A uniform marble rolls down a symmetric bowl, starting from rest at the top of the left side. The top of each side is a distance h above the bottom of the bowl. The left half of the bowl is rough enough to cause the marble to roll without slipping, but the right half has no friction because it is coated with oil.

Answers

Answer 1

Answer:

[tex]h' = \dfrac{5}{7}h[/tex]

Explanation:

To find how far will the smooth side will the marble go in the upper direction, measured vertically from the bottom (leave your answer in terms of h)?

From the given information:

The potential energy for the marble starting at rest is:

PE = m*g*h

In the bottom of the bowl; the marble exhibit a linear and rotational K.E

[tex]K.E_{total} = K.E _{linear} + K.E _{rot}[/tex]

[tex]K.E_{total} = \dfrac{1}{2}mv^2+I\omega^2[/tex]

[tex]K.E_{total} = \dfrac{1}{2}mv^2+ \dfrac{1}{2}( \dfrac{2}{5}mR^2) ( \dfrac{v}{R})^2[/tex]

[tex]K.E_{total} = \dfrac{1}{2}mv^2+ \dfrac{1}{5}mv^2[/tex]

[tex]K.E_{total} = (\dfrac{5+2}{10})mv^2[/tex]

[tex]K.E_{total} = \dfrac{7}{10}mv^2[/tex]

By applying Conservation of energy, The Total Energy occurring in the marble when it started at rest is the same as the total energy when it gets to the midpoint in the bowl.

i.e.

[tex]P.E = K.E_{total}[/tex]

[tex]mgh = \dfrac{7}{10 }mv^2[/tex]

10 × mgh= 7mv²

making v² the subject of the formula, we get:

[tex]v^2 = \dfrac{10}{7 }gh[/tex]

Let us remember that the rotational K.E occurring at the midpoint of the bowl is still unchanged at the time the marble is moving to the left side.

Thus, by applying the Conservation of energy balance:

The linear K.E at the midpoint = The P.E of the marble

[tex]\dfrac{1}{2}mv^2 = mgh'[/tex]

Making h' the subject, we get:

mv² = 2mgh'

Divide both sides by m

v² = 2gh'

Recall that [tex]v^2 = \dfrac{10}{7 }gh[/tex]

[tex]\dfrac{10}{7} gh = 2gh'[/tex]

10 gh = 14 gh'

Divide both sides by 2g

5h = 7h'

[tex]h' = \dfrac{5}{7}h[/tex]


Related Questions

Please help! Will mark Brainliest :)

Answers

Answer:

i have to say whether its correct or wrong yep

Answer:

C) The direction the car is traveling

Explanation:

Velocity is a vector that contains both direction and magnitude (Speed)

We already know the magnitude... all you need is the direction.

Hope this helps :)

3. What are the forces present on the rope?​

Answers

Answer:

The pulling force that acts along a stretched flexible connector, such as a rope or cable, is called tension, T. When a rope supports the weight of an object that is at rest, the tension in the rope is equal to the weight of the object: T = mg.

A charged atom or molecule is called an ion.
True
False

Answers

Answer:

True

Explanation:

Answer:

True

hopefuly this is helpful

energy of fossil fuels is also derieved from solar energy​

Answers

Answer:

Explanation:

All the energy in oil, gas, and coal originally came from the sun, captured through photosynthesis.for example when  we burn wood to release energy that trees capture from the sun, we burn fossil fuels to release the energy that ancient plants captured from the sun. We can think of this energy as having been deposited in a natural solar power bank over millions of years.

So, in one sense, gasoline-burning cars, coal-burning power plants, and homes heated by natural gas are all solar powered!

Formed at the boundary of two converging continental tectonic plates is called a Mountain formation

True


False

Answers

Answer:

True

Explanation:

At the boundary of two converging continental tectonic plates, a mountain is formed. This is because the collision results in the emergence of mountains.

The density of both plates are nearly similar and lesser than that of the mantle below. This makes the two plates grind together and bulge upward. The Himalaya mountain range is one of such example. In a continental - continental crust collision, mountains are formed.

As the grinding continues, the builds upward more and more.

