A merry-go-round with a rotational inertia of 600 kg m2 and a radius of 3.0 m is initially at rest. A 20 kg boy approaches the merry-go-round along a path tangent to the rim of the at a speed of 5.0 m/s. Determine the angular velocity of the system after the boy hops on the merry-go-round.

Answers

Answer 1

Answer:

The velocity of the merry-go-round after the boy hops on the merry-go-round is 1.5 m/s

Explanation:

The rotational inertia of the merry-go-round = 600 kg·m²

The radius of the merry-go-round = 3.0 m

The mass of the boy = 20 kg

The speed with which the boy approaches the merry-go-round = 5.0 m/s

[tex]F_T \cdot r = I \cdot \alpha = m \cdot r^2 \cdot \alpha[/tex]

Where;

[tex]F_T[/tex] = The tangential force

I =  The rotational inertia

m = The mass

α = The angular acceleration

r = The radius of the merry-go-round

For the merry go round, we have;

[tex]I_m \cdot \alpha_m = I_m \cdot \dfrac{v_m}{r \cdot t}[/tex]

[tex]I_m[/tex] = The rotational inertia of the merry-go-round

[tex]\alpha _m[/tex] = The angular acceleration of the merry-go-round

[tex]v _m[/tex] = The linear velocity of the merry-go-round

t = The time of motion

For the boy, we have;

[tex]I_b \cdot \alpha_b = m_b \cdot r^2 \cdot \dfrac{v_b}{r \cdot t}[/tex]

Where;

[tex]I_b[/tex] = The rotational inertia of the boy

[tex]\alpha _b[/tex] = The angular acceleration of the boy

[tex]v _b[/tex] = The linear velocity of the boy

t = The time of motion

When the boy jumps on the merry-go-round, we have;

[tex]I_m \cdot \dfrac{v_m}{r \cdot t} = m_b \cdot r^2 \cdot \dfrac{v_b}{r \cdot t}[/tex]

Which gives;

[tex]v_m = \dfrac{m_b \cdot r^2 \cdot \dfrac{v_b}{r \cdot t} \cdot r \cdot t}{I_m} = \dfrac{m_b \cdot r^2 \cdot v_b}{I_m}[/tex]

From which we have;

[tex]v_m = \dfrac{20 \times 3^2 \times 5}{600} = 1.5[/tex]

The velocity of the merry-go-round, [tex]v_m[/tex], after the boy hops on the merry-go-round = 1.5 m/s.


Related Questions

If an object travels 245 km in 5 hours, what was the speed of the object?

Answers

Answer:

49kmph

Explanation:

speed=distance/time = 245/5

When your body takes in food, what type of energy does it get from the food?

Answers

Answer: Chemical Energy

Explanation:

Glucose and other food molecules are broken down by controlled stepwise oxidation to provide chemical energy in the form of ATP and NADH.

Comparing the reactants and the products of a chemical reaction, which observation can best be used to argue that the reaction is endothermic?(1 point)

The volume of the reactants is greater than the volume of the products.

The total energy of the reactants is equal to the total energy of the products.

There are fewer chemical bonds in the reactants than there are chemical bonds in the products.

The temperature of the reactants is greater than the temperature of the products.

Answers

Answer:

D) The temperature of the reactants is greater than the temperature of the products.

Explanation:

All the answers:

1. A) The reactants are unlit charcoal, and the products are charcoal that has already burned and released its energy

2. C) sugar + oxygen → carbon dioxide + water + energy

3. D)  iron + oxygen → rusted iron + energy

4. A) an endothermic reaction, because ice absorbs heat to become liquid water

5. D) The temperature of the reactants is greater than the temperature of the products.

We can argue that a reaction is endothermic when the temperature of the reactants is greater than the temperature of the products.

What is an endothermic reaction?

An endothermic reaction is a chemical reaction accompanied by the absorption of heat.

Comparing the reactants and the products of a chemical reaction, which observation can best be used to argue that the reaction is endothermic?

