A 5.41 kg ball is attached to the top of a vertical pole with a 2.37 m length of massless string. The ball is struck, causing it to revolve around the pole at a speed of 4.75 m/s in a horizontal circle with the string remaining taut. Calculate the angle θ, between 0∘ and 90∘, that the string makes with the pole. Use g=9.81 m/s2.

Answers

Answer 1

Answer:

θ = 66º

Explanation:

This exercise of Newton's second law must be solved in part, let's start by finding the slowing down acceleration of the ball

           a = v² / r

the radius of the circle is

          sin θ = r / L

          r = L sin θ

           

we substitute

          a = v² /L sin θ

now let's write Newton's second law

vertical axis

            T_y -W = 0

             T_y = W

radial axis

            Tₓ = m a                 (1)

let's use trigonometry for the components of the string tension

             cos θ = T_y / T

             sin θ = Tₓ / T

             Tₓ = T sin θ

we substitute in 1

            T sin θ = [tex]\frac{m \ v^2}{L \ sin \theta}[/tex]

             T L sin² θ = m v²

we write our system of equations

             T cos θ  = m g

             T L sin ² tea = m v²

we divide the two equations

             L [tex]\frac{sin^2 \theta}{cos \theta}[/tex] = v² / g

             (1 -cos²)/ cos θ  = [tex]\frac{v^2 }{g \ L}[/tex]

             1 - cos² θ  =  [tex]\frac{4.75^2}{9.81 \ 2.37}[/tex]   cos θ

             cos² θ + 0.97044 cos θ -1   = 0

we change variable    cos  θ = x

             x² + 0.97044 x - 1 =0

             x= [tex]\frac{-0.97 \pm \sqrt{0.97^2 - 4 1} }{2}[/tex]

           since the square root is imaginary there is no real solution to the problem, suppose that the radius is 1 m r = 1 m

           T sin θ = [tex]\frac{m \ v^2}{ r}[/tex]

           T cos θ  = m g

resolved

           tan θ =  [tex]\frac{v^2}{ r g}[/tex]

           θ = tan⁻¹ ( 4.75²/ 1 9.81)

           θ = 66º


Related Questions

A certain superconducting magnet in the form of a solenoid of length 0.28 m can generate a magnetic field of 7.0 T in its core when its coils carry a current of 80 A. The windings, made of a niobium-titanium alloy, must be cooled to 4.2 K. Find the number of turns in the solenoid.

Answers

Answer:

The number of turns in the solenoid is 19506.

Explanation:

Length of solenoid, L = 0.28 m

Magnetic field, B = 7 T

Current, I = 80 A

Let the number of turns is N.

The formula used to find the magnetic field is

[tex]B = \frac{\mu 0N I}{L}\\\\7 = \frac{4 \times 3.14\times 10^{-7}\times N\times 80}{0.28}\\\\N = 19506[/tex]

5. Can you get the machine with efficiency 100% in practice? Why?

Answers

Answer:

No,

Explanation:

Efficiency of a machine is always less than 100% as output energy is always less than the input energy, because some energy is lost to overcome friction.

Describe the term of inertia with the respect of motion

Answers

Answer:

Inertia can be defined as the tendency of an object or a body to continue in its state of motion or remain at rest unless acted upon by an external force.

Explanation:

Motion can be defined as a change in the location (position) of a physical object or body with respect to a reference point.

This ultimately implies that, motion would occur as a result of a change in location (position) of an object with respect to a reference point or frame of reference i.e where it was standing before the effect of an external force.

Inertia can be defined as the tendency of an object or a body to continue in its state of motion or remain at rest unless acted upon by an external force.

Newton's First Law of Motion is also known as Law of Inertia and it states that, an object or a physical body in motion will continue in its state of motion at continuous velocity (the same speed and direction) or, if at rest, will remain at rest unless acted upon by an external force.

The inertia of an object such as a truck is greatly dependent or influenced by its mass; the higher quantity of matter in a trailer, the greater will be its tendency to continuously remain at rest.

In conclusion, inertia is applicable to all physical objects.

