1. An electrical motor spins at a constant 1121 rpm. If the armature radius is 4

Question

1.

An electrical motor spins at a constant 1121 rpm. If the armature radius is 4.8 cm, what is the acceleration of the edge of the rotor?

2.

A glass flask has a volume of 700 ml at a temperature of 20° C. The flask contains 697 ml of mercury at an equilibrium temperature of 20°C. The temperature is raised until the mercury reaches the 700 ml reference mark. The coefficients of volume expansion of mercury and glass are 18 x 10-5 K-1 and 2.0 x 10-5 K-1, respectively. The temperature at which this occurs, in °C, is closest to:

Explanation / Answer

1)

given,

angular speed, w=1121 rev/min

w=1121*(2pi/60) rad/sec

w=117.33 rad/sec

radius, r=4.8 cm

acceleration a=r*w^2

= 4.8*10^-2*(117.33)^2

= 661 m/sec^2

2)

volume of the glass flask v1=700 ml at temperature T1=20 oc

volume of mercury v1'=697 ml at temperature T1=20 oc

volume of mercury v2'=700 ml at temperature T2=?

here,

final volume (v2) of the flask and mercury is same,

and

v2=v1(1+gamma_glass*(T2-T1))

v2'=V1'(1+gamma_mercuty*(T2-T1))

now,

v2=-v2'

v1(1+gamma_glass*(T2-T1))=-v1'(1+gamma_mercuty*(T2-T1))

700(1+18*10^-5*(T2-20))=-697(1+2*10^-5*(T2-20))

1.0043(1+18*10^-5*(T2-20))=-(1+2*10^-5*(T2-20))

====>

T2=46.77 oC

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