The volume of the reactants is greater than the volume of the products. False. There is no relation between the volume and the endothermicity.The total energy of the reactants is equal to the total energy of the products. False. If the total energy is equal, there is no heat (energy) absorption.There are fewer chemical bonds in the reactants than there are chemical bonds in the products. False. We must consider not only the number of bonds, but also their energies, to establish if a reaction is endothermic.The temperature of the reactants is greater than the temperature of the products. True. If the reaction is endothermic and absorbs heat from the surroundings, the temperature of the reactants will be greater than the temperature of the products.

We can argue that a reaction is endothermic when the temperature of the reactants is greater than the temperature of the products.

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Some of the types of energy in the electromagnetic spectrum will be familiar, such as X-rays, microwaves, and radio waves. The most important part of the spectrum in photosynthesis is visible light. What are the colors of the visible spectrum

Answers

Answer:

Red, orange, yellow, green, cyan, blue, violet.

Explanation:

As we know that the energy of every photon of light directly depends on the size of the wavelength. As short as the wavelength would be as greater the energy delivered by each photon of light would be. Thus, the colors displayed in the visible electromagnetic spectrum would include 'red, orange, yellow, green, cyan, blue, violet' with different wavelengths.

Katrina pushes off a flat sidewalk on her new skateboard.
What causes her to move?
O A. The force of her push overcomes the forces of gravity and friction
OB. The force of gravity overcomes the forces of her push and friction
o C. The force of friction overcomes the normal force of the skateboard and the force of gravity.
o D. The normal force of the skateboard overcomes the force of her push and the force of gravity

Answers

Answer:

The force of her push overcomes the forces of gravity

Explanation:

The force of her push overcomes the forces of gravity and friction. The correct option is A.

What is friction?

Friction is basically the force that restricts solid surfaces, fluid layers, and material elements from sliding against each other.

There are various kinds of friction: Dry friction is the force that opposes the relative lateral motion of two in contact solid surfaces.

Friction is defined as the force that opposes the movement of one solid object over another. Friction is classified into four types: static friction, sliding friction, rolling friction, and fluid friction.

Gravity causes objects to accelerate as they fall to the ground. Acceleration is a change in velocity, which is a measurement of the speed and direction of motion.

Katrina pushes her new skateboard off a flat sidewalk. Her push overcomes the forces of gravity and friction.

Thus, the correct option is A.

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What type of device is a refrigerator?
A. A heat pump that uses work to move heat
B. A heat pump that uses heat to do work
C. A heat engine that uses work to move heat
D. A heat engine that uses heat to do work

Answers

A heat pump that uses work to move heat

Every surface has different ____________________ of friction.
I'll make u brainliest if you know it, AND HURRY

Answers

Answer:

amounts

Explanation:

every surface has different amounts of friction

hope this helps :) plz brainliest?

Answer:

Amounts of frictions

Explanation:

take for example a football player it is harder to push a  sled

ADD NOTE
QUESTION GUIDE
EXIT TI
1. A 15 N force is exerted on a box, moving it 25m in the same direction.

According to the above diagram, what is the magnitude of work done on the box?

Answers

Answer:

375J

Explanation:

Given parameters:

Force exerted on the box = 15N

Distance moved  = 25m

Unknown:

Magnitude of work done on the box = ?

Solution:

Work done is a function of the force applied to move a body through a distance.

    Work done  = Force x distance

Now;

     Work done  = 15 x 25  = 375J

Is the normal force equivalent to the weight of an object?

Answers

Answer:

No.

Explanation:

If there are no applied forces, normal force is usually equivalent to the weight of the object but if there are outside force (force that makes the object to move) especially if it's inclined, then the inclined force would then affect the normal force.

If a car is traveling forward at 15 M/S, how fast will be going in 1.2 seconds if the acceleration is 10 M/s2?

Answers

Answer:

Vf=27m/s

Explanation:

Vf=Vi+at

Lets substitute the known variables into the equation:

Vf=15+10×1.2

Vf=27m/s

So itll be going 27metres per second

Periodic waves with a wavelength of 0.50 meter move with a speed of 0.30 meter in medium A. When the waves enter medium B, they travel at 0.15 meter per second. Calculate the wavelength of the waves in medium B.

Answers

Answer:

0.25 m

Explanation:

Refraction occurs when the velocity or wavelength of a wave changes at the interface between two media.

