Answer:
The fundamental frequency is 10 Hz
Explanation:
The frequency of the fundamental mode of the string is given by;
[tex]f_o =\frac{1}{2l}\sqrt{\frac{T}{\mu }[/tex]
where;
L is length of the string = 2.5 m
T is tension of the string, = 10 N
μ is mass per unit length = m / L = 0.01 / 2.5 = 0.004 kg/m
Substitute the given values and solve for the frequency;
[tex]f_o =\frac{1}{2l}\sqrt{\frac{T}{\mu }}\\\\ f_o =\frac{1}{2*2.5}\sqrt{\frac{10}{0.004}}\\\\ f_o = 0.2\sqrt{2500}\\\\ f_o = 0.2 *50\\\\f_o = 10 \ Hz[/tex]
Therefore, the fundamental frequency is 10 Hz
What is the mass of a cylinder of silicon (in units of grams) that is 4.00 cm in diameter and 10.55 cm long?
Answer:
309.02g
Explanation:
According to the information given in this question, the cylinder has the following:
Mass = ?
Length/height = 10.55cm
Diameter = 4.00cm
Volume of a cylinder = πr²h
Where; π = pie (3.142 or 22/7)
r = radius (cm)
h = height
Note that, radius = diameter/2
Hence, radius (r) = 4.00/2
r = 2.00cm.
V = πr²h
V = 22/7 × 2² × 10.55
V = 22/7 × 42.2
V = 928.4/7
V = 132.628cm³
Density = mass/volume
Hence, mass = density × volume
Where density of silicon is 2.33g/cm³
Mass = 2.33g/cm³ × 132.628cm³
Mass = 309.02g
If the stars at the turnoff point in a star cluster have masses of about four solar masses, how old is the cluster
Answer:
age of the cluster is 3.125 × 10⁸ years
Explanation:
Given that;
stars at the turnoff point in a star cluster have masses of about 4 solar masses
Age of the cluster?
we know that the main sequence lifetime of a star in solar lifetime(t) is related to the mass of the star in solar masses(M). expressed as
ζ = M^(-5/2)
our M is 4, so we substitute
ζ = 4^(-5/2)
ζ = 0.03125 solar lifetime
now convert the lifetime of star cluster into years
ζ = 0.03125 solar lifetime × (10¹⁰ years / 1 solar lifetime)
ζ = 312,500,000 ≈3.124 × 10⁸ years
therefore age of the cluster is 3.125 × 10⁸ years
What is the drift speed of the electrons when there is a voltage drop of 118.8 V across the wire? Assume there is one conduction electron per atom.
Answer:
Explanation:
If e be the charge on the electron and v be its drift speed after undergoing voltage drop of 118.8 V
eV = 1/2 m v²
1.6 x 10⁻¹⁹ x 118.8 = 1/2 x 9.1 x 10⁻³¹ v²
v² = 41.775 x 10¹²
v = 6.46 x 10⁶ m /s
drift speed of electron = 6.46 x 10⁶ m /s
Determine the average velocity of the cart during the time interval from frame 100100 to frame 124124. For all vector quantities, we’ll use the convention that right is positive and left is negative.
The video showing the movement of the cart during the time interval is gotten from the link;
https://mediaplayer.pearsoncmg.com/assets/_frames.true/frames.true_white_ruler
Answer:
V_avg = 1.8 m/s
Explanation:
From the video, the distance moved by the cart during the 24 frames is 18 cm or 0.18 m.
Now, the speed is at the rate of 240 frames per seconds.
Now, average velocity is given as;
V_avg = distance/time
Time = 24 frames/240 frames/s
Time = 0.1 s
Thus;
V_avg = 0.18/0.1
V_avg = 1.8 m/s
A toy cork gun contains a spring whose spring constant is 10.0 N/m. The spring is compressed 5.00 cm and then used to propel a 6.00-g cork. The cork, however, sticks to the spring for 1.00 cm beyond its unstretched length before separation occurs. The muzzle velocity of this cork is:
Answer:
2 m/s
Explanation:
We will apply the law of conservation of energy to solve this.
