What If? What would be the new angular momentum of the system (in kg · m2/s) if each of the masses were instead a solid sphere 15.0 cm in diameter? (Round your answer to at least two decimal places.)

Answers

Answer 1

Answer:

Final answer:

To find the new angular momentum of the system if each of the masses were solid spheres, calculate the moment of inertia for each sphere using the formula (2/5) × m × r^2. Multiply the moment of inertia of each sphere by the angular velocity of the system to find the new angular momentum.

Explanation:

The angular momentum of a system can be found by multiplying the moment of inertia of the system with its angular velocity.

If each of the masses were instead a solid sphere 15.0 cm in diameter, we would need to calculate the moment of inertia of each sphere using the formula for the moment of inertia of a solid sphere, I = (2/5) × m × r^2, where m is the mass and r is the radius of the sphere.

Once we have the moment of inertia for each sphere, we can multiply it by the angular velocity of the system to find the new angular momentum.

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Answer 2

Answer:

Final answer:

The new angular momentum, given the same angular speed, will be 0.9 times the original, as the moment of inertia for the system is replaced with that of solid spheres of given mass and radius.

Explanation:

The question is asking for the new angular momentum of a sphere with a given diameter if we replace each of the masses in a given system with it. To compute the new angular momentum, it's crucial to recognize that angular momentum (L) is given by the product of the moment of inertia (I) and angular velocity (w). The moment of inertia for a solid sphere is given by (2/5)mr^2, where m is the mass and r is the radius of the sphere. Since angular velocity has not been specified in the question, it would be assumed to remain unchanged.

So, for this specific system, each mass is replaced with a solid sphere of mass 20 kg and radius 15 cm (or 0.15 m). Thus using the formula for solid sphere inertia, I = (2/5)*(20 kg)*(0.15 m)^2 = 0.9 kg*m^2. If w remains the same, then the new angular momentum L = I * w will be 0.9 times the original angular momentum. This is because w is the same but the moment of inertia has a new value due to the shape and size of the new masses.

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Power P is the rate at which energy E is consumed per unit time. Ornithologists have found that the power consumed by a certain pigeon flying at velocity v m/s is described well by the function P(v)=16v−1+10−3v3 J/s. Assume that the pigeon can store 5×104 J of usable energy as body fat. Find the velocity vp min that minimizes power consumption. (Use decimal notation. Give your answer to two decimal places.)

Answers

Answer:

Explanation:

P(v) = 16 / v + 10⁻³ v³

differentiating on both sides

dP / dt = - 16 / v² + 3 x 10⁻³ v²

For maxima and minima , the condition is

dP / dt = - 16 / v² + 3 x 10⁻³ v² = 0

v² = 160 / 3 x 10²

v² = 73 m/s

v = 8.54 m /s

To know the condition of minima

again differentiating

d²P / dt² = - 16 x -2 / v² + 6 x 10⁻³ x v

= 32 / v³ + 6 x 10⁻³ x v

= + ve quantity

So at v_p = 8.54 m /s , power consumption will be minimum .

If a person’s weight is W on the surface of the earth, calculate what it would be, in terms of W, at the surface of (a) the moon;
(b) Mars;
(c) Jupiter.

Answers

Answer:b

Explanation:

A wooden block with mass 1.05 kg is placed against a compressed spring at the bottom of a slope inclined at an angle of 35.0 degrees (point A). When the spring is released, it projects the block up the incline. At point B, a distance of 4.90m up the incline from A, the block is moving up the incline at a speed of 5.10 m/s and is no longer in contact with the spring. The coefficient of kinetic friction between the block and incline is 0.55. The mass of the spring is negligible. Calculate the amount of potential energy that was initially stored in the spring.

Answers

The amount of potential energy that was initially stored in the spring due to the wooden block is 65.3 joules.

What is potential energy?

Potential energy is the energy which body posses because of its position.

The potential energy of a body is given as,

$PE=mgh$

Here, (m) is the mass of the body, (g) is the gravitational force and (h) is the height of the body.

The energy stored in the spring is the sum of all the potential energy, kinetic energy and the energy dissipated due to friction. Therefore, it can be given as,

$E=mgh+(1)/(2)mv^2+\mu mgd\cos\theta$

Here, the mass of the wooden block is 1.05 kg . Angle of inclination is 35.0 degrees (point A). The distance from point B is 4.90m up the incline from A.

The speed of the block is 5.10 m/s and the coefficient of kinetic friction between the block and incline is 0.55. Therefore, put the values in the above formula as,

$E=1.05(9.81)(4.9\sin(35))+(1)/(2)(1.05)(5.1)^2+(0.55)(1.05)(9.8)(4.9)\cos(35)\nE=65.3\rm J$

Hence, the amount of potential energy that was initially stored in the spring due to the wooden block is 65.3 joules.

