A mass of 0.250 kg is attached to a spring and undergoes simple harmonic oscillations with a period of 0.640 s. What is the force constant of the spring?

Answers

Answer 1

Answer:

Force constant of the spring (k) = 24.07 N/m

Concept/Theory:

The period [tex] \sf (T_s) [/tex] of a spring-mass system is proportional to the square root of the mass (m) and inversely proportional to the square root of the force constant of the spring (k).

Equation of period:

[tex] \boxed{ \bf{T_s = 2 \pi \sqrt{\dfrac{m}{k}}}}[/tex]

Explanation:

Mass = 0.250 kg

Period = 0.640 s

By substituting values in the equation, we get:

[tex] \rm \longrightarrow 0.640 = 2 \pi \sqrt{\dfrac{0.250}{k}} \\ \\ \rm \longrightarrow 2 \times 3.14 \sqrt{ \dfrac{0.25 0}{k} } = 0.640 \\ \\ \rm \longrightarrow 6.28 \sqrt{ \dfrac{0.250}{k} } = 0.640 \\ \\ \rm \longrightarrow \sqrt{ \dfrac{0.250}{k} } = \frac{0.640}{6.28} \\ \\ \rm \longrightarrow \frac{0.250}{k} = { \bigg(\frac{0.640}{6.28} \bigg) }^{2} \\ \\ \rm \longrightarrow \frac{k}{0.250} = \bigg( { \frac{6.28}{0.640} \bigg) }^{2} \\ \\ \rm \longrightarrow k = \bigg( { \frac{6.28}{0.640} \bigg) }^{2} \times 0.250 \\ \\ \rm \longrightarrow k = 24.07 \: N/m[/tex]

Answer 2

The force constant of the spring is approximately 24.038 newtons per meter.

As we are talking about Simple Harmonic Motion. In this exercise we need to determine the Spring Constant ([tex]k[/tex]), in newtons per meter, from the equation of the Period ([tex]T[/tex]), in seconds, which is described below:

[tex]T = 2\pi\cdot \sqrt{\frac{m}{k} }[/tex] (1)

Where [tex]m[/tex] is the mass of the moving element, in kilograms.

If we know that [tex]T = 0.640\,s[/tex] and [tex]m = 0.250\,kg[/tex], then the spring constant of the spring is:

[tex]0.640 = 2\pi\cdot \sqrt{\frac{0.250}{k} }[/tex]

[tex]\sqrt{\frac{0.250}{k} } \approx 0.102[/tex]

[tex]\frac{0.250}{k} \approx 0.0104[/tex]

[tex]k \approx 24.038\,\frac{N}{m}[/tex]

The force constant of the spring is approximately 24.038 newtons per meter.

Please see this question related to Simple Harmonic Motion for further details: https://brainly.com/question/17315536

A Mass Of 0.250 Kg Is Attached To A Spring And Undergoes Simple Harmonic Oscillations With A Period Of

Related Questions

A car’s brakes decelerate it at a rate of -2.40 m/s2. If the car is originally travelling at 13 m/s and comes to a stop, then how far, in meters, will the car travel during that time?

Answers

Answer:

Approximately [tex]35.2\; \rm m[/tex].

Explanation:

Given:

Initial velocity: [tex]u = 13\; \rm m \cdot s^{-1}[/tex].

Acceleration: [tex]a = -2.40\; \rm m \cdot s^{-2}[/tex] (negative because the car is slowing down.)

Implied:

Final velocity: [tex]v = 0\; \rm m \cdot s^{-1}[/tex] (because the car would come to a stop.)

Required:

Displacement, [tex]x[/tex].

Not required:

Time taken, [tex]t[/tex].

Because the time taken for this car to come to a full stop is not required, apply the SUVAT equation that does not involve time:

[tex]\begin{aligned} x &= \frac{v^2 - u^2}{2\, a} \\ &= \frac{{\left(0\; \rm m \cdot s^{-1}\right)}^2 - {\left(13\; \rm m \cdot s^{-1}\right)}^2}{2\times \left(-2.40\; \rm m\cdot s^{-2}\right)} \approx 35.2\; \rm m \end{aligned}[/tex].

