PHYSICS
PHYSICS
5th Edition
ISBN: 2818440038631
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 10, Problem 113P

(a)

To determine

The magnitude of tension in the ribbon.

(a)

Expert Solution
Check Mark

Answer to Problem 113P

The magnitude of tension in the ribbon is 0.0513N.

Explanation of Solution

The density of the air is 1.29kg/m3, the density of helium is 0.179kg/m3, radius of the balloon is 12.0cm, mass of the balloon is 2.80×103kg and acceleration due to gravity is 9.80m/s2.

Write the expression to calculate the total mass of the balloon and helium.

M=ρ(43πr3)+m

Here, ρ is the density of the helium, M is the total mass of the balloon and helium, m is the mass of the balloon alone and r is the radius of the balloon.

Write the expression for the tension in the ribbon.

T=FbMg

Here, T is the tension in the ribbon, Fb is the buoyant force and g is the acceleration due to gravity.

Write the expression for buoyant force.

Fb=ρ0(43πr3)g

Here, ρ0 is the density of the air.

Rewrite the equation for T using the above equation.

T=ρ0(43πr3)gMg

Substitute the expression for M in the above equation to rewrite.

T=ρ0(43πr3)g(ρ(43πr3)+m)gT=((43πr3)(ρ0ρ)m)g

Substitute 1.29kg/m3 for ρ0, 0.179kg/m3 for ρ, 12.0cm for r, 2.80×103kg for m and 9.80m/s2 for g in the above equation to calculate T.

T=((43π(12.0cm(102m1cm))3)(1.29kg/m30.179kg/m3)2.80×103kg)9.80m/s2=0.0513N

Conclusion:

Therefore, the magnitude of tension in the ribbon is 0.0513N.

(b)

To determine

The magnitude of time period of oscillation.

(b)

Expert Solution
Check Mark

Answer to Problem 113P

The magnitude of time period of oscillation is 2.69s.

Explanation of Solution

The length of the ribbon is 2.30m.

Write the expression to calculate the spring constant.

kTl

Here, k is the spring constant and l is the length of the ribbon.

Write the expression to calculate the time period.

T=2πMk

Here, T is the time period.

Use kTl and the expression for M in the above equation to rewrite.

T=2π(ρ(43πr3)+m)lT

Substitute 2.80×103kg for m, 0.179kg/m3 for ρ, 12.0cm for r, 0.0513N for T and 2.30m for l in the above equation to calculate T.

T=(0.179kg/m3(43π(12.0cm(102m1cm))3)+2.80×103kg)2.30m0.0513N=2π(0.0041kg)2.30m0.0513N=2.69s

Conclusion:

Therefore, the magnitude of time period of oscillation is 2.69s.

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Chapter 10 Solutions

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