The initial spring potential energy = final spring potential energy + kinetic energy of cork, this means that
1/2kx² = 1/2kx'² + 1/2mv², and this is
kx² = kx'² + mv²
From the question, we are given that
k = 10N/m
x = 5cm = 0.05 m
x' = 1cm = 0.01 m
m = 6g = 0.006 kg
Substituting these values to the formula, and we get,
10(0.05)² = 10(0.01)² + 0.006v²
10 * 0.0025 = 10 * 0.0001 + 0.006 v²
0.025 = 0.001 + 0.006v², multiplying all sides by 1000, we have
25 = 1 + 6v²
6v² = 25 - 1
6v² = 24
v² = 24 / 6
v² = 4
v = √4
v = 2 m/s
⇒25 - 1 = 6v²
⇒v² = 24/6 = 4
⇒v = 2 m/s
as seen from above, a 73.8 kg water skier is pulled by a 105 N force at a 22.5 angle, while the water creates a 74.8 N force pulling directly backward. What is the y-component of the total force on the skier?
Answer:
40.2 N
Explanation:
I'm an Acellus student who got it correct.
The magnitude of y-component of the total force on the skier is 40.18 N.
What is force?Force is an influence which tends to set a stationary body in motion or stop a moving body, or which tends to change the speed and direction of a moving body, or which tends to change the shape and size of body.
Given parameters:
Mass of the water: M = 73.8 kg.
Magnitude of force acting at 22.5° angle is: F₁ = 105 N.
Magnitude of force acting at directly backwards is: F₂ = 74.8 N.
We have to find: the y-component of the total force on the skier = ?
As F₂ acting directly backwards, this force has no y-component.
Hence, resultant y-component of the total force on the skier
= F₁ sin22.5°
= 105 ×sin22.5° N.
= 40.18 N.
Hence, magnitude of y-component of the total force on the skier is 40.18 N.
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A charged particle is injected at 109 m/s into a 0.0691‑T uniform magnetic field perpendicularly to the field. The diameter of its orbit is measured and found to be 0.0427 m. What is the charge–to–mass ratio of this particle?
We know, radius of the orbit is given by :
[tex]r=\dfrac{mv}{qB}[/tex]
So, ratio is given by :
[tex]\dfrac{q}{m}=\dfrac{v}{Br}\\\\\dfrac{q}{m}=\dfrac{109\ m/s}{0.0691 \ T \times 0.0427\ m}\\\\\dfrac{q}{m}=36942.01 \ C/kg\\\\\dfrac{q}{m}=3.69\times 10^{4}\ C/kg[/tex]
Therefore, the charge–to–mass ratio of this particle is [tex]3.69\times 10^{4}\ C/kg[/tex] .
Hence, this is the required solution.
A car comes to a stop in 3 s from the moment the driver applies the brakes. If the initial angular velocity of the tires was 57 rad/s, what is their angular acceleration (assumed constant) over this time interval
Answer:
-19rad/s
Explanation:
Given
Initial angular velocity w0 = 57rad/s
Time = 3s
Final angular velocity wf = 0rad/s (car comes to stop)
Required
angular acceleration (α)
Using the equation of motion
wf = w0 + αt
Substitute the given value and get α;
0 = 57 + 3α
-57 = 3α
α = -57/3
α = -19rad/s (the negative sign shows that the car decelerated over time)
"We want to know how microgravity will
affect ____
Answer:
humans
Explanation:
mhm
A person weighing 200 pounds stands on snowshoes. If the area of each snowshoe is 400 square inches, the pressure on the snow is
Answer:
0.5 pounds per square inches (ibs/in²)
Explanation:
The pressure of an object refers to the force it exerts per unit area i.e. F/a. In this question, the force, F, is created by the weight, W, of the snowshoe. Hence, pressure is calculated thus:
P = W/A
Where; P = Pressure (ibs/in²)
W = Weight of object (ibs)
A = surface area (in²)
In this question, weight = 200 pounds, Area = 400 square inches
Hence, pressure = 200/400
Pressure (P) = 2/4
Pressure (P) = 0.5 ibs/in²
. Explain what a flyback diode is and why such a device is often placed in parallel with the coil in a relay circuit
Answer:
Explained below.
