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V125BC [204]
2 years ago
7

A reasonable estimate of the moment of inertia of an ice skater spinning with her arms at her sides can be made by modeling most

of her body as a uniform cylinder. Suppose the skater has a mass of 64 kg. One-eight of that mass is in her arms, which are 60 cm long and 20 cm from the vertical axis about which she rotates. The rest of her mass is approximately in the form of a 20-cm-radius cylinder. a. Estimate the skater's moment of inertia to two significant figures. b. If she were to hold her arms outward, rather than at her sides, would her moment of inertia increase, decrease, or remain unchanged? Explain.
Physics
1 answer:
alexgriva [62]2 years ago
8 0

Answer:

a) I = 1.44 Kg.m²

b) I = 3.12 Kg.m²

As rarm increases, her moment of inertia will increase.

Explanation:

Given

The skater's mass: M = 64 Kg

Mass of both arms: m = (M/8) = 64 Kg / 2 = 8 Kg

Mass of one arm: = marm = m/2 = 8 Kg / 2 = 4 Kg

Mass of her rest body: Mcyl = M - 2m = 64 Kg - 8 Kg = 56 Kg

rarm = 0.20 m

Rcyl = 0.20 m

Larm = 0.60 m

a) We apply the equation (Using the Steiner Theorem)

I = Icyl + Iarms

I = (Mcyl*Rcyl²/2) + 2*marm*rarm²

I = (56 Kg*(0.20 m)²/2) +2(4 Kg)(0.20 m)²

I = 1.44 Kg.m²

b) Suppose that the center of the mass of her outstretched arm is in the middle, so that the mass of the arm will be at a distance of 50 cm, then

rarm = 0.50 m

We apply the same equation, then

I = Icyl + Iarms

I = (Mcyl*Rcyl²/2) + 2*marm*rarm²

I = (56 Kg*(0.20 m)²/2) +2(4 Kg)(0.50 m)²

I = 3.12 Kg.m²

As rarm increases, her moment of inertia will increase.

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The motorcycle travelled 69.73 m during these 3.1 s.

Explanation:

In order to calculate the distance that the motorcycle travelled we first need to obtain the acceleration rate that was used to brake the vehicle. We do that by using the following formula:

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What is meant by the statement "Motion is relativel"?
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3 years ago
A mine car (mass=390 kg) rolls at a speed of 0.50 m/s on a horizontal track, as the drawing shows. A 250-kg chunk of coal has a
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Answer:

v=0.60 m/s

Explanation:

Given that

m ₁= 390 kg ,u ₁= 0.5 m/s

m₂ = 250 kg ,u₂ = 0.76 m/s

As we know that if there is no any external force on the system the total linear momentum of the system will be conserve.

Pi = Pf

m ₁u ₁+m₂u₂ = (m₂ + m ₁ ) v

Now putting the values in the above equation

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If the total momentum of a system is changing:
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Answer:

(d) a net external force must be acting on the system

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According to Newton's second law of motion, " Force applied to a body (system) is directly proportional to the rate of change of momentum of the body (system) which takes place in the direction of the applied force (external force).

F ∝ΔMV

Therefore, If the total momentum of a system is changing, a net external force must be acting on the system.

(d) a net external force must be acting on the system

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