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Sidana [21]
3 years ago
12

A spherical steel ball bearing has a diameter of 2.540 cm at 26.00°C. (Assume the coefficient of linear expansion for steel is 1

1 ✕ 10−6 (°C)−1. )
(a) What is its diameter when its temperature is raised to 91.0°C? (Give your answer to at least four significant figures.) 165.1 Incorrect: Your answer is incorrect. Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. cm
(b) What temperature change is required to increase its volume by 1.100%
Physics
1 answer:
Lunna [17]3 years ago
7 0

Answer: a)2.542cm

Explanation:

According to area expansivity which is defined as change in area per unit area for degree rise in kelvin.

Area expansivity= A2-A1/A1(¶2-¶1)

A2-A1 is change in area

¶2-¶1 is temperature change

A2 if final area

A1 is initial area

¶2 is final temp = 91°C

¶1 is initial temp= 26°C

coefficient of linear expansion for steel is 11 ✕ 10−6 (°C)−1.

Area of the spherical steel ball = Πd²/4

A1= Π×2.54²/4

A1 = 5.07cm²

Area expansivity = 2×linear expansion = 2×11 ✕ 10−6 (°C)−1.

= 22 ✕ 10−6 (°C)−1.

Substituting in the formula to get final area A2

22 ✕ 10−6 (°C)−1 = A2-5.07/5.07(91-26)

22 ✕ 10−6 (°C)−1 = A2-5.07/329.55

A2-5.07 = 0.0073

A2 = 0.0073+5.07

A2= 5.0073cm²

To get final diameter

A2=Πd²/4

5.0073=Πd²/4

20.309 = Πd²

d² = 20.309/Π

d²=6.46

d= √6.46

d= 2.542cm

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Explanation:

So, the very first thing we nee to do when solving this problem is draw a diagram that represents it. In the attached picture I show a diagram for each part of this problem.

part a)

So, for her to move in a direction directly opposite her starting point, the x-component of her velocity must be de same as the velocity of the river in the opposite direction. We can use this fact to find the angle we need. If we analize the triangle I drew in the diagram, we can ses that:

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When solving for theta, we get that:

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so now we can substitute the corresponding values:

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for part b, we need to find what the y-component for the velocity of the boat is for an angle of 210° as shown in the problem, so we get that:

V_{y}=5.60km/hr*cos(210^{o})

V_{y}=-4.85km/hr

The woman will head in a negative 5.60km distance from one side to the other, so we get that the time it takes her to go to the other side of the river is:

t=\frac{y}{V_{y}}

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part c)

In order to find the time it takes her to travel 2.80km down and up the river, we need to find the velocities she will have in both directions. First, down stream:

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V_{us}=5.60km/hr-2.80km/hr=2.80km/hr

Once we got these two velocities we will now need to find the time to take each trip:

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t_{us}=\frac{x}{v_{us}}

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so the total time will be:

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