   Chapter 13, Problem 54P

Chapter
Section
Textbook Problem

An astronaut on the Moon wishes to measure the local value of g by timing pulses traveling down a wire that has a large object suspended from it. Assume a wire of mass 4.00 g is 1.60 m long and has a 3.00-kg object suspended from it. A pulse requires 36.1 ms to traverse the length of the wire. Calculate gMoon from these data. (You may neglect the mass of the wire when calculating the tension in it.)

To determine
The value of g on the moon.

Explanation

Given info: The mass of the wire is 4.00g . The length of the wire is 1.60m . The mass of the object suspended is 3.00kg . A pulse requires 36.1ms traversing the length of the wire.

The wave speed in a stretched string is given as,

v=Fμ

• v is the wave speed
• F is the tension in the string
• μ is the mass per unit length of the string or the linear density of the string

Rearrange in terms of F .

F=μv2 (I)

From Newton’s law the tension on the string will be mass times acceleration due to gravity.

F=mgmoon (II)

From (1) and (2),

μv2=mgmoongmoon=μv2m (III)

The linear density of the string will be,

μ=mL

• m is the total mass of the wire
• L is the length of the wire

Substituting 4.00g for m and 1.60m for L to find μ .

μ=4.00g1.60m=4.00×103kg1.60m=2.50×103kgm-1

The speed of the pulse will be,

v=LΔt

• Δt is the time taken to travel the length of the wire

Substituting 1

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