Using a scale of 1 cm to represent 10 N, find the size and direction of the resultant of forces of 50 N
and 30 N acting at the angle of 45 O to each other.

Answer:

a) The velocity when it passes the equilibrium point is [tex]\pm 2.451[/tex] meters per second.

b) The velocity when it is 0.10 meters from equilibrium is [tex]\pm 1.567[/tex] meters per second.

c) The total energy of the system is 1.802 joules.

d) The equation describing the motion of the mass, assuming that initial position is a maximum is [tex]x(t) = 0.13\cdot \sin (18.850\cdot t +0.5\pi)[/tex].

Explanation:

a) If all non-conservative forces can be neglected and spring has no mass, then the mass-spring system exhibits a simple harmonic motion (SHM). The kinematic formula for the position of the system ([tex]x(t)[/tex]), measured in meters, is:

[tex]x(t) = A\cdot \sin(\omega \cdot t +\phi)[/tex] (1)

Where:

[tex]A[/tex] - Amplitude, measured in meters.

[tex]\omega[/tex] - Angular frequency, measured in radians per second.

[tex]t[/tex] - Time, measured in seconds.

[tex]\phi[/tex] - Phase, measured in radians.

The kinematic equation for the velocity formula of the system ([tex]v(t)[/tex]), measured in meters per second, is derived from (1) by deriving it in time:

[tex]v(t) = \omega\cdot A\cdot \cos (\omega\cdot t+\phi)[/tex] (2)

The velocity when it passes the equilibrium point occurs when the cosine function is equal to 1 or -1. Then, that velocity is determined by following formula:

[tex]v = \pm \omega\cdot A[/tex] (3)

The angular frequency is calculated by this expression:

[tex]\omega = 2\pi\cdot f[/tex] (4)

Where [tex]f[/tex] is the frequency, measured in hertz.

If we know that [tex]f = 3\,hz[/tex] and [tex]A = 0.13\,m[/tex], then the velocity when it passes the equilibrium point, which is the maximum and minimum velocities of the mass:

[tex]\omega = 2\pi\cdot (3\,hz)[/tex]

[tex]\omega \approx 18.850\,\frac{rad}{s}[/tex]

[tex]v = \pm \left(18.850\,\frac{rad}{s} \right)\cdot (0.13\,m)[/tex]

[tex]v = \pm 2.451\,\frac{m}{s}[/tex]

The velocity when it passes the equilibrium point is [tex]\pm 2.451[/tex] meters per second.

b) First, we need to determine the spring constant of the system ([tex]k[/tex]), measured in newtons per meter, in terms of the angular frequency ([tex]\omega[/tex]), measured in radians per second, and mass ([tex]m[/tex]), measured in kilograms. That is:

[tex]k = \omega^{2}\cdot m[/tex] (5)

If we know that [tex]\omega \approx 18.850\,\frac{rad}{s}[/tex] and [tex]m = 0.60\,kg[/tex], then the spring constant is:

[tex]k = \left(18.850\,\frac{rad}{s} \right)^{2}\cdot (0.60\,kg)[/tex]

[tex]k = 213.194\,\frac{N}{m}[/tex]

Lastly, we determine the velocity when the mass is 0.10 meters from equilibrium by the Principle of Energy Conservation:

[tex]U_{k} + K = K_{max}[/tex] (6)

[tex]\frac{1}{2}\cdot k\cdot x^{2} + \frac{1}{2}\cdot m\cdot v^{2} = \frac{1}{2}\cdot m\cdot v_{max}^{2}[/tex] (7)

Where:

[tex]U_{k}[/tex] - Current elastic potential energy, measured in joules.

[tex]K[/tex] - Current translational kinetic energy, measured in joules.

[tex]K_{max}[/tex] - Maximum translational kinetic energy, measured in joules.

[tex]v[/tex] - Current velocity of the system, measured in meters per second.

[tex]m[/tex] - Mass, measured in kilograms.

[tex]v_{max}[/tex] - Maximum velocity of the system, measured in meters per second.

If we know that [tex]k = 213.194\,\frac{N}{m}[/tex], [tex]x = 0.10\,m[/tex], [tex]m = 0.60\,kg[/tex] and [tex]v_{max} = \pm 2.451\,\frac{m}{s}[/tex], then the velocity of the mass-spring system is:

[tex]\frac{k}{m} \cdot x^{2} + v^{2} = v_{max}^{2}[/tex]

[tex]v^{2} = v_{max}^{2}-\frac{k}{m}\cdot x^{2}[/tex]

[tex]v = \sqrt{v_{max}^{2}-\frac{k\cdot x^{2}}{m} }[/tex] (8)

[tex]v = \sqrt{\left(\pm 2.451\,\frac{m}{s} \right)^{2}-\frac{\left(213.194\,\frac{N}{m} \right)\cdot (0.10\,m)^{2}}{0.60\,kg} }[/tex]

