Sub unit 6.1”Power in Mechanical Systems”

• Introduction using @ a 10 Minute video– Video shoes real life scenarios, equations,

terms, and labels for both SI and English units.– After video we have the following power point

lecture that discusses terms and their interpretations, formulas and their labels, and we finish with sample problems to identify the students abilities to use the new information.

• Power: Rate of doing work

• Power rating: maximum rate at which each machine can do work

• www.teachertube.com/view_video.php?viewkey=b9e96fefd21d68ab729c

Subunit 1Power in Mechanical Systems

Linear Mechanical Systems

Work = Force applied to

object

x Distance object moves along the direction of the force

acting on it

W = f x dPower =Work done by applied forceTime to do the work

P = Wt

P = f x dt

P = f x dt

P = f x V

Power = force x speed

Rotational Mechanical Systems

Work =

Torque applied

x Angle moved throughW = T x θ

P = Wt

P =T x θt

Since ω = θ/t

P = T x ω

Power = torque x angular speed

Units for Mechanical Power

English SI

ft•lbssec

horsepower

Joulesec

N•msecwatt

1 horsepower = 746 watts

1 horsepower = 550 ft•lbssec

• Efficiency: ratio of work out to work in or ratio of power out (Pout) to power in (Pin)

Efficiency

Power In = Work Intime

Power Out = Work Outtime

% efficiency = Power OutPower In

X 100

Or…

% efficiency = Work OutWork In

X 100

• Given: A steel casting weighs 200 pounds. It is

raised 3 ft in 4 sec at a constant speed.

• Find : horsepower of cylinder used to lift the steel casting.

• 1st …

• 2nd …

Sample Problem

P = 200 lb x 3 ft4 sec

= 150 ft•lb/sec

P = f x V

P = f x d

tV = d/t = 3 ft

4 sec = .75 ft/sec

P = (200 lbs) (.75 ft/sec) = 150 ft•lb/sec

• Given: A crate weighs 980N and is lifted 2 meters

in 2 sec. The winch pulls the cable a dist.

Of 8 meters with a force of 272N in the

same 2 sec.

• Find :– A.) Input power (in watts) supplied to block and tackle by the winch

– B.) Output power (in watts) of block and tackle used in lifting crate

– C.) Efficiency of block and tackle

Sample Problem

• A.

• B.

• C.

Sample Problem Cont.

Pin = Fin x Din

Time= (272 N) (8m)

2 sec= =1088 N•m

sec

Pout = Fout x Dout

Time= (980 N) (2m)

2sec= 980 N•m

sec=

Efficiency = Pout

Pin X 100 = 980 watts

1088 watts= .90 x 100 =

980 watts

90%

1088 watts

• Given: An electric motor has a shaft torque of

.73 lb•ft when rotating at 1800 rpm.• Find : horsepower of the shaft

Sample Problem

P = T x ω

ω =

1800( )revmin ( )1 min

60 sec ( 6.28 rad.rev )= 188.4 rad/sec

P = .73 lb•ft x 188.4 rad/sec = 137.5ft•lbsec

P = 137.5ft•lbsec x

1 hp .550 ft•lb

sec

= .25 hp

• Given: a piston in a compressor has a

flywheel with a rate of 1100 rpm

(115rad/sec) Torque is 65 N•m

• Find : hp of flywheel

Sample Problem

P = T x ω

65 N•m x 115 rad/sec = 7475 watts

( )( )7475 watts 1hp746 watts

= 10.0 hp

ουσ

Lab Demos