Explanation:
A flyback diode is simply defined as a diode that is connected across an inductor in order to eliminate the sudden spike in voltage that's seen across an inductive load when its supply current is unexpectedly reduced or interrupted. This sudden spike in voltage is known as flyback.
It's very important to place this flyback diode in parallel with the coil in a relay circuit because it allows current to pass through with minimal resistance thereby preventing flyback voltage from building up when power is disconnected.
A uniform plank 8.00 m in length with mass 30.0 kg is supported at two points located 1.00 m and 5.00 m, respectively, from the left-hand end. What is the maximum additional mass you could place on the right-hand end of the plank and have the plank still be at rest
Answer:
30 kg
Explanation:
Given that a uniform plank 8.00 m in length with mass 30.0 kg is supported at two points located 1.00 m and 5.00 m, respectively, from the left-hand end. What is the maximum additional mass you could place on the right-hand end of the plank and have the plank still be at rest ?
Taking the moment at the middle
Sum of Clockwise moment = sum of anticlockwise moments
Sum of clockwise moment will be:
30 × ( 4 - 1 ) = 30 × 3 = 90Nm
At equilibrium, the sum of anticlockwise moments will be equal to sum of clockwise moment.
90 = 30 × ( 5 - 4 ) + M
90 = 30 × 1 + M
90 = 30 + M
M = 90 - 30
M = 60
Moment = W × distance
Let the minimum distance = 2
60 = 4W
W = 60/2
W = 30 kg
Therefore, the maximum mass will be 30kg
A car accelerates in the +x direction from rest with a constant acceleration of a1 = 1.89 m/s^2 for t1 = 20 s. At that point the driver notices a tree limb that has fallen on the road and brakes hard for t2 s until it comes to a stop. Required:a. Write an expression for the car's speed just before the driver begins braking, v1.b. If the limb is on the road at a distance of 550 meters from where the car began its initial acceleration, will the car hit the limb?c. How far, in meters, from the original location of the limb will the car be when it stops?
Answer:
A.) 37.8 m/s
B.) No
C.) 172 m
Explanation:
Given that car accelerates in the +x direction from rest with a constant acceleration of a1 = 1.89 m/s^2 for t1 = 20 s. At that point the driver notices a tree limb that has fallen on the road and brakes hard for t2 s until it comes to a stop. Required:
a.) Write an expression for the car's speed just before the driver begins braking, v1.
Since the car accelerate from rest, initial velocity U = 0
Using first equation of motion
V1 = U + at
V1 = 1.89 × 20
V1 = 37.8 m/s
b.) If the limb is on the road at a distance of 550 meters from where the car began its initial acceleration, will the car hit the limb?
Using third equation of motion
V^2 = U^2 + 2as
37.8^2 = 0 + 2 × 1.89 × S
1428.84 = 3.78S
S = 1428.84 / 3.78
S = 378m
Since the limb is on the road at a distance of 550 meters from where the car began its initial acceleration, we can therefore conclude that the car will not hit the limb.
c. How far, in meters, from the original location of the limb will the car be when it stops?
550 - 378 = 172 m
The car will be 172 metres from the limb.
A cyclist who is riding a bike, whose wheels have a radius of r, is moving with constant speed v, along a flat straight road. The cyclist realizes that there is a single rock stuck between the threads of his tires that is causing the bike to vibrate violently. How frequently do the vibrations caused by the rock occur
Answer:
[tex]f = \frac{v}{2\pi r }[/tex]
Explanation:
A cyclist riding a bike whose wheels have a radius of r, moving with constant speed v along a flat straight road.
The frequency of the vibrations is the same as the frequency of the rotation of the wheel and this can be represented as below
V = R(w ) where ; w = [tex]2\pi f[/tex]
[tex]f = \frac{v}{2\pi r }[/tex]
Calculate the energy stored in a spiral spring
of force constant is 800 N/m compressed by
1.2 m
Answer:
W=k[tex]x^{2}[/tex]/2 = 576 j
Explanation:
An 8.5 kg bowling ball initially at rest is dropped from the top of a building. The ball hits the ground with an acceleration of 9.8 m/s2. Find the net force on the falling ball.