[tex]v \approx \pm 1.567\,\frac{m}{s}[/tex]

The velocity when it is 0.10 meters from equilibrium is [tex]\pm 1.567[/tex] meters per second.

c) The total energy of the system ([tex]E[/tex]), measured in joules, can be determined by the following expression derived from the Principle of Energy Conservation:

[tex]E = \frac{1}{2}\cdot m\cdot v_{max}^{2}[/tex] (9)

If we know that [tex]m = 0.60\,kg[/tex] and [tex]v_{max} = \pm 2.451\,\frac{m}{s}[/tex], then the total energy of the system is:

[tex]E = \frac{1}{2}\cdot (0.60\,kg)\cdot \left(\pm 2.451\,\frac{m}{s}\right)^{2}[/tex]

[tex]E = 1.802\,J[/tex]

The total energy of the system is 1.802 joules.

d) Given that initial position of the mass-spring system is a maximum, then we conclude that the equation of motion has the following parameters: ([tex]A = 0.13\,m[/tex], [tex]\omega \approx 18.850\,\frac{rad}{s}[/tex] and [tex]\phi = 0.5\pi\,rad[/tex])

From (1) we obtain the resulting formula:

[tex]x(t) = 0.13\cdot \sin (18.850\cdot t +0.5\pi)[/tex] (10)

The equation describing the motion of the mass, assuming that initial position is a maximum is [tex]x(t) = 0.13\cdot \sin (18.850\cdot t +0.5\pi)[/tex].

Answer:

First answer to the first question is Two people pulling a rope with the same force in a opposite direction.  The other one would be 2.72N        

Explanation:

Hope this helps you :)

Answer:

Electrical to Thermal

Answer:

v = 15.65 m/s

Explanation:

We use conservation of mechanical energy between initial (i) and final (f) states:

Pi + KEi = Pf + KEf

At the top of the cave at the instant the bat starts to fall, there is only potential energy since the bat's velocity is zero.

Pi = m g h = 600 J

and the KEi = 0 J (no velocity)

Knowing the height of the cave's roof (12.8 m) , we can find the mass of the bat:

m = 600 J / (g 12.5) = 4.9 kg

Using conservation of mechanical energy, the final state is:

Pf + KEf = 600 J

with Pf = 0 (just touching the ground)

KEf= 1/2  4.9 (v^2)

and we solve for the velocity:

600 J = 0 + 1/2  4.9 (v^2)

v^2 = 600 * 2 / 4.9 = 244.9

v = 15.65 m/s

Answer:

No

Explanation:

Answer:

No

Explanation:

Tornadoes are usally produced in the Midwest regions. Hurricanes are made with water, not clouds. So, no, hurricanes cannot produce tornadoes.

Hello!!

For calculate the Velocity of the wave let's applicate the formula:

[tex]\boxed{V=f*\lambda}[/tex]

[tex]\textbf{Being:}[/tex]

[tex]\sqrt{}[/tex] V = Velocity = ?

[tex]\sqrt{}[/tex] f = Frequency = 300 Hz

[tex]\sqrt{}[/tex] [tex]\lambda[/tex] = Wavelength = 1,1 m

⇒ [tex]\text{Then let's \textbf{replace it according} we information:}[/tex]

[tex]V = 300 \ Hz * 1,1 \ m[/tex]

⇒ [tex]\text{Let's resolve it: }[/tex]

[tex]V = 330 \ m / s[/tex]

[tex]\textbf{Result:}\\\text{The velocity is \textbf{330 meters per second}}[/tex]

Answer:

For calculate the Velocity of the wave let's applicate the formula:

V = Velocity = ?

f = Frequency = 300 Hz

 = Wavelength = 1,1 m

⇒  

⇒  

Explanation:

Answer:

with the increase in mass of the object , the force of gravitation increases that eventually increases the potential energy if the object is still fixed in its relative position with surrounding objects.

Explanation:

hopes this will help you

Answer:

i think it's d

Explanation:

Answer:

D

Explanation:

i feel like this one is it

Explanation:

Given that,

Magnitude of vector A, |A| = 15

Magnitude of vector B, |B| = 25

We need to find the magnitude of this sum.

The maximum sum of the resultant vector,

[tex]R_{max}=|A_1|+|A_2|\\\\=15+25\\\\=45[/tex]

The minimum sum of the resultant vector,

[tex]R_{min}=|A_1|-|A_2|\\\\=15-25\\\\=-10[/tex]

So, the magnitude of this sum either 45 or -10.