We know that refractive index=

Wavelength in medium A/wavelength in medium B = velocity in medium A/velocity in medium B

Let the wavelength of medium B be a

0.5/a = 0.3/0.15

0.5 × 0.15 = 0.3 × a

a= 0.5 × 0.15/0.3

a= 0.25 m

A nickel atom has an atomic number of 28 and an atomic mass of 59. What
is the structure of this atom?
A. It has a central nucleus composed of 28 protons and 31 neutrons,
surrounded by an electron cloud containing 28 electrons.
B. It has a central nucleus composed of 28 protons and 28 neutrons,
surrounded by an electron cloud containing 31 electrons.
C. It has a central nucleus composed of 31 protons and 28 neutrons,
surrounded by an electron cloud containing 28 electrons.
D. It has a central nucleus composed of 28 protons and 59 neutrons,
surrounded by an electron cloud containing 28 electrons.

Answers

A nickel atom has an atomic number of 28 and an atomic mass of 59. It has a central nucleus composed of 28 protons and 31 neutrons, surrounded by an electron cloud containing 28 electrons.

What is an atom?

The atom consists of matter that may be split without releasing electrical charges.

It's also the smallest unit of matter with chemical element features. As a result, the atom is the fundamental unit of science.

In the nucleus, proton and the neutron is existing. The condition of the atom to be electrically neutral is that the number of the proton and electron should be the same.

A nickel atom has an atomic number of 28 and an atomic mass of 59. In the nucleus, proton and the neutron is existing,the atom is the fundamental part of the particle.

In that, condition, It has a central nucleus composed of 28 protons and 31 neutrons, surrounded by an electron cloud containing 28 electrons.

Hence, option A is correct.

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While riding her bike, Ms. Parker average a velocity of 20m/s. If she maintains that velocity for a time of 20 seconds, how far does she rides?

Answers

Answer:

400 m

Explanation:

20m/s x 20s = 400m

What is the direction of the net force when one force is pulling down and one force is pushing to the right?

Answers

Answer:  If the net force on an object is zero, its acceleration will be zero. For example in free fall, the net force on an object equals its weight - the one force pulling on it. If 2 forces push or pull on an object in opposite directions, and the two forces cancel .

Explanation: PLEASE MARK ME AS BRAINLIEST!

We have that the  direction of the net force when one force is pulling down and one force is pushing to the right is given as

[tex]\theta=tan^{-1}(\frac{Down force}{Right force})[/tex]

From the question we are told that:

One force is pulling down and one force is pushing to the right

Generally,

When two or more forces are acting in the same direction we have that the Resultant for or net for is a sum of the forces involved

Therefore

When one force is pulling down and one force is pushing to the right the Net force is in a direction that obeys the law

[tex]\theta=tan^{-1}\frac{y-axis\ force}{x-axis\ force}[/tex]

Therefore

[tex]\theta=tan^{-1}(\frac{Down force}{Right force})[/tex]

 

In conclusion

The direction of the net force when one force is pulling down and one force is pushing to the right is given as

[tex]\theta=tan^{-1}(\frac{Down force}{Right force})[/tex]

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the spot directly above the focus on the surface of the earth​

Answers

Answer:

Epicenter

Explanation:

-The hypocenter is the point within the earth where an earthquake rupture starts. The epicenter is the point directly above it at the surface of the Earth. Also commonly termed the focus.

-The location below the earth's surface where the earthquake starts is called the hypocenter, and the location directly above it on the surface of the earth is called the epicenter. Sometimes an earthquake has foreshocks.

A total charge of 7.5 mC passes through a cross-sectional area of a wire in 0.9 s. What is the current in the wire

Answers

Answer:

the  current in the wire is  0.008333333  A

Explanation:

The computation of the current in the wire is as follows;

Current in the wire is

= Total charge ÷ cross sectional area of the wire

= 7.5 × 10^-3C ÷ 0.9s

= 0.008333333  A

Hence, the  current in the wire is  0.008333333  A

We simply applied the above formula so that the correct current of the wire could come

And, the same is considerd and relevant too

Please help!!!! Will mark brainliest.

Spiderman, on a strand of web, accelerates upward at 1.3 m/s2. If spiderman has a mass of 76 kg,
what is the force in the strand of webbing?