Answer:
The answer is 83.3 NExplanation:
The force acting on an object given it's mass and acceleration can be found by using the formula
force = mass × accelerationFrom the question we have
force = 8.5 × 9.8
We have the final answer as
83.3 NHope this helps you
An object with a mass of 10 kg accelerates 16 m/s2 when an unknown force is applied to it what is the amount of force
Answer:
[tex] \huge{ \boxed {\bold{ \tt{160 \: N}}}}[/tex]
Explanation:
Given :Mass ( m ) = 10 kgAcceleration ( a ) = 16 m / s²To find :Force = ?We know,[tex] \boxed{ \sf{Force = Mass \: \times \: Acceleration}}[/tex]
[tex] \sf{➛ force \: = 10\: \times 16}[/tex]
[tex] \sf{➛ force = 160 \: Newton}[/tex]
The amount of force is 160 N
Hope I helped!
Best regards! :D
~TheAnimeGirl
5. A basketball is passed 15 m due West, then 20 m north. What is the total distance the
basketball travelled?
Answer:
35 meters
20+15=35
draw a roller coaster track that starts with one large hill, then is followed
by a valley and another, smaller hill.
Draw a cart in four positions on the track as outlined below.
i. Draw the first cart at the top of the first hill. Label it A.
ii. Draw the second cart going down the first hill into the valley. Label it B.
iii. Draw the third cart at the bottom of the valley. Assume that the height of the cart in
this position is zero. Label it C.
iv. Draw the last cart at the top of the second, smaller hill. Label it D.
okay, this is the part that I don't know lol. ill give you brianlist or whatever its called:
Type one to two paragraphs describing the changes in potential and kinetic energy of the cart.
Be sure to discuss how the potential and kinetic energy of the cart changes at each of the four
positions along the track, and explain why these changes occur.
Answer:
The cart starts out in position A with high potential energy, low kinetic energy, and some thermal energy. As the cart progresses into position B, the kinetic energy begins to increase and the potential energy begins to decrease; as the thermal energy increases as thermal energy from the track is transferred to the cart through friction. Once the cart reaches position C, it has high kinetic energy, low potential energy, and some thermal energy. At position D, the cart has high potential energy, low kinetic energy, and some thermal energy. The potential energy throughout is correlated to gravity, the kinetic energy is correlated to momentum, and the thermal energy is correlated to friction. The potential energy is at its maximum during position A, and its minimum at position C; the kinetic energy is at its maximum during position C, and its minimum at position A; the thermal energy is at its maximum during position B, and its minimum at position A.
Explanation:
At the top of the hill the cart has maximum potential energy and zero kinetic energy. At the valley the cart has maximum kinetic energy and zero potential energy.
According to the principle of conservation of mechanical energy when an object changes position, the mechanical of the object is always conserved.
An object has maximum potential energy at maximum height.When the object is at lowest point, it has maximum kinetic energy.The sum of kinetic energy and potential energy of the object at any point is the total mechanical energy.
M.A = P.E + K.E
At the top of the hill the cart has maximum potential energy and zero kinetic energy. At the valley the cart has maximum kinetic energy and zero potential energy.
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How many different uniquecurrents will there be in this circuit? How many different "branch" are there in this circuit where the currents could differ.
Answer:
hello your question is incomplete attached below is the missing circuit diagram
answer : 3 unique currents
Explanation:
From the circuit attached below it can be seen that there will be Three(3) unique currents flowing through this circuit and the Branches where this currents could differ is at the Three(3) resistors
In part A, the metal object was heated in water. If some of the hot water was transferred to the calorimeter along with the metal object, what effect would this have on the calculated value of the specific heat of the metal
Answer:
The calculated value of the specific heat capacity of the metal will be larger than the actual value
Explanation:
If some of the hot water is transferred to the Calorimeter along with the metal object whose specific heat is to calculated the effect will be that the calculated value of the specific heat of the metal will be larger than normal
this can be explained with the equation below
= heat transferred to liquid in which metal was / Δ T metal
where ΔTmetal < heat transferred to liquid
If the current density is 1.55 and the drift velocity is , how many charge carriers are present? The charge on electron is .(Enter your answer to three significant figures.)