Answer:

a

 [tex]\Delta P = 7558.6 \ Pa[/tex]

b

 [tex]h_1 = 10 \ m[/tex]

Explanation:

From the question we are told that

   The position of the column of mercury in the barometer is  [tex]h = 736 \ mm = 0.76 \ m[/tex]\

   The density of mercury is  [tex]\rho = 13,000 \ kg / m^3[/tex]

Generally the  pressure of the atmosphere at that column is mathematically represented as  

         [tex]P = \rho * g * h[/tex]

=>      [tex]P =13 000 * 9.8 * 0.736[/tex]

=>      [tex]P = 93766.4 \ Pa[/tex]

Generally the atmospheric pressure at sea level (Generally the pressure before the change in level of the mercury column)  is  [tex]P_a = 101325 \ Pa[/tex]

Generally the change in air pressure  is mathematically represented as

      [tex]\Delta P = P_a - P[/tex]

=>   [tex]\Delta P = 101325 - 93766.4[/tex]

=>   [tex]\Delta P = 7558.6 \ Pa[/tex]

Generally the height which the column will rise to is mathematically evaluated as  

         [tex]h_1 = \frac{P}{ \rho_w * g }[/tex]

Here [tex]\rho_w[/tex] is the density of water with value  [tex]\rho_w = 1000 \ kg/m^3[/tex]

So

       [tex]h_1 = \frac{ 93766.4}{ 1000 * 9.8 }[/tex]

=>   [tex]h_1 = 10 \ m[/tex]

Answer:d

Explanation: oil would form droplets but only tiny ones because it’s surface tension is lower than that of water

Both water and vegetable oil would made droplets but Oil would form  only very tiny droplets because its surface tension is lower than that of water.

Surface tension is the propensity for liquid surfaces that are at rest to condense into the smallest surface area. Razor blades and insects (like water striders), which have a higher density than water, can float on the surface of the water without even becoming partially buried because to surface tension.

Surface tension at liquid-air contacts originates from the liquid molecules' stronger attraction to one another due to cohesion than to the air molecules (due to adhesion).

As the surface tension of the oil is lower than that of water, it forms droplets will smaller size.

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Answer:

A

Explanation:

Weight = 55 * 9.8 = 539 N

Scale = 686 N

Since the scale reading is larger than the lady’s weight, the elevator must be accelerating as it moves upward.

Net upward force = 686 – 539 = 147 N

147 = 55 * a

a = 147 ÷ 55

The acceleration is approximately 2.67 m/s^2.

Answer:

Power_input = 85.71 [W]

Explanation:

To be able to solve this problem we must first find the work done. Work is defined as the product of force by distance.

[tex]W = F*d[/tex]

where:

W = work [J] (units of Joules)

F = force [N] (units of Newton)

d = distance [m]

We need to bear in mind that the force can be calculated by multiplying the mass by the gravity acceleration.

Now replacing:

[tex]W = (80*10)*3\\W = 2400 [J][/tex]

Power is defined as the work done over a certain time. In this way by means of the following formula, we can calculate the required power.

[tex]P=\frac{W}{t}[/tex]

where:

P = power [W] (units of watts)

W = work [J]

t = time = 40 [s]

[tex]P = 2400/40\\P = 60 [W][/tex]

The calculated power is the required power. Now as we have the efficiency of the machine, we can calculate the power that is introduced, to be able to do that work.

[tex]Effic=0.7\\Effic=P_{required}/P_{introduced}\\P_{introduced}=60/0.7\\P_{introduced}=85.71[W][/tex]

Answer:

Organisms 2 and 3

Explanation:

Answer:

this is a homework helping website I don't know If I can help you with this problwm

Answer:

0.78 m

Explanation:

I just did a hw question for this its just 344  divided by 440

Answer:

[tex]\boxed{\boxed{\sf all \ of \ the \ above }}[/tex]

Good conductors have: current moves easily,  low resistance,   conserves energy-easy for electrons to move. Hence, Option (C) is correct.

Materials that easily permit the flow of electricity are referred to be electrical conductors. Conductivity is the quality of conductors that enables them to conduct electricity.

Electric current is the name given to the movement of electrons through conductor. Voltage is the amount of power necessary to cause that current to flow through the conductor.

Such an element receives a charge that is dispersed along its entire surface, causing the electrons inside the element to migrate. Charges are transferred to an electrical conductor, and they disperse until the minimal force of repulsion between electrons in locations of excess electrons. Such an item transfers its charge to another conductor when it comes into contact with it, reducing the overall repulsion caused by charge in the process.

Learn more about conductor here:

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Answer:

When an object moves with a constant speed in a circular path, then its motion is called as Circular motion.

Examples of Uniform Circular Motion :--

The moon moves in uniform circular motion around the earth.

A stoned tied to a thread and rotated in circular motion.

An athlete running on a circular track.