(6). A car travels in a straight line from city A to city B at a speed of 60kmh-1

. Then return

from city B to city A along the original route at a speed of 40kmh-1

. The distance between

the two cities is 120 km. What is the average speed of the vehicle?

1. 30kmh-1

2. 45kmh-1

3. 48kmh-1

4. 60kmh-1​

Answers

i think that the answer is 4. 60kmh!

A car is running uniformly with the velocity of 72km/h3, what is its acceleration?




Answers

Answer: a =0

Explanation:

A 0.0780 kg lemming runs off a
5.36 m high cliff at 4.84 m/s. What
is its potential energy (PE) when it
jumps?

Answers

Answer:

4.097 Joules

Explanation:

Applying,

P.E = mgh............... Equation 1

Where P.E = Potential energy, m = lemming mass, h = height, g = acceleration due to gravity

From the question,

Given: m = 0.0780 kg, h = 5.36 m

Constant: g = 9.8 m/s²

Substitute these values into equation 1

P.E = 0.0780(9.8)(5.36)

P.E = 4.097 Joules.

Hence the potential energy is 4.097 Joules

Answer:

4.097 J

Explanation:

can anyone please help me​

Answers

Answer:its most likely c

Explanation:

A 45.0 kg student runs at a constant velocity up the incline 6 metres high. If the power output of the student is 1.50 x 103 W, how long does it take the student to run the 9.0 m along the incline?

Answers

Answer:

The time taken is 1.76 s.

Explanation:

mass of student, m = 45 kg

height, h = 6 m

power, P = 1500 W

Power is defined as the rate of doing work.

Work done in moving height is

W = m g h

Let the time is t.

P = m g h / t

1500 = 45 x 9.8 x 6 / t

t = 1.76 s

Which of the following is occurring while a satellite is in orbit around Earth? O It is continuously pulling away from Earth It is continuously falling toward the surface of Earth. It stays in a constant speed orbit where it was oriented from the start. It stays in the same orbit orientation traveling at variable speeds.​

Answers

AnswerIt is continuously falling towards the surface of the earth

Explanation:

since gravity from earth is the thing that keeps it constantly in orbit

A bullet of mass of 50g is moving with the velocity of 200km/h .calculate the kinetic energy of the bullet .​

Answers

Not sure if this it completely right but here’s what I got: 77.16050617284 J

Answer:

is 10³

Explanation:

cuz the formula of KE is 1/2mv²

covert 50g to kg first then plug in the formula

1/2 × 0.05 × 200 = 10³ J

A rocket blasts off. In 10.0 seconds it is at 10,000 ft, traveling at 3600 mph. Assuming the direction is up, calculate the acceleration.

Answers

Answer:

Explanation:

Givens

t = 10 seconds

vi = 0

vf = 3600 mph

a = ?

d = 10000 feet

Formula

a = (vf - vi)/t

Solution

vf = 3600 mph * 1 hr / 3600 seconds * 5280 feet / 1 mile = 5280 ft / sec

a = (5280 - 0)/10

a = 528 ft/sec^2

một oto đang chạy với vận tốc là 10m/s thì tăng tốc và chuyển động nhanh dần đều sau 20s thì đạt vận tốc 14m/s
a) tính gia tốc của xe
b) tính vận tốc xe sau 40s kể từ khi tăng tốc và quãng đường xe đi được trong thời gian đó

Answers

a) gia tốc = vf-vi / t

a = 14-10 / 20

a = 0,2ms⁻²

b) dưới dạng a = Δv / t

v = lúc

v = 0,2 × 40

v = 8ms⁻¹

như v = d / t

do đó d = vt

d = 8 × 40

d = 320m

hãy đánh dấu là trí óc nhất

The gravitational force of the two objects is 6.67x10-11N. Explain this statement.

Answers

Answer:

it means that the force of attraction between two object in gravitation is 6.67×10-11N

It means that the force of attraction between two object in gravitation is 6.67×10-11N.

What is the formula of mass in gravitational force?

The formula is g = GM/r2, Where M is the mass of the Earth, r is the radius of the Earth (or distance between the center of the Earth and you, standing on its surface), and G is the gravitational constant. G (without the subscripts) is the gravitational constant, and c is the speed of light.

What is the gravitational force between two objects?