Answer:
There are [tex]9.053\times 10^{14}[/tex] charge carriers.
Explanation:
Given that,
Current density (current per unit time), [tex]\dfrac{I}{A}=1.55\ A/cm^2=0.000155\ A/m^2[/tex]
The drift velocity of the electron, [tex]v_d=107\ cm/s=1.07\ m/s[/tex]
We need to find the no charge carriers present. The formula for drift velocity is given by :
[tex]v_d=\dfrac{I}{neA}\\\\\text{n is no of charge carriers}\\\\n=\dfrac{I}{eAv_d}\\\\n=\dfrac{0.000155}{1.6\times 10^{-19}\times 1.07}\\\\n=9.053\times 10^{14}[/tex]
So, there are [tex]9.053\times 10^{14}[/tex] charge carriers.
1. Two loads are connected in parallel to a 120 V source. If the 40 W lamp is left on for 3 hr/day and the 75 W lamp is left on for 5 hr/day calculate the current in each loa
Answer:
Explanation:
Since both loads at connected in parallel, the voltage across them will be the same.
The voltage across parallel connected loads are the same.
Let the loads be R1 and R2
Power = IV
I is the current
V is the voltage
P= V²/R
R = V²/P
Get the first load R1
R1 = V²/P1
R1 = 120²/40
R1 = 360ohms
Get the second load R2
R2 = V²/P2
R2 = 120²/75
R2 = 192ohms
Current in R1 will be;
P1 = I1²R1
I1² = P/R1
I1² = 40/360
I1² = 1/9
I1 = √1/9
I1 = 1/3
I = 0.33A
Current in R2(second load) will be;
P2 = I2²R2
I2² = P/R2
I2² = 75/192
I2² = 0.390625
I2 = √0.390625
I2 = 0.625A
What is the instrument used to measure amount of substance?
Answer:
Moles
Explanation:
Moles can be used to measure the quantity of any substance. A mole of water is a small mouthful; a mole of elephants is about the size of the planet Saturn.
A Category 1 hurricane with a radius of 70km has sustained tangential winds of about 33 m/s. What is the acceleration of a particle on th edge
of the hurricane.
Answer:
[tex]a_c=0.016 \ m/s^2[/tex]
Explanation:
Centripetal acceleration: Is the acceleration experienced by an object while in a uniform circular motion. It points toward the center of rotation and is perpendicular to the linear velocity v and has the magnitude:
[tex]\displaystyle a_c=\frac{v^2}{r}[/tex]
Where v is the linear velocity and r is the radius of the circle.
It's given a hurricane with a radius r=70 Km = 70,000 m has a tangential wind velocity of v=33 m/s. The acceleration of a particle lying on the edge of the hurricane is:
[tex]\displaystyle a_c=\frac{33^2}{70,000}[/tex]
[tex]\boxed{a_c=0.016 \ m/s^2}[/tex]
In the Daytona 500 auto race, a Ford Thunderbird and a Mercedes Benz are moving side by side down a straightaway at
67.0 m/s. The driver of the Thunderbird realizes that she must make a pit stop, and she smoothly slows to a stop over a
distance of 250 m. She spends 5.00 s in the pit and then accelerates out, reaching her previous speed of 67.0 m/s after a
distance of 360 m. At this point how far has the Thunderbird fallen behind the Mercedes Benz, which has continued at a
constant speed?
Answer:
945 m
Explanation:
First of all let's find the first acceleration before the first stop. We will use Newton's 3rd equation of motion;
v² = u² + 2as
a = (v² - u²)/2s
In this first motion, the initial velocity is given as u = 67 m/s, while the final velocity which is the stop is v = 0 m/s and the distance is s = 250 m
Thus;
a = (0² - 67²)/(2 × 250)
a = -4489/500
a = -8.978 m/s²
Now, to get the time spent for this 250 m distance, we will use Newton's 2nd law of motion;
s = ut + ½at²
Plugging in the relevant values;
250 = 67t + ½(-8.978)t²
250 = 67t - 4.489t²
4.489t² - 67t + 250 = 0
Using quadratic formula, we will arrive at;
t = 7.463 s
Now, we are told that she accelerates out, reaching her previous speed of 67.0 m/s after a distance of 360 m. Thus, let's calculate the time it took to accelerate after a distance of 360 m.