In other words, this car would travel approximately [tex]35.2\; \rm m[/tex] before coming to a stop.

Does anyone skateboard still?

Answers

Answer:

yes

Explanation:

people still skateboard that is an easy question

student measures the weight of a bag of bananas with a spring balance.
Describe what is inside a spring balance and explain how it works.

Answers

A spring balance measures the weight of an object by opposing the force of gravity acting with force of an extending spring. May be used to determine mass as well as weight by recalibrating the scale. Some spring balances are available in gram or kilogram markings and are used to measure the mass of an object. Spring balances consist of a cylindrical tube with a spring inside. One end (at the top) is fixed to an adjuster which can be used to calibrate the device. The other end is attached to a hook on which you can hang masses etc.

A vehicle travels with an average speed of sav = 15 mi/hr.

Answers

Put more points and I’ll answer



An ant is crawling along a yardstick that is pointed with the O-inch mark to the east and the 36-Inch mark to the west. It starts at the 19-inch mark, crawls to the 27-inch

mark, then moves to the 7-inch mark. What was the total distance the ant traveled?

Answers

Answer:

33 Inches

Explanation:

The movement of the ant is sketched in the attached image. The ant moved from the 19-inch mark to 27-inch mark covering a distance of 13 Inches (27 - 19). Finally, it moved from the 27-inch mark to 7-inch mark covering a distance of 20 Inches (27 - 7).

Total Distance covered = 13 + 20 = 33 Inches.

Hence, the total distance the ant traveled is 33 Inches.

How does increasing the width of a wire affect a circuit?

A. It restricts the flow of electrons.

B. It reduces the voltage

C. It allows electrons to flow more easily

D. It increases the resistance

Whoever gets this right I’ll give brainliest. Be sure that the answer is right. I’d love a explanation too if you could include one.

Answers

Answer:

The resistance of a wire decreases with increasing thickness.

Explanation:

Hope this helped!

Answer: C it allows electrons to flow more easily

Explanation:i got it right i hope this helps you

A jogger runs north 6 km, 5 km east, and 4 km north again. Time is 1.9 hr. What is average velocity?

Answers

Answer:

Average velocity = 5.9 km/ hr (or 1.64 m/s).

Explanation:

Velocity = [tex]\frac{displacement}{time}[/tex]

It is a vector quantity and has an SI unit of m/s.

Displacement = [tex]\sqrt{x^{2} + y^{2} }[/tex]

x = 5 km east

y = 6 km north + 4 km north

  = 10 km north

So that,

Displacement = [tex]\sqrt{5^{2} + 10^{2} }[/tex]

                       = [tex]\sqrt{25 + 100}[/tex]

                       = [tex]\sqrt{125}[/tex]

                       = 11.1803

Displacement = 11.18 km = 11180 m

Time = 1.9 hr = 6840 seconds

Average velocity = [tex]\frac{11.180}{1.9}[/tex]

             = 5.8842

Average velocity = 5.9 km/ hr

The average velocity is 5.9 km/ hr (or 1.64 m/s).

I want to know about the inventions caused due to rain. Like the Benjamin Franklin's Lightning Conductor. I have to make a chart.​

Answers

Franklin had been waiting for an opportunity like this. He wanted to demonstrate the electrical nature of lightning, and to do so, he needed a thunderstorm.

He had his materials at the ready: a simple kite made with a large silk handkerchief, a hemp string, and a silk string. He also had a house key, a Leyden jar (a device that could store an electrical charge for later use), and a sharp length of wire. His son William assisted him.

Franklin had originally planned to conduct the experiment atop a Philadelphia church spire, according to his contemporary, British scientist Joseph Priestley (who, incidentally, is credited with discovering oxygen), but he changed his plans when he realized he could achieve the same goal by using a kite.

In the pictire ,can we separate hydrogen (H) from oxygen (O)?

Paanswer nga po.....​

Answers

A.)

Water is the name of the pure substance H₂O

B.)

Hydrogen and Oxygen are the compound of water

C.)

Yes, we can

D.)

