PHYSICS
PHYSICS
5th Edition
ISBN: 2818440038631
Author: GIAMBATTISTA
Publisher: MCG
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Question
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Chapter 20, Problem 97P

(a)

To determine

The rotational speed of the armature of the generator.

(a)

Expert Solution
Check Mark

Answer to Problem 97P

The rotational speed of the armature of the generator is 1.3×103rev/min_.

Explanation of Solution

Write the expression for motional emf.

  εm=NBAω        (I)

Here, N is the number of turns, B is the magnetic field, A is the area of cross section, ω is the angular speed.

Substitute, πr2 for A in equation (I).

  εm=NB(πr2)ω        (II)

Conclusion:

Substitute, 150 for N, 0.20T for B, 0.018m for r, and 4.2V for εm in equation (II) to obtain the rotational speed.

  4.2V=(150)(0.20T)π(0.018m)2ωω=4.2V(150)(0.20T)π(0.018m)2=137.5rads×1rev2πrad60s1min=1.3×103rev/min

Therefore, the rotational speed of the armature of the generator is 1.3×103rev/min_.

(b)

To determine

The average torque and instantaneous torque applied by bicycle tire to the generator.

(b)

Expert Solution
Check Mark

Answer to Problem 97P

The average torque applied by bicycle tire to the generator is 0.044Nm_, and the instantaneous torque applied by bicycle tire to the generator is 0.087Nm_.

Explanation of Solution

Write the expression for average torque.

  τav=Pavω        (III)

Here, Pav is the average power, and ω is the angular frequency.

Conclusion:

Substitute, 60W for Pav, and 137.5/s for ω in equation (III) to find the average torque.

  τav=60W137.5/s1J/s1W1Nm1J=0.044Nm

Substitute, 12.0W for Pm, and 137.5/s for ω in equation (III) to find the maximum instantaneous torque.

  τav=12.0W137.5/s1J/s1W1Nm1J=0.087Nm

Therefore, the average torque applied by bicycle tire to the generator is 0.044Nm_, and the instantaneous torque applied by bicycle tire to the generator is 0.087Nm_.

(c)

To determine

The linear speed of the bicycle to supply emf of 4.2V.

(c)

Expert Solution
Check Mark

Answer to Problem 97P

The linear speed of the bicycle to supply emf of 4.2V is 1.4m/s_.

Explanation of Solution

Write the expression for the linear speed of the bicycle.

  v=rshaftωshaft        (IV)

Here, rshaft is the radius of the shaft.

Conclusion:

Substitute, 0.010m for rshaft, and 137.5/s for ωshaft in equation (IV) to find the linear speed.

  v=(0.010m)(137.5/s)=1.4m/s

Therefore, the linear speed of the bicycle to supply emf of 4.2V is 1.4m/s_.

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