subject

Physics, 31.03.2020 04:39 ramseynikki87

A 4.40-kilogram hoop starts from rest at a height 1.70 m above the base of an inclined plane and rolls down under the influence of gravity. What is the linear speed of the hoop's center of mass just as the hoop leaves the incline and rolls onto a horizontal surface

ansver

Answers: 1

Show answers

Answers

ansver

Answer from: 999supergirl

The linear velocity is v=4.08m/s

Explanation:

According to the law of conservation of energy

The potential energy possessed by the hoop at the top of the inclined plane is converted to the kinetic energy at the foot of the inclined plane

The kinetic energy can be mathematically represented as

$KE = \frac{mv^2}{2} + \frac{Iw}{2}$

Where is the moment of inertia possessed by the hoop which is mathematically represented as

I = mr^2

Here R is the radius of the hoop

is the angular velocity which the hoop has at the bottom of the lower part of the inclined plane which is mathematically represented as

$w = \frac{v}{r}$

Where v linear speed of the hoop's center of mass just as the hoop leaves the incline and rolls onto a horizontal surface

Now expressing the above statement mathematically

$potential \ energy = \frac{mv^2}{y} + \frac{Iw^2}{2}$

$mgh = \frac{mv^2}{y} + \frac{Iw^2}{2}$

=> $mgh =\frac{mv^2}{2} + \frac{(mr^2)(\frac{v}{r})^2 }{2}$

=> $mgh = \frac{mv^2}{2} + \frac{mv^2}{2}$

=> mgh = mv^2

=> $v = \sqrt{gh}$

Substituting values

$v = \sqrt{9.81 * 1.7}$

v=4.08m/s

ansver

Answer from: dayaan009

vcm = 4.08 m/s

Explanation:

Assuming the inclined plane is frictionless, and that the hoop is rolling without slippling, the total mechanical energy of the hoop must be conserved:

$\Delta K + \Delta U = 0 (1)$

As the hoop starts from rest, the change in kinetic energy will be equal to the final kinetic energy of the hoop.This kinetic energy will have a part of rotational kinetic energy (due to the rotation around an axis passing through the center of the hoop), and a translational part, due to the translation of the center of mass.This kinetic energy can be written as follows:

$K_{tot} = \frac{1}{2} * I_{hoop} *\omega^{2} + \frac{1}{2} * m *v_{cm}^{2} (2)$

where Ihoop, is the moment of inertia of the hoop = m*r².If the hoop rolls without slipping, there exists a fixed relationship between the angular velocity ω and the velocitity of the center of mass vcm, as follows:

$\omega = \frac{v_{cm} }{r}$

Replacing the values of I and ω in (2), we have:

$K_{tot} = \frac{1}{2} * m*r^{2} * (\frac{v_{cm} }{r} )^{2} + \frac{1}{2} * m *v_{cm}^{2} = \\ \\ K_{tot} = m*v_{cm} ^{2}$

This change in kinetic energy must be equal to the change in gravitational potential energy.If we choose as our zero reference level the bottom of the incline, the change in gravitational potential energy is as follows:

$\Delta U = U_{f} - U_{o} = 0 - m*g*h = - m*g*h$

From (0), simplifying common terms and rearranging, we can solve for vcm, as follows: $v_{cm} =\sqrt{g*h} =\sqrt{1.70 m* 9.8 m/s2 } = 4.08 m/s$

ansver

Answer from: Quest

gravititional force is a force that is acting around you, it is non-contactable and it is a force that pulls you to the core of the earth.

brainliest

ansver

Answer from: Quest

i don't understand is there any other way you can rephrase it plz let me know in the comments and i will do it.

explanation:

Another question on Physics

question

Physics, 22.06.2019 09:30

Acar drives toward the right over the top of a hill, as shown below. which arrow represents the centripetal acceleration? w x y z

Answers: 3

question

Physics, 22.06.2019 11:30

Why is the energy that results from a roller coaster's position at the top of a hill referred to as potential energy?

Answers: 1

question

Physics, 22.06.2019 13:40

Dao makes a table to identify the variables used in the equations for centripetal acceleration. what quantities belong in cells x and y?

Answers: 2

question

Physics, 22.06.2019 18:30

Which word expression describes how much to calculate pressure

Answers: 1

You know the right answer?

A 4.40-kilogram hoop starts from rest at a height 1.70 m above the base of an inclined plane and rol...

Questions

question

Health, 24.11.2020 18:20

Flexibility Program - Plan a stretching routine for your profiled person to include: A specific stretch for each of the 8 major muscle groups of the b...

question

Mathematics, 24.11.2020 18:20

A seagull is 19 feet above sea level. A fish swimming at the opposite distance of the seagull. What integer represents the fish?...

question

Health, 24.11.2020 18:20

Who is allowed in the goal area. A. Offense B. Defense C. Goalie D. Both B. and C....

question

Mathematics, 24.11.2020 18:20

The Yates family’s cell phone bill is $175 a month. How much will they pay for a year (12 months)?...

question

English, 24.11.2020 18:20

The only language that should be used in fictional stories is . • the standard grammar that is taught in schools • the vernacular and dialect a...

question

History, 24.11.2020 18:20

6. The representatives took a Oath declaring the allegiance and commitment to reform. O Bastille Tennis Court O New Constitution

question

Mathematics, 24.11.2020 18:20

Multiply. Do not round your answer. Be sure to include a decimal point in your answer. 1.7 · 11.59 =...

question

English, 24.11.2020 18:20

What do Dylan Thomas’s “Do Not Go Gentle into That Good Night” and C*mmings’s “my father moved through dooms of love” have in common? A. Both...

question

English, 24.11.2020 18:20

LESSON 1 The Crossover Prior to Reading The Crossover Students need to understand that “theme” is the moral or lesson of the story and h...

question

Spanish, 24.11.2020 18:20

Which of the following is grammatically correct? 1. ¿Cuál es tú teléfono? 2. ¿Cuál tu teléfono? 3. ¿Cual es tu telefono? 4. ¿Cuál e...

question

Mathematics, 24.11.2020 18:20

Can yall help my lil sister zhavia she won't leave me alone

question

Health, 24.11.2020 18:20

Who need free points cause today is my birthday. hahaha...

question

Biology, 24.11.2020 18:20

Why are Punnet squares specific to each offspring? PLEASE HELP. I WILL GIVE BRAINLIEST AND A LOT OF POINTS....

question

Mathematics, 24.11.2020 18:20

What matrix results from −8·A?...

question

Social Studies, 24.11.2020 18:20

Can you smell them... *sniff sniff*... their coming Gasp, gasp, gasp BE GONE .

question

Biology, 24.11.2020 18:20

What type of temperatures and moisture content does Continental Polar have? Warm Temps/Dry Air Cold Temps/Moist Air Warm Temps/ Moist A...

question

English, 24.11.2020 18:20

Help sap give points

question

Chemistry, 24.11.2020 18:20

If 21.4 grams of hydrogen reacts completely with 120.3 grams of oxyge to form hydrogen peroxide, what percent by mass of hydrogen in hydrogen peroxide...

question

History, 24.11.2020 18:20

Help Is it a b c or d ...

question

Mathematics, 24.11.2020 18:20

Enter the number of rows needed and the number of seats that will be left over. 826 seats and 42 seat per rowrows extra seats...

More questions: Physics Another questions

Questions on the website: 13722367