This process known as Electrolysis

5.
An 80 newton force and a 45 newton force act on an object
as shown below.
80 N
30°
4S N
Which of the following vectors would bets represent an
equilibrant when added to this system?
(1) 24 N to the left (3) 24 N to the right
(2) 114 N to the right (4) 45 N to the left
Tirant Showroiculations

Answers

Answer:

the answer is a time your welcome

Answer:

(1)

Explanation:

What does the underlined word mean in the following sentence? El conejo viene el día de Pascua de Resurrección. Easter Christmas Holidays Thanksgiving

Answers

Answer:easter

Explanation:

Answer:

Easter

Explanation:

did it on edge, and searched it up

Which of the following would probably need the greatest force to overcome its inertia?
option 1 a tennis ball 2 a sports ar 3 a dump truck and four a bicycle

Answers

Answer:

A dump truck.

Explanation:

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.

In physics, Sir Isaac Newton's first law of motion is 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.

Mathematically, it is given by the formula;

[tex] F = ma[/tex]

Where;

F represents force measured in Newton.m represents the mass of an object measured in kilograms.a represents acceleration measured in meter per seconds square.

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

Hence, a dump truck would probably need the greatest force to overcome its inertia because it has more mass than all the other objects in the category. Also, the mass of an object is directly proportional to its inertia, as well as the force applied.

Answer:As one of Newton's Laws of Gravitational force The answer would Be a dump truck because it includes one of Newton's Laws of Gravitational force in the abstract Laws of gravity.

A 50 g mass is freely hanging from a horizontal meter stick at a distance of 99 cm from the pivot. Calculate the weight force W that the mass exerts on the meter stick? ·Calculate the torque that the weight force exerts about the pivot? 4. What does the pivot exert on the meter stick?

Answers

Answer:

W = 0.49 N

τ = 0.4851 Nm

Force

Explanation:

The weight force can be found as:

W = mg

W = (0.05 kg)(9.8 m/s²)

W = 0.49 N

The torque about the pivot can be found as:

τ = W*d

where,

τ = torque

d = distance between weight and pivot = 99 cm = 0.99 m

Therefore,

τ = (0.49 N)(0.99 m)

τ = 0.4851 Nm

The pivot exerts a  FORCE on the meter stick because the pivot applies force normally over the stick and has a zero distance from stick.

differences between a resultant and a equilibrium​

Answers

Answer:

I found "As nouns the difference between resultant and equilibrium is that resultant is anything that results from something else; an outcome while equilibrium is the condition of a system in which competing influences are balanced, resulting in no net change. is following as a result or consequence of something."

Explanation:

a 1000kg car uses a breaking force of 10,000N to stop in two second. What is the change in momentum of the car?

Answers

Answer:

ΔP =  20000 N s

Explanation:

To solve this problem we use the relation between momentum and moment

         I = Δp

let's calculate the momentum

         I = ∫F dt

if we use the average force

       I = F t

       I = 10000 2

       I = 20000 N s

therefore with the first equation

        ΔP = I = 20000 N s

A jet airplane with a 75.0 m wingspan is flying at 260 m/s. What emf is induced between the wing tips in V if the vertical component of the Earth’s magnetic field is 3.00 × 10-5 T?

Answers

Answer:

0.585V

Explanation:

Given that:

B = 3.00 × 10-5 T

l = 75.0 m

v = 260 m/s

From Blv = emf between the wing tips

= 3.00 × 10-5 T × 75×260

= 117/200

= 0.585V

Hence, the emf between the wing tips is 0.585V

A small block of mass m1 = 0.4 kg is placed on a long slab of mass m2 = 2.8 kg. Initially, the slab is stationary and the block moves at a speed of vo = 3 m/s. The coefficient of kinetic friction between the block and the slab is 0.15 and there is no friction between the slab and the surface on which it moves.

Determine the speed v1.

Determine the distance traveled by the slab before it reaches the speed v1.

Answers

Answer:

v₁ = 0.375 m / s ,   x = 0.335 m

Explanation:

Let's analyze this interesting exercise, the block moves and has a friction force with the tile, we assume that the speed of the block is constant, so the friction force opposes the block movement. For the only force that acts (action and reaction) this friction force exerted by the block that is in the direction of movement of the tile.

