February 25, 2020

PROBLEM 13.46

A chair-lift is designed to transport 1000 skiers per hour from the base A to

the summit B. The average mass of a skier is 70 kg and the average speed of

the lift is 75 m/min. Determine (a) the average power required, (b) the

required capacity of the motor if the mechanical efficiency is 85 percent and

if a 300 percent overload is to be allowed.

PROBLEM 13.47

It takes 15 s to raise a 1200-kg car and the supporting 300-kg hydraulic

car-lift platform to a height of 2.8 m. Determine (a) the average output

power delivered by the hydraulic pump to lift the system, (b) the average

power electric required, knowing that the overall conversion efficiency

from electric to mechanical power for the system is 82 percent.

PROBLEM 13.48

The velocity of the lift of Problem 13.47 increases uniformly from zero to

its maximum value at mid-height 7.5 s and then decreases uniformly to

zero in 7.5 s. Knowing that the peak power output of the hydraulic pump is

6 kW when the velocity is maximum, determine the maximum life force

provided by the pump.

PROBLEM 13.47 It takes 15 s to raise a 1200-kg car and the supporting

300-kg hydraulic car-lift platform to a height of 2.8 m. Determine

(a) the average output power delivered by the hydraulic pump to lift the

system, (b) the average power electric required, knowing that the overall

conversion efficiency from electric to mechanical power for the system is

82 percent.

PROBLEM 13.49

(a) A 120-lb woman rides a 15-lb bicycle up a 3-percent slope at a constant speed of 5 ft/s. How much power

must be developed by the woman? (b) A 180-lb man on an 18-lb bicycle starts down the same slope and

maintains a constant speed of 20 ft/s by braking. How much power is dissipated by the brakes? Ignore air

resistance and rolling resistance.

PROBLEM 13.50

A power specification formula is to be

derived for electric motors which drive

conveyor belts moving solid material at

different rates to different heights and

distances. Denoting the efficiency of the

motors by

η

and neglecting the power

needed to drive the belt itself, derive a

formula (a) in the SI system of units for

the power P in kW, in terms of the mass

flow rate m in kg/h, the height b and

horizontal distance l in meters, and (b) in

U.S. customary units, for the power in hp,

in terms of the material flow rate

w

in

tons/h, and the height b and horizontal

distance l in feet.

PROBLEM 13.51

A 1400-kg automobile starts from rest and travels 400 m during a

performance test. The motion of the automobile is defined by the relation

4000ln(cosh0.03 ),xt=

where x and t are expressed in meters and seconds,

respectively. The magnitude of the aerodynamic drag is

2

0.35 ,Dv

=

where

D and

v

are expressed in newtons and m/s, respectively. Determine the

power dissipated by the aerodynamic drag when (a) t = 10 s, (b) t = 15 s.

PROBLEM 13.52

A 1400-kg automobile starts from rest and travels 400 m during a

performance test. The motion of the automobile is defined by the relation

0.0005

3.6

x

ae

−

=

, where a and x are expressed in

2

m/s

and meters,

respectively. The magnitude of the aerodynamic drag is

2

0.35 ,Dv=

where D and

v

are expressed in newtons and m/s, respectively. Determine

the power dissipated by the aerodynamic drag when (a) x = 200 m,

(b) x = 400 m.

PROBLEM 13.53

The fluid transmission of a 15-Mg truck allows the engine to deliver an essentially constant power of 50 kW

to the driving wheels. Determine the time required and the distance traveled as the speed of the truck is

increased (a) from 36 km/h to 54 km/h, (b) from 54 km/h to 72 km/h.

PROBLEM 13.54

The elevator E has a weight of 6600 lbs when fully loaded and is connected as

shown to a counterweight W of weight of 2200 lb. Determine the power in hp

delivered by the motor (a) when the elevator is moving down at a constant speed

of 1 ft/s, (b) when it has an upward velocity of 1 ft/s and a deceleration of

2

0.18 ft/s .

PROBLEM 13.54 (Continued)