A satellite revolving around Earth.

force between the two charges (+q1 and +q2),if they are at a distance 'a' is

F1=1/4pieEo q1q2/d^2................ (1)

when the metal spheres are in contact the charge flow from one sphere to another till both the sides acquires the same charge. here q1 and q2 are of same sign,hence after contact each sphere will have a charge

[tex] \binom{q1 + q2 }{2} [/tex]

now,the force between them,

f2=1/4pieEo

(q1+q2/2)^2/d^2

from eq (1)and eq (2)

f2=f1 (q1+q2)^2/4q1q2

Answer:

[tex]Relative\ Velocity = 105m/s[/tex]

Explanation:

Given

[tex]V_A = 45m/s[/tex]

[tex]V_B = 60m/s[/tex]

Required

Determine the speed of B w.r.t A

The question implies that, we determine the relative velocity of B w.r.t A

Because both trains are moving towards one another, the required velocity is a [tex]sum\ of\ velocities\ of[/tex] both trains:

This is shown below:

[tex]Relative\ Velocity = V_A + V_B[/tex]

[tex]Relative\ Velocity = 45m/s + 60m/s[/tex]

[tex]Relative\ Velocity = 105m/s[/tex]

Answer:

MA = 2.5

Explanation:

Given that,

Effort force applied to a screwdriver to pry the lid off of a can= 40 N

The screwdriver applies 100n of force to the lid = 100 N

We need to find the mechanical advantage of the screwdriver. Mechanical advantage of a machine is given by the ratio of load to the effort.

m = load/effort

= 100/40

= 2.5

Hence, the MA of the screwdriver is 2.5

Answer:

here u go

Explanation:

Earth's rotation is the rotation of planet Earth around its own axis. Earth rotates eastward, in prograde motion. As viewed from the north pole star Polaris, Earth turns counterclockwise.

Answer:

v = 16.87 m/s

Explanation:

Given that,

Distance, d = 1.25 miles

d = 2011.68 m

Time, t = 1 minute 59.2 seconds

= 60 s + 59.2 s

= 119.2  s

We need to find the average speed of the horse. It is given by total distance covered divided by total time.

[tex]v=\dfrac{2011.68 \ m}{119.2\ s}\\\\=16.87\ m/s[/tex]

So, his average speed is 16.87 m/s.

Answer:

200 joules

Explanation:

work=force×distance

Answer:

Explanation:

The density of a substance is the ratio of its mass to its volume. Its unit of measurement is kg[tex]m^{-3}[/tex].

i.e density, ρ = [tex]\frac{mass}{volume}[/tex]

1a. To determine the density of the acetic acid, Rachael needs to know the mass and volume of the acid.

i. Measure the mass of the given beaker using the mass balance.

ii. Transfer the acetic acid into the beaker, and measure the new mass using the mass balance.

iii. Subtract the mass of the beaker from the new mass to determine the mass of the acetic acid.

iv. Measure the volume of the acid on the scale of the beaker.

v. Divide the value of the mass by its volume to determine its density of the acetic acid.

b. Given that the density is 1.05 g/[tex]cm^{3}[/tex], and volume is 200 [tex]cm^{3}[/tex].

Then,

density = [tex]\frac{mass}{volume}[/tex]

1.05 = [tex]\frac{mass}{200}[/tex]

mass = 1.05 x 200

         = 210 g

mass = 210 g

2. Length of titanium = 0.40 m

   Area of titanium = 0.05 [tex]m^{2}[/tex]

mass = 90.0 kg

density = [tex]\frac{mass}{volume}[/tex]

But,

volume = area x length

            = 0.05 x 0.4

           = 0.02 [tex]m^{3}[/tex]

density of titanium = [tex]\frac{90}{0.02}[/tex]

                = 4500 kg[tex]m^{-3}[/tex]

Answer:

here are the options.

Answer:

the energy that is associated with temperature or D

Explanation:

Hope this helps

Answer:

The force will be "[tex]9.8\times 10^{-3} \ N[/tex]".

Explanation:

The given values are:

Mass,

m = 1 gram

Angle,

Ф = 20°

As we know,

⇒ [tex]F=mg[/tex]

On substituting the given values in the above expression, we get

⇒     [tex]=(1.0\times 10^{-3})(9.8)[/tex]

⇒     [tex]=9.8\times 10^{-3} \ N[/tex]

because of gravitional pull

Answer:

it implies our universe is expanding

The magnetic field between the magnets causes the charged particles within the wire to move.

According Faraday's law of electromagnetic induction, whenever their is a relative motion of a conductor is magnetic field, an emf will be induced in the conductor and the strength of the induced emf is directly proportional to the rate of change of magnetic flux linking the circuit.

The motion of the electrons is due to magnetic field created by the permanent magnet of the electric generator.

Thus, the magnetic field between the magnets causes the charged particles within the wire to move.

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