We can also see that the isolated system formed by the block and the tile will reach a stable speed where friction cannot give the system more energy, this speed can be found by treating the system with the conservation of linear momentum.

initial moment. Right at the start of the movement

       p₀ = m v₀ + 0

final moment. Just when it comes to equilibrium

      [tex]p_{f}[/tex] = (m + M) v₁

how the forces are internal

       p₀ =p_{f}

       m v₀ = (m + M) v₁

       v₁ = m /m+M    v₀

let's calculate

       v₁ = 0.4 /(0.4 + 2.8)  3

       v₁ = 0.375 m / s

 

Let's apply Newton's second law to the Block, to find the friction force

Y axis

       N - W = 0

       N = W

       N = m g

where m is the mass of the block

the friction force has the formula

      fr = μ N

      fr = μ m g

We apply Newton's second law to slab    

X axis

       fr = M a

where M is the mass of the slab

       μ m g = M a

       a = μ g m / M

let's calculate

       a = 0.15  9.8  0.4 / 2.8

       a = 0.21 m / s²

With kinematics we can find the position

       v²= v₀²+2 a x

as the slab is initially at rest, its initial velocity is zero

       v² = 2 a x

       x = v2 / 2a

let's calculate

        x = 0.375²/2 0.21

        x = 0.335 m

A college student has just bought a small computer that weighs 50N. Her apartment is on the 5th floor which is 35 meters up. How much work must she do to drag her computer up the stairs?​

Answers

Answer:

W = 1750 J

Explanation:

It is given that,

Weight of a computer, F = 50 N

A student wants to keep it on the 5th floor which is 35 meters up.

We need to find the work done by her to drag her computer up the stairs. Let it is W. Using the formula of work as follows :

W = F d

Put all the values,

W = 50 N × 35 m

W = 1750 J

So, 1750 J of work is done by her to drag the computer up the stairs.

A relaxed spring of length 0.15 m stands vertically on the floor; its stiffness is 1070 N/m. You release a block of mass 0.5 kg from rest, with the bottom of the block 0.6 m above the floor and straight above the spring. How long is the spring when the block comes momentarily to rest on the compressed spring?

Answers

Answer:

x' = 0.085 m = 8.5 cm

Explanation:

The law of conservation of energy says that:

Potential Energy Stored in Spring = Loss in Gravitational Potential Energy of Block

(1/2)kΔx² = mgh

where,

k = stiffness of spring = 1070 N/m

Δx = change in length of spring = ?

m = mass of block = 0.5 kg

g = 9.8 m/s²

h = height of block above spring = 0.6 m - 0.15 m = 0.45 m

Therefore,

(1/2)(1070 N/m)Δx² = (0.5 kg)(9.8 m/s²)(0.45 m)

Δx = √[2(2.205 Nm)/(1070 N/m)]

Δx = 0.064 m

but,

Δx = x - x' = 0.15 m - x' = 0.064 m

x' = 0.15 m - 0.064 m

x' = 0.085 m = 8.5 cm

Suppose you have a 2000 Watt water heater that is on for a total of 150 hours a month. How much will this cost you at a rate of 10 cents per kW*hr?

Answers

Answer:

$30

Explanation:

Given that,

Power of a water heater, P = 2000 Watts

It is on for a total of 150 hours a month.

2000 Watts = 2 kW

Time, t = 150 hours

Energy used by the water heater is given by :

[tex]E=P\times t\\\\E=2\ kW\times 150\ h\\\\E=300\ kWh[/tex]

It is also mentioned that the cost is 10 cents per kWhr.

Since, $1 = 100 cents

10 cents = $0.1

So, the total cost for the month is :

Cost = 300 × 0.1

Cost = $30

So, the required cost is $30.

A rocket traveling at 36.96 m/s is accelerated uniformly to 74.44 m/s over a 21.37 s interval. What is its displacement during this time?

