Answer:
x = 0.667 cos 10.69 t + 0.383)
Explanation:
This is a simple harmonic movement exercise, the general solution is
x = A cos (wt + Ф)
w² = k / m
In this exercise, the initial displacement is that it corresponds to the amplitude of the movement.
A = 8 in. (1 ft. 12 in.) = ⅔ ft. = 0.6667 ft.
x = 1.5 in = 0.125 ft
We look for the constant k with Hooke's law
F = -kx
the force applied is the weight of the body F = W = mg
-mg = - k x
k = m g / x
we substitute
k = m 32.16 / 0.125
k = 257.28 m
we substitute
w = √257.28
w = 16.04 rad / s
we substitute in the expression of the position
x = 0.667 cos (16.04 t + Ф)
to find the constant fi we look for the velocity
v = dx / dt
v = - 0.667 16.04 sin (16.04 t +Ф)
indicate the values of v = 4 ft / s for t = 0
- 4 = -10.6934 sin Ф
remember angles are in radians
Ф = sin⁻¹ (4/106934)
Ф = 0.383
we substitute
x = 0.667 cos 10.69 t + 0.383)
During a circus act, an elderly performer thrills the crowd by catching a cannon ball shot at him. The cannon ball has a mass of 72.0 kg and its horizontal component of velocity is 6.50 m/s just before the 65.0 kg performer catches it. If the performer is initially motionless on nearly frictionless roller skates, what is his speed immediately after catching the cannon ball
Answer:
3.416 m/s
Explanation:
Given that:
mass of cannonball [tex]m_A[/tex] = 72.0 kg
mass of performer [tex]m_B[/tex] = 65.0 kg
The horizontal component of the ball initially [tex]\mu_{xA}[/tex] = 6.50 m/s
the final velocity of the combined system v = ????
By applying the linear momentum of conservation:
[tex]m_A \mu_{xA}+m_B \mu_{xB} = (m_A+m_B) v[/tex]
[tex]72.0 \ kg \times 6.50 \ m/s+65.0 \ kg \times 0 = (72.0 \ kg+65.0 \ kg) v[/tex]
[tex]468 kg m/s + 0 = (137 kg)v[/tex]
[tex]v = \dfrac{468\ kg m/s }{137 \ kg}[/tex]
v = 3.416 m/s
Constants Periodic Table Part A Carla holds a ball 1.5 m above the ground. Daniel, leaning out of a car window, also holds a ball 1.5 mm above the ground. Daniel drives past Carla at 40 mph and, just as he passes her, both release their balls at the same instant.
Whose ball hits the ground first?
The balls will hit the ground simultaneously.
Daniel's.
Carla's The answer can't be determined from the data provided
Answer:
correct answer is c
The balls will hit the ground simultaneously
Explanation:
This is an exercise in kinematics, let's analyze each case separately
Carla. Holds the ball at an initial height y = 1,5m and releases the ball therefore its initial velocity is zero v₀ = 0
y = y₀ + v₀ t - ½ gt²
0 = y₀ + 0 - ½ g t²
t = [tex]\sqrt{\frac{2y_o}{g} }[/tex]
Daniel This holds the ball at I = 1.5 m and releases the ball as it passes by Carla, therefore the initial velocity is
horizontal vox = 40 mph
vertical v_{oy} = 0
y = y_{oy}I + v_{oy} t - ½ g t²
0 = y_{oy} + 0 - ½ g t²
t = [tex]\sqrt{\frac{2 y_o}{g} }[/tex]
we can see that they both spend the same time reaching the ground
t = [tex]\sqrt{2 \ 1.5 / 9.8}[/tex]
t = 0.55 s
The correct answer is c
The balls will hit the ground simultaneously
what is parallelogram law of vector addition ???
Answer:
According to the parallelogram law of vector addition if two vectors act along two adjacent sides of a parallelogram(having magnitude equal to the length of the sides) both pointing away from the common vertex, then the resultant is represented by the diagonal of the parallelogram passing through the same common vertex
Explanation:
amount of pressure of liquid increases with ?
Answer: Pressure increases as the depth increases.
Answer:
depths cause it help it with a lot and that it the answer
A bullet has a mass of 0.0042kg. The muzzle velocity of the bullet coming
out of the barrel of the rifle is 993m/s. What is the KE of the bullet as it
exits the gun barrel?
Answer:
KE= 1/2mv^2= 1/2*0.0042kg*993m/s= 2.0853joule
Which of the following statements best describes energy conservation in heat engines?
A. The heat engine's energy is exhausted to the outside system.
B. The sum of the heat placed into the hot reservoir and the work collected equals the energy transferred from the cold reservoir.
C. A volume of heat is discharged to the cold body where some waste energy is in a form of heat in this engine.
D. The work derived from the heat engine is equal to the energy placed into the hot reservoir.
Phosphorus (P) is an element with an atomic number of 15 and an atomic mass of 31. How many neutrons are in an atom of phosphorus? A.15 B.16 C.31 D.46
(31-15 = 16).
Explanation:
the element phosphorus (P) has an atomic number of 15 and a mass number of 31. Therefore, an atom of phosphorus has 15 protons, 15 electrons, and 16 neutrons
Phosphorus (P) is an element with an atomic number of 15 and an atomic mass of 31, there are 16 neutrons in an atom of phosphorus, therefore the correct answer is option B
What is the atomic number?The total number of protons present in an atom is known as the atomic number of that atom. The atomic number has no correlation either with the number of neutrons or the number of electrons present inside an atom.