Answers

Answer:

Approximately [tex]8.4 \times 10^{2}\; \rm N[/tex], assuming that [tex]g = 9.8\; \rm m \cdot s^{-2}[/tex].

Explanation:

Let [tex]m[/tex] and [tex]a[/tex] denote the mass and acceleration of Spiderman, respectively.

There are two forces on Spiderman:

Downward gravitational attraction from the earth: [tex]W = m \cdot g[/tex].Upward tension force from the strand of web [tex]F(\text{tension})[/tex].

The directions of these two forces are exactly opposite of one another. Besides, because Spiderman is accelerating upwards, the magnitude of [tex]F(\text{tension})[/tex] (which points upwards) should be greater than that of [tex]W[/tex] (which points downwards towards the ground.)

Subtract the smaller force from the larger one to find the net force on Spiderman:

[tex](\text{Net Force}) = F(\text{tension}) - W[/tex].

On the other hand, apply Newton's Second Law of motion to find the value of the net force on Spiderman:

[tex](\text{Net Force}) = m \cdot a[/tex].

Combine these two equations to get:

[tex]m \cdot a = (\text{Net Force}) = F(\text{tension}) - W[/tex].

Therefore:

[tex]\begin{aligned}& F(\text{tension})\\ &= m \cdot a + W \\ &= m \cdot (a + g)\\ &= 76\; \rm kg \times \left(1.3\; \rm m \cdot s^{-2} + 9.8\; \rm m \cdot s^{-2}\right)\\ &\approx 8.4\times 10^{2}\; \rm N\end{aligned}[/tex].

By Newton's Third Law of motion, Spiderman would exert a force of the same size on the strand of web. Hence, the size of the force in the strand of the web should be approximately [tex]8.4\times 10^{2}\; \rm N[/tex] (downwards.)

Bert is playing on his school's basketball team and one of the players on the other team continues to push him off balance when the referee isn't looking. Bert is getting frustrated as the other player is beating him to the ball almost every time by using this illegal tactic. How should Bert handle this situation in a responsible manner?

Refuse to shake hands with the other team at the end of the game and call them all dirty players
Take a flop and fall down purposely the next time the player does it to get the ref's attention
Talk to his team captain and ask him to alert the referee to keep a better eye on the player
When the ref isn't looking push the other player off balance when he has the opportunity

Answers

Answer:

Talk to his team captain and ask him to alert the referee to keep a better eye on the player.

Answer:

C - talk to coach and ask to alert the ref

Explanation:

I took the test

How is the weight formula similar to the force formula? W=mg and F=ma*
1.They both have mass in them
2.They both have acceleration
3.Gravity causes acceleration
4.All of the above
5.None of the above

Answers

It is number 2 lolololol


11. Which has the greater acceleration: a car that increases its speed from 50 km/h to 60 km/h, or a bike that
goes from 0 km/h to 10 km/h in the same time? Explain.


Answers

Answer:

they are the same

Explanation:

change in speed is 10km/h for both, and the time is the same for both. they have the same acceleration.

A 0.061 kg golf ball is struck by a golf club with a force of 299.4 N. The change in velocity of the ball is 54.3 m/s. How much time is the ball in contact with the club?​

Answers

Answer:

The time the ball is in contact with the club is approximately 0.011063 seconds

Explanation:

The question is with regards to Newton's second law of motion which states that a force is equal to the rate of change of momentum produced

The given parameters are;

The mass of the ball, m = 0.061 kg

The force with which the ball is struck with the golf club, F = 299.4 N

The change in velocity of the ball, Δv = 54.3 m/s

By Newton's second law, we have;

[tex]F_{net} = \dfrac{\Delta P}{\Delta t} = \dfrac{m \times \Delta v}{\Delta t}[/tex]

Where;

Δt = The time it takes the momentum of the object to change = The time the ball is in contact with the club

Substituting the known values, we get;

[tex]F_{net} = F =299.4 = \dfrac{0.061 \times 54.3}{\Delta t}[/tex]

[tex]\therefore \Delta t = \dfrac{0.061 \times 54.3}{299.4} \approx 0.011063[/tex]

The time the ball is in contact with the club = Δt ≈ 0.011063 seconds.