Answers

Answer:

s = 1190.3 m = 1.19 km

Explanation:

First we find the acceleration by using first equation of motion:

Vf = Vi + at

where,

Vf = Final Velocity = 74.44 m/s

Vi = Initial Velocity = 36.96 m/s

a = acceleration = ?

t = time = 21.37 s

Therefore,

74.44 m/s = 36.96 m/s + a(21.37 s)

a = (74.44 m/s - 36.96 m/s)/21.37 s

a = 1.75 m/s²

Now, we use 2nd equation of motion to find distance covered (s):

s = Vi t + (1/2)at²

s = (36.96 m/s)(21.37 s) + (1/2)(1.75 m/s²)(21.37 s)²

s = 789.83 m + 400.47 m

s = 1190.3 m = 1.19 km

A car weighing 1,356 N is speeding down a highway with a velocity of 83 km/h. What is the momentum of this car

Answers

Answer:

The momentum of the car is 3190.74 kgm/s

Explanation:

Given;

weight of the car, w = 1,356 N

velocity of the car, v = 83 km/h = 23.06 m/s

The mass of the car is given by;

m = w/g

where;

g is acceleration due to gravity = 9.8 m/s²

m = 1356 / 9.8

m = 138.367 kg

The momentum of this car is given by;

P = mv

P = (138.367 x 23.06)

P = 3190.74 kgm/s

Therefore, the momentum of the car is 3190.74 kgm/s

A 0.200 H inductor is connected in series with a 88.0 Ω resistor and an ac source. The voltage across the inductor is vL=−(12.0V)sin[(487rad/s)t].

Required:
a. Derive an expression for the voltage vR across the resistor. Express your answer in terms of the variables L, R, VL (amplitude of the voltage across the inductor), ω, and t .
b. What is vR at 2.00 ms? Express your answer with the appropriate units.

Answers

Answer:

a.  (VL)R/ωL[1 - cos[ωt]]  = (10.84 V)[1 - cos[(487rad/s)t]]

b. 1.084 mV

Explanation:

a. Since it is a series circuit, the current in the inductor is the same as the current in the resistor.

Now, the voltage across the inductor vL = -Ldi/dt.

So, the current, i = -1/L∫vLdt.

Now, vL = −(12.0V)sin[(487rad/s)t] and L = 0.200 H

Substituting these into i, we have

i = -1/L∫vLdt

= -1/0.200H∫[−(12.0V)sin[(487rad/s)t]]dt.

= -[−(12.0V)]/0.200H∫[sin[(487rad/s)t]]dt.

= 60V/H∫[sin[(487rad/s)t]]dt

Integrating i, we have

i = 60V/H ÷ [(487rad/s)[-cos[(487rad/s)t]] + C

at t = 0, i(0) = 0

0 = 60V/H ÷ [(487rad/s)[-cos[(487rad/s)× 0]] + C

0 = 60V/H ÷ [(487rad/s)[-cos[0]] + C

0 = 60V/H ÷ [(487rad/s)[-1]+ C

C = 60V/H ÷ [(487rad/s)

So, i = 60V/H ÷ [(487rad/s)[-cos[(487rad/s)t]] + 60V/H ÷ [(487rad/s)

i =  60V/H ÷ [(487rad/s)[1 - cos[(487rad/s)t]]

i = (0.123A)[1 - cos[(487rad/s)t]] = VL/ωL[1 - cos[ωt]] where ω = 487rad/s and VL = 12.0 V and L = 0.200 H

So, the voltage across the resistor vR = iR where R = resistance of resistor = 88.0 Ω

So, vR = iR = VL/ωL[1 - cos[ωt]] × R = (VL)R/ωL[1 - cos[ωt]]

=  (0.123A)[1 - cos[(487rad/s)t]] × 88.0 Ω

= (10.84 V)[1 - cos[(487rad/s)t]]

b. vR at t = 2.00 ms = 0.002 s

So, vR = (10.84 V)[1 - cos[(487rad/s)(0.002)]]

= (10.84 V)[1 - cos[0.974]]

= (10.84 V)[1 - 0.9999]

= (10.84 V)(0.0001)

= 0.001084

= 1.084 mV

write an email to your friend about your
preparation for the upcoming exam

Answers

Answer:

You will be very glad to know that my preparation for HSC examination is very good. I have prepared myself for the HSC Examination 2015. I am confident that I will obtain very good marks in the examination. I have revised them several times and I am hopeful of obtaining distinction marks in all the subjects.

Explanation:

This is from Brainly hope this person helped you

A rolling ball moves from x1 = 8.0 cm to x2 = -4.1 cm during the time from t1 = 2.9 s to t2 = 6.0 s .