Since she stayed from rest in this phase, then initial velocity (u) = 0 m/s.
Like in the first phase, we can find the acceleration from;
a = (v² - u²)/2s
a = (67² - 0²)/(2 × 360)
a = 4489/720
a = 6.235 m/s²
Thus, we can find the time for this 360 m phase by using; s = ut + ½at², we have;
360 = 0 + ½(6.235)t²
Multiply through by 2 to get;
6.235t² = 720
t² = 720/6.235
t² = 115.477145
t = √115.477145
t = 10.746 s
We are told that she spends 5 s in the pit. Thus;
Total time is;
t_total = 7.463 + 5 + 10.746
t_total = 23.209 s
Distance covered by the Mercedes Benz = 67 × 23.209 = 1555 m
Total distance covered by Thunderbird = 250 + 360 = 610 m
Thus, distance of Thunderbird behind Mercedes Benz is = 1555 - 610 = 945 m
Select the choice that does NOT describe an acceleration .
А pedaling faster
B coasting
C turning a corner
D hitting the brakes
Answer:
Answer
b) Coasting does not dedcribe acceleration
If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges
Complete question is;
A 13g bullet traveling 230 m/s penetrates a 2.0 kg block of wood and emerges going 170 m/s. If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?
Answer:
0.39 m/s
Explanation:
From the question, we can deduce that there is no external force acting on the
system in the horizontal direction. This means that momentum will be conserved for the system of the 2 kg block & the bullet.
Thus;
Initial momentum(p_i) = final momentum(p_f)
Mass of bullet; = 13g = 0.013 kg
Mass of Block = 2 kg
Speed of bullet = 230 m/s
Speed of Block = 170 m/s
We know that formula for momentum is; p = mv.
Thus, the initial momentum of the (bullet + block) is given as;
p_i = 0.013 × 230
Final momentum is;
p_f = (0.013 × 170) + (2 × v_f)
Where v_f is the speed at which the bullet emerges.
Since p_i = p_f from conservation of momentum, then;
(0.013 × 230) = (0.013 × 170) + (2 × v_f)
2.99 = 2.21 + 2v_f
2.99 - 2.21 = 2v_f
0.78 = 2v_f
v_f = 0.78/2
v_f = 0.39 m/s
A car accelerates from rest to 95 km/h in 5 seconds, what is the average acceleration of the car in m/s2
Answer:
The average acceleration of the car is 5.2778 [tex]\frac{m}{s^{2} }[/tex]
Explanation:
The acceleration of an object is a magnitude that indicates how the speed of the object changes in a unit of time. That is, acceleration relates changes in velocity with the time in which they occur.
The expression for the calculation of the acceleration is:
[tex]acceleration=\frac{change of velocity}{time}[/tex]
In this case:
acceleration=?change of velocity= final velocity - initial velocity= 95 km/h - 0 km/h (because the car accelerates from rest)= 95 km/htime= 5 secondsFirst, it is convenient to express the change in velocity in units of m/s, where 1 h = 3,600 s and 1 km = 1,000 m.
[tex]change of velocity= 95 \frac{km}{h} =95\frac{1,000 m}{3,600 s} =26.3889 \frac{m}{s}[/tex]
So, replacing in the definition of acceleration:
[tex]acceleration=\frac{26.3889\frac{m}{s} }{5 s}[/tex]
acceleration= 5.2778 [tex]\frac{m}{s^{2} }[/tex]
The average acceleration of the car is 5.2778 [tex]\frac{m}{s^{2} }[/tex]
What do feathers, fur, overcoats, and whale blubber all have in common?
A. They are all good conductors of heat.
B. They all generate heat.
C. They are all electrical conductors.
D. They are all heat insulators.
Answer:
D. They are all heat insulators.
Explanation:
Those things mentioned above are examples of heat insulators. As a heat insulator, it helps to prevent the heat from leaving the body thereby keeping the body warm and risk free.Feathers in birds and overcoat in humans helps to keep the bodies of the wearer safe and warm during the cold season.