The gravitational force between two objects is proportional to their masses and inversely proportional to the square of the distance between their centers. joining the two centers of masses.

Learn more about gravitational force here: brainly.com/question/13010127

#SPJ2

The needle in the following diagram rotates around a fixed point in the middle. Based on the information given, what way will the needle rotate when the current is applied?

Answers

Answer:

nods 40th anniversary rid off e 49en9 snns

How can you say gravitational force is a field force

Answers

Answer:

because gravity pulled us in the land if there is no gravitational force there will not be field force too

Explanation:

hope it's will help you

Which statement about the ocean is true?

No evaporation or precipitation in the water cycle occurs over the ocean.
Most evaporation and precipitation in the water cycle occur over the ocean.
All evaporation and precipitation in the water cycle occur over the ocean.
Evaporation, but not precipitation, in the water cycle occurs over the ocean.

Answers

Answer:

most evaporation and precipitation in the water cycle occus over the ocean

The option Most evaporation and precipitation in the water cycle occur over the ocean. is the correct answer

In isoelectric focusing gel electrophoresis a. there is a pH gradient that parallels the electric field gradient b. particular care must be taken to ensure the same pH along the length of the gel c. the electric current is allowed to fluctuate d. the electric circuits of the apparatus must be very well insulated

Answers

Answer:

a. there is a pH gradient that parallels the electric field gradient.

Explanation:

Gel electrophoresis is a technique used to separate DNA fragments according to their size. DNA samples are loaded in the wells and then electric current is applied to pull the DNA fragments out from the gel. Isoelectric gel electrophoresis is a process in which negatively charged DNA fragments are separated from the gel.

What will happen to the velocity and momentum of each ball when the small ball hits the heavier large ball?

Answers

most of the momentum is transferred to the ball on top. Since the collision in this situation is elastic, momentum is conserved, meaning the momentum of both balls before hitting the floor is equal to the momentum of both balls right after the collision.

The small ball will transfer its momentum to the heavier ball. Since the momentum gets conserved. The velocity will depend upon the mass of the balls.

What is the law of conservation of momentum?

According to the law of conservation of momentum. The momentum of the body before the collision is always equal to the momentum of the body after the collision.

The momentum of the body is given by the product of the mass and velocity of the body.

According to the law of conservation of momentum

Momentum before collision =Momentum after collision

Hence the small ball will transfer its momentum to the heavier ball.

To learn more about the law of conservation of momentum refer;

https://brainly.com/question/1113396

một hòn đá có khối lượng 5kg bay với vận tốc 72kg/h . động lượng của hòn đá là

Answers

Answer:

Momentum = 100 Kgm/s

Explanation:

Given the following data;

Speed = 72 km/h

Mass = 5 kg

To find the momentum of the stone;

First of all, we would have to convert the value of speed to meter per seconds.

Conversion:

72 km/h to m/s = (72 * 1000)/3600 = 20 m/s

Momentum can be defined as the multiplication (product) of the mass possessed by an object and its velocity. Momentum is considered to be a vector quantity because it has both magnitude and direction.

Mathematically, momentum is given by the formula;

Momentum = mass * velocity

Substituting the values into the formula, we have;

Momentum = 5 * 20

Momentum = 100 Kgm/s

Give reason.


b} String roller is an example of wheel and axel .Why?

Answers

Explanation:

string roller is called an example of wheel and axel because The thin rod which needs to be turned is called the axle and the wider object fixed to the axle, on which we apply force is called the wheel.

hence the we apply force on the roller and the string gets tight.

A man has 60w bulbs and a 240w water heater in his apartment. If the bulbs and the water heater are switched on for four hours daily and the cost of electricity is N1.20 per KWh calculare his bill in 30 days

Answers

Answer: [tex]N43.2[/tex]

Explanation:

Given

Power consumption of bulb and water are [tex]60\ W[/tex] and [tex]240\ W[/tex]

If the Devices are on for four hours

Total power of devices [tex]60+240=300\ W[/tex]

Energy consumed for 4 hours is

[tex]\Rightarrow 300\times 4=1200 Wh\\\Rightarrow 1.2\ kWh[/tex]

For 30 days it is [tex]1.2\times 30=36\ kWh[/tex]

Cost for 30 days [tex]36\times 1.2=43.2\ N[/tex]

(Q008) Magnetic anomalies are a. found only on the seafloor. b. measured with an instrument called an inclinometer. c. defined as the angle between which a compass needle points and the longitude at that point. d. places where the magnetic field strength is either greater or less than the expected strength.