Answers

Complete Question

A rolling ball moves from [tex]x_1 = 8.0 \ cm[/tex] to [tex]x_2 = - 4.1 \ cm[/tex] during the time from [tex]t_1 = 2.9 s[/tex]  to  [tex]t_2 = 6.0s[/tex]

What is its average velocity over this time interval?

Answer:

The velocity is  [tex]v = 3.903 \ m/s[/tex]

Explanation:

From the question we are told that

    The first position of the ball is  [tex]x_1 = 8.0 \ cm[/tex]

    The second position of the ball is  [tex]x_2 = - 4.1 \ cm[/tex]

Generally the average velocity is mathematically represented as

       [tex]v = \frac{ x_1 - x_2}{t_2 - t_1}[/tex]

=>    [tex]v = \frac{ 8 - -4.1 }{ 6 - 2.9 }[/tex]

=>    [tex]v = 3.903 \ m/s[/tex]

What is Hydroelectric energy used for? Use in your own words.

Answers

Hydroelectric energy, also called hydroelectric power or hydroelectricity, is a form of energy that harnesses the power of water in motion—such as water flowing over a waterfall—to generate electricity. People have used this force for millennia. Over two thousand years ago, people in Greece used flowing water to turn the wheel of their mill to ground wheat into flour.

What is the result of increasing the speed at which a magnet moves in and
out of a wire coil?
O A. The current in the wire increases.
B. The magnetic field around the magnet decreases.
C. The current in the wire decreases.
O D. The magnetic field around the magnet increases.

Answers

Answer:

Explanatio

Increasing the speed of the relative motion between the coil and the magnet – If the same coil of wire passed through the same magnetic field but its speed or velocity is increased, the wire will cut the lines of flux at a faster rate so more induced emf would be produced. 3)n:

A car travels 23.0 m/s for 1.0 hours and then accelerates for 30.0 seconds to reach 40.0 m/s.  What was the total distance traveled by this car

Answers

Answer:

s = 83.85 km

Explanation:

First we calculate the distance covered by car, while traveling at constant speed:

s₁ = v₁t₁

where,

s₁ = distance covered at constant speed = ?

v₁ = constant speed = 23 m/s

t₁ = time of travel at constant speed = 1 hr = 3600 s

Therefore,

s₁ = (23 m/s)(3600 s)

s₁ = 82800 m = 82.8 km

Now, we calculate the distance travelled in accelerated motion. First we use 1st equation of motion to find acceleration:

Vf = Vi + at₂

where,

Vf = Final velocity = 40 m/s

Vi = Initial Velocity = 30 m/s

a = acceleration = ?

t₂ = time = 30 s

Therefore,

40 m/s = 30 m/s + a(30 s)

a = 10 m/s/30 s

a = 0.33 m/s²

Now, we use 2nd equation of motion for distance:

s₂ = Vi t₂ + (1/2)at₂²

s₂ = (30 m/s)(30 s) + (1/2)(0.33 m/s²)(30 s)²

s₂ = 900 m + 150 m

s₂ = 1050 m = 1.05 km

So, the total distance covered was:

s = s₁ + s₂

s = 82.8 km + 1.05 km

s = 83.85 km

A typical atomic polarizability is 1 × 10-40 (C·m)/(N/C). If the q in p = qs is equal to the proton charge e, what charge separation s could you produce in a typical atom by applying

Answers

Answer:

s = 6.25 10⁻²² m

Explanation:

Polarizability is the separation of electric charges in a structure, in the case of the atom it is the result of the separation of positive charges in the nucleus and the electrons in their orbits, macroscopically it is approximated by

                p = q s

               s = p / q

let's calculate

              s = 1 10⁻⁴⁰ / 1.6 10⁻¹⁹

              s = 0.625 10⁻²¹ m

              s = 6.25 10⁻²² m

We see that the result is much smaller than the size of the atom, therefore this simplistic model cannot be taken to an atomic scale.

A car covers a distance of 200m. If its velocity is 20 m/s, calculate the time taken. ​

Answers

Answer:

10 seconds

Explanation:

velocity=displacement/time
Other Questions
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