A string of length 4m is extended by 0.02m, when a load of 0.4kg is suspended at its end. What will be the length of the string, when the applied force is 15N

Answers

Answer:

ima have to say c

Explanation:

or A or B or D choose ur best answer

Calculate the pressure created when a force of 200N is applied over an area of 20
m2​

Answers

Answer:

10 pa

Explanation:

Pressure = Force / Area

Pressure = 200 / 20

Pressure = 10 pa

Find the force of an object is the mass is 2 kg and the acceleration is 5 m/s2.

Answers

Answer:

10 N

Explanation:

The force acting on an object given it's mass and acceleration can be found by using the formula

force = mass × acceleration

From the question we have

force = 2 × 5

We have the final answer as

10 N

Hope this helps you

why is it not advisable to touch a canvas tent from inside when it is raining?​

Answers

Answer: When you touch wet canvas, surface tension will draw water to your finger. However, the drop left behind where you touched, like any irregular point on an overhead surface, will draw condensation from inside the tent if it is humid.

A friend tells you she is having trouble sleeping and feels really stressed. What lifestyle change would you suggest to reduce these problems?

Answers

Answer: I personally recommend less screen time. As the Hollidays are approching, maybe spend time hanging decorations or going on hikes.

Explanation:

Answer:

1. Ask her if there's anything going on in her life that she would like to talk to you about.

2. Make sure she drinks lots of water and eats the right amount of food. Not treating your body right will mostly make you feel stressed.

3. Make sure she's staying active. Staying indoors, watching TV 24/7 with the doors closed, and over-eating is very unhealthy. Germs can also build-up and cause infections which would lead you to feel uneasy.

4. And most importantly, make sure she's not in a rocky relationship.

I NEED HELP WITH THIS ASAP!!! Wet Lab - Coulomb's Law lab from edge!!

Answers

Answer:

Srry for the delay but this might help ppl in the future

Explanation:

PEACE OUT!

In the picture below, label which particle is the solute and which is the solvent ​

Answers

The black circles are the solvent and the open circles are the solute

What is operating a vocation​

Answers

Answer:

(I UNDERLINED AND MADE ITALIC THE MOST IMPORTANT INFORMATION) A vocation is an occupation to which a person is especially drawn or for which they are suited, trained, or qualified. Though now often used in non-Latin vocātiō 'a call, summons')religious contexts, the meanings of the term originated in Christianity.  (from

Explanation:

A call, summons, or impulsion to perform a certain function or enter a certain career, esp. a religious one. Vocation is defined as a call to do something, especially regarding religious work. The woman's desire to become a nun is an example of vocation. a strong impulse or inclination to follow a particular activity or career. a divine call to God's service or to the Christian life. a function or station in life to which one is called by God: the religious vocation; the vocation of marriage. There are many different types of vocations in today's society. The three significant vocations are, single life, married life, and religious life. Single life is one of the three types of vocation. Definition of Vocation and Career: Vocation is what you strive to do in your life. It is the career you want to be in. Career, on the other hand, is a series of jobs, even change of professions, in a lifetime of an individual. Vocation is literally your "calling", what you are good for or destined for. It usually is a property/talent/predisposition of your person. A mission, in contrast, is a particular task given to you. Even if you are on "a mission from God", there may be retirement from it eventually.

Need help immediately please

Answers

I need help to lol

How do we define energy efficiency?

A. The ratio of the actual output energy to the input energy

B. The ratio of the power gain to power loss

C. The product of input power and output power

D. The sum of potential and kinetic energy

Answers

Answer:

it is b bro that's what it is

A spacecraft orbiting Earth is both moving forward and

a. at terminal velocity
b. experiencing resistance
c. weightless
d. towards earth

Answers

Answer:  (A) At terminal velocity ...

Explanation:

At terminal velocity

Bicycle A with mass 40 Kg is traveling with a velocity of 4 m/s and Bicycle B with mass 20 Kg is traveling with a velocity of 2m/s. The two bicycles have kinetic energy
Calculate it and state which bicycle has higher energy and why?

Answers

Answer:

bicycle A has a greater K.E.

Explanation:

K.E = 1/2mv²

bicycle A = 1/2 × 40 × 4² = 320J

bicycle B = 1/2 × 20 × 2² = 100J

bicycle A has a greater K.E. because it has bigger mass and moves with faster velocity

Of all the Group 13 metals, I am the one with the least mass.

Answers

Answer:

Boron has the least mass

Boron has the least mass

tin shears have longer handles than the scissors used to cut cloth why ​

Answers

Answer:

A pair of scissors used to cut a piece of cloth has blades longer than the handles so that the blades move longer on the cloth than the movement at the handles.