Answers

Answer: D. places where the magnetic field strength is either greater or less than the expected strength.

Explanation:

Magnetic anomaly refers to the change in the magnitude of the magnetic field of the Eatth with respect to the location's expected value.

Magnetic anomalies are places where the magnetic field strength is either greater or less than the expected strength. Therefore, the correct option is D.

Explain how a submarine
floats on the water surface
and dives down into water.

Answers

Answer:

A submarine uses tanks that are filled with compressed air and when it is needed the air is released and takes on water which increase the density making it sink but when the water is pushed out the sub marine density is decreased making it float

20.In case the conductor is a heating appliance, then this energy(w) is converted into heat(H) i.e

A. w=H C. w=I2Rt

B. w=VIt D. all of above​

Answers

Answer:

not sure just need points

Explanation:

a+b+c

Explain the effects of force giving example​

Answers

Answer:

1) Can change the state of an object(rest to motion/ motion to rest):For example, pushing a heavy stone in order to move it. 2) May change the speed of an object if it is already moving. 4) May bring about a change in the shape of an object. For example, blowing air in balloon.

Explanation:

Effect of force Can change the state of an object(rest to motion/ motion to rest):For example, pushing a heavy stone in order to move it.

A person carries a box of 100 kg. What is the weight of the box? (g= 9.8 m/s2)​

Answers

Answer:

980 newton

Explanation:

100×9.8 = 980

Why are houses in hot areas painted in white while those in cold areas painted with dull colours

Answers

Answer:

Because white color reflects back the heat coming from the sun while dull colors absorb the heat.

25 POINTS 25 POINTS 25 POINTS 25 POINTS 25 POINTS

Assignment: Build an Electromagnet and a Motor Investigation

Electromagnet
1. How many paper clips did the wire wrapped around the nail just a few times pick up?

2. Which electromagnet design was most successful in picking up the most paper clips?

3. Would wrapping the wire more times around the nail make the electromagnet stronger or weaker?

4. What do you think the result would be if an iron nail that was much thicker was used?

5. What do you think would happen if a wooden stick was chosen as the core instead of the iron nail?

Motor
1. Describe the components that are necessary to make a motor run? What do they each provide? (example: battery provides voltage source)


2. Describe how the homemade motor makes mechanical energy from electrical energy.





3. What are three appliances in your house that use a motor that turns electrical energy into mechanical energy?

Answers

All the paper clips, coiled wire with nail and wrapping or coiling the wire more times are the correct answers.

All the paper clips will the wire wrapped around the nail just a few times pick up. A coiled wire with nail in the center is the electromagnet design which is most successful in picking up the most paper clips. Wrapping or coiling the wire more times around the nail make the electromagnet more stronger.

If an iron nail that was much thicker was used, it will make the magnet stronger that leads to strong electromagnetism. There are three main parts that is necessary for making a motor i.e. a rotor, a stator and a commutator.

These three parts use the attractive and repulsive forces of electromagnetism, causing the motor to spin continually as long as it receives a steady flow of electric current. Motors comprise of loops of wire in a magnetic field.

When current is passed through the loops, the magnetic field exerts a torque on the loops, which rotates the shaft that leads to the generation of electricity. Water pump, mixer and washing machine are three appliances in your house that use a motor that turns electrical energy into mechanical energy.

https://brainly.com/question/24278437

the unit of force and pressure are called derived unit​

Answers

Answer:

yes

Explanation:

because they can be derived in the form of base units

Based on its location on the periodic table, which element is the best
electrical insulator?
A. Iron (Fe)
O B. Sulfur (S)
O C. Calcium (Ca)
D. Silver (Ag)

Answers

Answer:

B

Explanation:

Nonmetal is better insulator than metals

Answer:

B

Explanation:

Just took the quiz.

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