N force at a 37 from horizontal for 2. 0 km.

Calculate the work done when a girl pulls a 4. 0 kg box with a rope at a o 37 from horizontal for 2. 0 m. 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 o up a 37 incline for 50. 0 m in 2. 5 hrs. m = 0. 20 Calculate: FT, W, & P

A 50. 0 g box is o accelerated up a 53 incline for 50. 0 m at 250 2 cm/s. m = 0. 20 Calculate: FA, vf, 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 (Fe).

Machines • The force exerted by the machine is called the resistant force (Fr).

Mechanical Advantage • The ratio of resistant force to effort force

Mechanical Advantage Fr MA = F e

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

Wo = Wi or Frdr = Fede or Fr/Fe= de/dr

Ideal Mechanical Advantage de IMA = d r

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

Efficiency = Wo X 100 % Wi

Efficiency = MA X 100 % IMA

Simple Machines Lever Inclined plane Wedge Wheel & Axle Screw Pulley

Lever Fr dr de Fe

Fr dr de Fe IMA = de/dr = length de/length dr

Inclined Plane de dr Fr Fe

de dr Fr Fe a IMA = de/dr = length hyp/hyp sin a

Wedge ½ Fr Fe ½ Fr

½ Fr Fe ½ Fr a IMA = de/dr = cos ½ a

Screw Fe Fr

Pulley Fr Fe

Fr Fe IMA = the number of lines pulling up

Wheel & Axle Fr Fe

Fr IMA = ratio of effort wheel radius/resistant wheel radius Fe

A 100. 0 Mg trolley is o pulled at 750 cm/s up a 53 inclined railway for 5. 0 km. m = 0. 20 Calculate: FA, 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, & efficiency

A 350 N force is applied to push a 50. 0 kg box up o a 20. 0 m ramp at 37 from horizontal. Calculate: IMA, & efficiency

A pulley with an efficiency of 80. 0 % with 5 interconnecting ropes lifts a 100. 0 kg load. Calculate: IMA, & FA

A 1. 0 m handle is connected to 5. 0 cm wheel. The efficiency of this system is 90. 0 %. Calculate IMA, & the force required to pull a 500 kg object connected to the wheel.

A 100. 0 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 k. N 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 100. 0 kg block (m =. 20) slides from rest down a o 50. 0 m ramp at 37 from horizontal. At the bottom of the ramp, it collides with a 25 kg box (m =. 25) & stops. Calculate:

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

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, di, FA, Wo, Wi, & P. 10. 0 m r = 5. 0 cm 1. 0 Mg 2. 0 m

A 50. 0 Mg elevator is raised 200. 0 m in 3. 0 minutes at a constant speed. Calculate: FAupward, W, &P

A 200. 0 kg sled (m = 0. 10) slides from rest down a 500. 0 m incline o at 37 from horizontal. Calculate: F , F//, Ff, Fnet, a, t, vf, Wo, P, & Kmax