While shears used for cutting metals have short blades and long handles because as it enables us to overcome large resistive force by a small effort.

Jupiter has many moons that are in its orbit. It largest Ganymede of its smaller moons is Europa. Assuming their the same distance form the planets surface, which moon would experience a stronger gravitational field?

Answers

Answer:

Ganymede

Explanation:

Larger size

An object moving in the +x axis experiences an acceleration of 2.0 m/sec2 This means the object is​

Answers

Answer:

When we say that an object moving in the +x axis experiences an acceleration of 2.0 m/sec2, it really means the object is increasing its velocity by 2.0 m/s in every second.

Explanation:

As we know that Acceleration is the rate of change of velocity with respect to time, in terms of both speed and direction.

i.e.

a = Δv/Δt

so when we say that an object moving in the +x axis experiences an acceleration of 2.0 m/sec2, it really means the object is increasing its velocity by 2.0 m/s in every second.

What is the momentum of a 10 kg object traveling at 4 m/s?*

Answers

Answer:

40kg.m/s

Explanation:

∆p=mv. 10kg*4m/s. ∆p= 40Nm

In a tug of war, when one team is pulling with a force of 80 N and the
other 60 N, what is the net force?

Answers

Answer:

The net force is 20N in the direction of the 80N force.

Explanation:

The net force is the resultant force acting on a body. This force is that singular force that will have the same magnitude and effect as the network of forces on a body.

 In this problem:

      Force 1 = 80N

      Force 2 = 60N

Net force  = Force 1  - Force 2

Net force  = 80N - 60N

Net force  = 20N

The net force is 20N in the direction of the 80N force.

Which of the following is a field (action-at-a-distance) force?

Fgrav


Ftens


Fspring


Fapp

Answers

Answer:

[tex]F_{grav}[/tex] is a field force, as gravity does not physically apply force and does not require proximity.

Explanation:

A girl is riding her bike at a speed of 12 m/s. She weighs 55 kg and her bike weighs 22 kg. What is the KE of the girl and her bike?

Answers

Answer:Kinetic energy of the girl and her bike is 5.544 kJ

Explanation:

Given that a girl is riding bike at speed of 12m/s

Also, mass of Girl is 55kg and mass of bike is 22kg

Let, Total mass of girl and bike be M=22+55=77kg

Now, Kinetic energy is given by K=

Hence, Kinetic energy of the girl and her bike will be

K=

K=

K=5544J

Thus, Kinetic energy of the girl and her bike is 5.544 kJ

describe how a ramp can make lifting an object easier without changing the amount of work done

Answers

In case of ramp less force is required but over a larger distance

What rules are used to balance a chemical equation?

Answers

Answer:

Count the number of hydrogen and oxygen atoms on each side of the arrow.

Explanation:

How much force is needed to accelerate a 1.5 kg physics book to an acceleration of 6
m/s^2?

Answers

Answer:

Force = 8.0 k g m / s

Explanation:

Force = mass x acceleration

Mass = 4.0 k g Acceleration = 2.0 m / s 2

Hence,force = ( 4.0 x 2.0 ) k g m / s 2 = 8.0 k g m / s 2

What is the velocity?

Answers

So velocity means speed (how fast something is moving) with a direction for math and science.

Example: Its the same thing as using the word like: Wow that car has a really high Velocity.

Hope this helps :D

Two cars are on a track and accelerate to 60 mph. At a certain point, both cars slam on the brakes. The distance it takes for each car to stop is then measured.

3. Name the independent variable:
4. Name the dependent variable:

Answers

Answer:

'distance' is a 'dependent' variable, and 'stopping' distance is 'an independent' variable.

Explanation:

As we know the independent variable is basically the variable the independent variable is the variable the researcher or a lab person tends to change or control, and its tendency to have a direct effect on the dependent variable.

In this example, two cars are on a track and accelerate to 60 mph. At a certain point, both cars slam on the brakes. The distance it takes for each car to stop is then measured.

It means the 'covering' distance depends upon where the cars tend to stop. It can be a long-distance depending upon how fat the cars go before both cars slam on the brakes.

Therefore, 'distance' is a 'dependent' variable, and 'stopping' distance is 'an independent' variable.

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