Chapter 10

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# Chapter 10 - PowerPoint PPT Presentation

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

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## Chapter 10

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### 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
Kinetic Energy
• vf2 = vi2 + 2ad
• vf2 - vi2 = 2ad

Kinetic Energy

• a = F/m
• vf2- vi2 = 2Fd/m

Kinetic Energy

½ mvf2- ½ mvi2

= Fd

Kinetic Energy

K = ½ mv2

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 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

Direction of applied force

a

Direction of movement

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

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

Power
• The rate of doing work

Power

• P = W/t

A 10.0 Gg crate is accelerated by a cable up a 37o incline for 50.0 m in 2.5 hrs. m = 0.20

Calculate: FT, W, & P

A 50.0 g box is accelerated up a 53o incline for 50.0 m at 250 cm/s2. 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).
• The ratio of resistant force to effort force
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

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

Wo

Wi

X 100 %

Efficiency =

MA

IMA

X 100 %

Simple Machines

Lever Inclined plane

Wedge Wheel & Axle

Screw Pulley

Lever

Fr

Fe

de

dr

Fr

Fe

de

dr

IMA = de/dr = length de/length dr

de

Fr

Fe

dr

a

IMA = de/dr =

length hyp/hyp sin a

Wedge

½ Fr

Fe

½ Fr

½ Fr

a

Fe

½ Fr

IMA = de/dr = cot ½ a

Screw

Fe

Fr

Pulley

Fe

Fr

IMA = the number

of lines

pulling up

Fe

Fr

IMA = ratio

of effort wheel

Fr

Fe

A 100.0 Mg trolley is pulled at 750 cm/s up a 53o 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, MA, & efficiency

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

A pulley with an efficiency of 80.0 % with 5 interconnecting ropes lifts a 100.0 kg load. Calculate:

IMA, MA, & FA

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

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, di, FA, Wo, Wi, & P.

10.0 m

1.0 Mg

2.0 m

r = 5.0 cm

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 at 37o from horizontal. Calculate: F,F//, Ff, Fnet, a, t, vf, Wo, P, & Kmax