Select the correct answer. The rules of volleyball today have been only slightly changed from the rules when the game was A True B. False Next​

Answers

B bbbbb bbbbbbbbbbbbbb bbbbbbbbbbbbbbbbbbbbb


1. When the two cars have the same mass, what is true about their
velocities?

Answers

Answer:

I mean they have the same amount of velocity

Scenario: The light bulb from the projector went out and the teacher was in the hallway. One student begins pressing buttons on the projector to fix it.

Questions to answer:

1. Was consent given (yes, no, unsure)?

2. What evidence do you have to prove your way of thinking?

3. How can you change the scenario to show that consent was given?

Answers

Answer:

1:No

2:The teacher was in the hall  so how would the child ask?

3: The child could have went into the hallway and asked the teacher if they could try and fix it.

Explanation:

Sorry if that isn't what your asking!

      </3 PureBeauty

Answer:

During lunch your friend asked you to come over after school, so you get on their bus to go home.

Questions to answer:

1. Was consent given (yes, no, unsure)?

2. What evidence do you have to prove your way of thinking?

3. How can you change the scenario to show that consent was given?

Explanation:1:No2:The teacher was in the hall so how would the child ask?3: The child could have gone into the hallway and asked the teacher if they could try and fix it.

Someone please help me

What is an isotope? (2 points)

Group of answer choices

Atoms of different elements that have different numbers of neutrons

Atoms of different elements that have different numbers of protons

Atoms of the same element that have different numbers of neutrons

Atoms of the same element that have different numbers of protons

Answers

the answer is C


**because i said so-

Answer:

The answer is C.) Atoms of the same element that have different numbers of neutrons.

Explanation:

I know this is right because i took the test!

Can a molecule of DNA contain 60% thymine? Why
or why not?

Answers

Answer:

The possibility of Adenine=40% and Thymine=60% is only in single stranded DNA molecule. In the question, the DNA sample referred is a single stranded DNA. If guanine=10% as guanine will always pair with cytosine, i.e.cytosine is also 10% then adenine and thymine accounts 80% as adenine will always pair with thymine.

A molecule of DNA cannot contain 60% thymine because this amount will surpass 100% in consideration of its complementary base.

DNA:

DNA or deoxyribonucleic acid is a biological molecule that stores genetic information in living cells.

DNA is a double stranded molecule that consists of nucleotide bases as follows:

AdenineThymine GuanineCytosine

According to Chargaff in his rule, the amount of adenine & thymine and guanine & cytosine in a DNA molecule is the same, which must equal 100% overall.

Therefore, if thymine is 60% in the DNA, adenine will also be 60%, which in total has already surpassed 100% without adding the other two bases.

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The answers plz....................

Answers

Answer:

The answer would be D

Explanation:

It's quite simple, the Universal Law of Gravitation states that all mass no matter the size, shape, or weight acts equally upon the force of gravity of the gravitational object. Basically, between all sizes, shapes, weights of masses, gravity applies the same gravitational force with all. Gravity with friction would be something else, which is also states in the Theory of Gravitation.

Potential energy due to an objects compression or extension is called ______ potential energy

Answers

Answer:

elastic potential energy

Answer:

elastic potential energy

Explanation:

mark me as brainlest

Bob who has a mass of 100 kg stands ona. Frictionless frozen lake with a 20 kg rock in his hands. He throws the rock forward with a velocity of +5 m/s. What is the velocity of bob after he throws the rock

A. -2 m/s
B. -1 m/s
C. 0 m/s
D. 1 m/s

Answers

Answer:

Option B

Explanation:

This involves the conservation of momentum:

m1v1 = m2v2

Now initially neither the rock nor Bob is moving. Then the rock moves forward with a velocity of 5 m/s, having a mass of 20 kg. But Bob moves back by the conservation of momentum, so at what velocity?

0 = 20(5) + 100(vf),

-100 = 100vf,

vf = - 1m/s

3.A carnival ride has a radius of 5.00 m and exerts an applied force of 987 N on an 80 kg rider.
a. Find the centripetal acceleration of the rider.
Given:
r =
F =
m =
Unknown:

a =?

Equation:

a = F / m

Answers

Answer:

gggn×2

lol

Explanation:

hujhyhhhgyhngfg

ojui

ukk

lol

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