Physics
Physics
3rd Edition
ISBN: 9781259233616
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 2, Problem 87P

(a)

To determine

The average speed of the signal.

(a)

Expert Solution
Check Mark

Answer to Problem 87P

The average speed of the signal is 1.0mm/s,

Explanation of Solution

Write the equation for average speed of the signal.

vavg=ΔxΔt (I)

Here, vavg is the average speed, Δx is the change in distance, and Δt is the change in time.

Conclusion:

Substitute 100nm for Δx and 0.10ms for Δt in equation (I).

vavg=100nm(1091n)0.10ms(1031m)=100×109m0.10×103s=1000×106m/s

Solve the above relation for velocity in terms of millimetre seconds.

vavg=1.0×103m/s(1mm103m)=1.0mm/s

Therefore, the average speed of the signal is 1.0mm/s,

(b)

To determine

The time taken by the signal to reach the brain.

(b)

Expert Solution
Check Mark

Answer to Problem 87P

The time taken by the signal to reach the brain is 20ms.

Explanation of Solution

Write the equation for time taken by the signal to the neuron.

tn=xv (II)

Here, tn is the time taken by the signal to the neuron, x is the distance pain signal travels into the neuron, and v is the speed of the pain signal travels.

Write the equation for the total time travel across the synapses and neuron to reach the brain.

ttot=tn+tsyn+tn+tsyn (III)

Here, ttot is the total time travel to reach the brain, tn is the time taken by the signal to reach neuron, and tsyn is the time taken by the synapses.

Rewrite the equation (III).

ttot=2tn+2tsyn=2(tn+tsyn) (IV)

Conclusion:

Substitute 1.0m for x and 100m/s for v in equation (II).

tn=1.0m100m/s=0.01s=10×103s(1ms103s)=10ms

Substitute 10ms for tn and 0.10ms for tsyn in equation (IV).

ttot=2(10ms+0.10ms)=20.2ms=20ms

Therefore, the time taken by the signal to reach the brain is 20ms.

(c)

To determine

The average speed of propagation of signal.

(c)

Expert Solution
Check Mark

Answer to Problem 87P

The average speed of propagation of signal is 99m/s.

Explanation of Solution

Write the equation for average speed of the signal.

vavg=ΔxΔt (V)

Here, vavg is the average speed of the propagation signal, Δx is the change in distance, and Δt is the change in time.

Conclusion:

Substitute 2.0m+2(100nm) for Δx and 20.2ms for Δt in equation (V).

vavg=2.0m+2(100nm)(109m1nm)20.2ms(103s1ms)=2.0m+200×109m20.2×103s=2.0m+0.0000002m20.2×103s=0.099×103m/s

Solve the above relation for velocity.

vavg=99m/s

Therefore, the average speed of propagation of signal is 99m/s.

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Chapter 2 Solutions

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