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Answer:

Explanation:

energy stored in spring initially

= kinetic + potential energy of block + energy dissipated by friction

= 1/2 mv² + mgh + μ mgcosθ x d

m is mass , v is velocity at top position , h is vertical height , μ is coefficient of friction ,θ is angle of inclination of plane

= m (1/2 v² + gh + μ gcosθ x d )

= 1.05 ( .5 x 5.1² + 9.8 x 4.9 sin35 + .55 x 9.8 cos35 x 4.9 )

= 1.05 ( 13.005 + 27.543 + 21.635)

= 65.3 J .

How can scientific method solve real world problems examples

Answers

The scientific method is nothing more than a process for discovering answers. While the name refers to “science,” this method of problem solving can be used for any type of problem

The position of a particle moving along the x-axis depends on the time according to the equation x = ct2 - bt3, where x is in meters, t in seconds, and c and b are positive constants. What are the units of (a) constant c and (b) constant b? Find a formula in terms of c, b, and t of the (c) velocity v and (d) acceleration a. (e) At what time t ≥ 0 does the particle reach its maximum x value?

Answers

Answer:

(a): $\rm meter/ second^2.$

(b): $\rm meter/ second^3.$

(c): $\rm 2ct-3bt^2.$

(d): $\rm 2c-6bt.$

(e): $\rm t=(2c)/(3b).$

Explanation:

Given, the position of the particle along the x axis is

$\rm x=ct^2-bt^3.$

The units of terms $\rm ct^2$ and $\rm bt^3$ should also be same as that of x, i.e., meters.

The unit of t is seconds.

(a):

Unit of $\rm ct^2=meter$

Therefore, unit of $\rm c= meter/ second^2.$

(b):

Unit of $\rm bt^3=meter$

Therefore, unit of $\rm b= meter/ second^3.$

(c):

The velocity v and the position x of a particle are related as

$\rm v=(dx)/(dt)\n=(d)/(dx)(ct^2-bt^3)\n=2ct-3bt^2.$

(d):

The acceleration a and the velocity v of the particle is related as

$\rm a = (dv)/(dt)\n=(d)/(dt)(2ct-3bt^2)\n=2c-6bt.$

(e):

The particle attains maximum x at, let's say, $\rm t_o$ , when the following two conditions are fulfilled:

$\rm \left ((dx)/(dt)\right )_(t=t_o)=0.$
$\rm \left ( (d^2x)/(dt^2)\right )_(t=t_o)<0.$

Applying both these conditions,

$\rm \left ( (dx)/(dt)\right )_(t=t_o)=0\n2ct_o-3bt_o^2=0\nt_o(2c-3bt_o)=0\nt_o=0\ \ \ \ \ or\ \ \ \ \ 2c=3bt_o\Rightarrow t_o = (2c)/(3b).$

For $\rm t_o = 0$ ,

$\rm \left ( (d^2x)/(dt^2)\right )_(t=t_o)=2c-6bt_o = 2c-6\cdot 0=2c$

Since, c is a positive constant therefore, for $\rm t_o = 0$ ,

$\rm \left ( (d^2x)/(dt^2)\right )_(t=t_o)>0$

Thus, particle does not reach its maximum value at $\rm t = 0\ s.$

For $\rm t_o = (2c)/(3b)$ ,

$\rm \left ( (d^2x)/(dt^2)\right )_(t=t_o)=2c-6bt_o = 2c-6b\cdot (2c)/(3b)=2c-4c=-2c.$

Here,

$\rm \left ( (d^2x)/(dt^2)\right )_(t=t_o)<0.$

Thus, the particle reach its maximum x value at time $\rm t_o = (2c)/(3b).$

Why do societies stratify?

Answers

Answer:

Because of gender, caste, race, wealth, and religion etc.

Explanation:

Social stratification means society is divided in different categories, class, layers or groups due to gender, caste, race, wealth, and religion etc.

Society stratifies due to the following regions:

(1) Gender discrimination means male- female difference.

(2) Unequal distribution of income and wealth

(3) Different types of religions

(4) Racism

(5) Type of education

(6) Social status etc.

Final answer:

Societies stratify, or divide their members into distinct groups or layers, based on various factors such as wealth, income, cultural beliefs, and status. Factors like prestige or age are also influential in some societies. Stratification systems can be either closed, allowing little social mobility, or open, where movement between classes is possible.

Explanation:

Societies stratify, or categorize people into different social standings, for various reasons. In many societies, stratification is an economic system, predominantly determined by wealth and income. Often, people interact chiefly with others of the same social standing, allowing economic and cultural factors to organize individuals into distinct groups or layers.

Societal stratification can also be driven by cultural beliefs that place value on specific attributes or characteristics such as prestige or age. For example, in some cultures, the elderly are esteemed, while in other societies, they are overlooked. Such cultural attitudes play a significant role in reinforcing stratification systems.

Also, stratification occurs when there is a difference in status or power between various societal roles, leading to a hierarchical organization of different groups - an example is the clear socioeconomic status (SES) division within society where individuals with more resources are seen at the top layer.

Closed and open stratification systems present themselves in different societies. Closed systems offer little opportunity for change in social position, whereas open systems, like class systems, are based on achievement, allowing movement and interaction between layers and classes.

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