As given in the problem Phosphorus (P) is an element with an atomic number of 15 and an atomic mass of 31
Total number of proton in phosphorus = 15
Total number of neutrons in the phosphorus = atomic mass - atomic number
Total number of neutrons in the phosphorus =31 -15
Total number of neutrons in the phosphorus = 16
Thus, the total number of neutrons in a phosphorus atom would be 16, therefore the correct answer is option B
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Một dây dẫn mảnh được uốn thành một
cung tròn bán kính 10cm, góc ở tâm
bằng 1200
, đặt trong không khí. Trong
dây dẫn có dòng điện cường độ 30A
chạy qua. Độ lớn của cảm ứng từ tại
tâm của cung tròn là bao nhiêu ?
a net force of 5N is applied to a 13kg mass. what is its acceleration?
Answer:
[tex]\boxed {\boxed {\sf a \approx 0.4 \ m/s^2}}[/tex]
Explanation:
According to Newton's Second Law of Motion, force is the product of mass and acceleration.
[tex]F= m \times a[/tex]
The net force is 5 Newtons and the mass is 13 kilograms. Let's convert the units for force to make the problem and unit cancellation easier.
1 Newton (N) is equal to 1 kilogram meter per square second (1 kg*m/s²) The net force of 5 N is equal to 5 kg*m/s²Now we know the values for 2 variables:
F= 5 kg*m/s²m= 13 kgSubstitute the values into the formula.
[tex]5 \ kg *m/s^2 = 13 \ kg * a[/tex]
Since we are solving for the accleration we must isolate the variable, a. It is being multiplied by 13 kilograms and the inverse of multiplication is division. Divide both sides by 13 kg
[tex]\frac {5 \ kg *m/s^2}{13 \ kg}= \frac{ 13 \ kg *a}{13 \ kg}[/tex]
[tex]\frac {5 \ kg *m/s^2}{13 \ kg}=a[/tex]
The units of kilograms (kg) cancel.
[tex]\frac {5 m/s^2}{13 }=a[/tex]
[tex]0.384615385\ m/s^2=a[/tex]
The original measurements of force and mass ( 5 and 13) have 1 and 2 significant figures. We must round our answer to the least number of sig figs: 1.
For the number we found, that is the tenths place. The 8 in the hundredth place (0.384615385) tells us to round the 3 up to a 4.
[tex]0.4 \ m/s^2 \approx a[/tex]
The acceleration is approximately 0.4 meters per square second.
Consider two identical stars, A and B. Star B is 10 times farther away than star A. What is the difference in magnitudes between the two stars?
You can't tell. It depends on other things besides just their distance.
IF the stars are really really "identical", then the magnitude of Star-B is the number that is 6 more than the magnitude of Star-A.
What is the rate at which distance changes called
Answer:
a yard
Explanation:
A violinist is tuning her violin to 440Hz. She plays the note while listening to an electronically generated tone and hears 3Hz, which increases to 4Hz when she tightens the violin. What was the frequency of the note played by the violin when she heard the 3 Hz beats
Answer:
[tex]X=438Hz[/tex]
Explanation:
From the question we are told that:
Beat Frequency [tex]Fb=440Hz[/tex]
Actual Frequency [tex]F_a=3Hz[/tex]
Generally the equation for Frequency Heard X is mathematically given by
[tex]X=beat\ frequency\ +\ actual\ frequency[/tex]
[tex]X=F_a+Fb[/tex]
[tex]X= 440Hz+3Hz[/tex]
[tex]X=438Hz[/tex]
Plz help!! WILL MARK BRAINLIEST :)
Which forces are easier to anticipate and
design for, internal or external? Why do
you think this is so?
Answer:
The external forces such as wind, water and the vibration of the earth when an earthquake happens create internal forces within a structure. Internal forces such as shear, tension and compression can destroy the inner framework of a building or a bridge even though it is made of super strong steel and concrete.
I Hope This Will Help You ...
A stretched rubber band is an example of which type potential energy
Answer: elastic potential energy
Explanation:
Answer:
Elastic potential energyExplanation:
A stretched rubber band has the potential to do work or change things. This form of energy is called elastic potential energy.
❣️✧Jess bregoli ✧❣️#keep learning!!A package of mass m is released from rest at a warehouse loading dock and slides down a 3.0-m-high frictionless chute to a waiting truck. Unfortunately, the truck driver went on a break without having removed the previous package, of mass 2m, from the bottom of the chute. Suppose the packages stick together. What is their common speed after the collision
Answer:
The speed of combined package after the collision is [tex]\frac{\sqrt(2gh)}{4}\\[/tex].
Explanation:
mass of first package = m
height , h = 3 m
mass of second package = 3 m
let the speed of first package is u as it strikes with the second package.
Use the third equation of motion
[tex]v^2 = u^2 + 2 gh \\\\u^2 = 0 + 2 g h \\\\u = \sqrt {2gh}[/tex]
Let the velocity of combined package after the collision is v.
Use the conservation of momentum
[tex]m\times u + 3m \times 0= (m + 3m)\times v\\\\m u = 4mv \\\\v=\frac {u}{4}\\\\v = \frac{\sqrt(2gh)}{4}\\\\[/tex]
Explain the phenomenon and change in potential energy
Answer:
Explanation:
The change in potential is then defined as the negative of the work done by that force. ... You can't have work done by gravity AND a change in gravitational potential energy. You have to do it one way or the other. This means that the most important step in solving work-energy problems is choosing a system.
the phenomenon is An object that has potential energy can transfer that energy into kinetic energy when the object begins to move, due to its mass or position. For example, a person jumping on a trampoline has potential energy when they reach the peak of a jump, and their force changes direction from upward to downward.
pair of two hollow cups is term as
Answer:
Magdeburg hemispheres are a pair of large copper hemispheres, with mating rims.
Explanation:
They were used to demonstrate the power of atmospheric pressure. When the rims were sealed with grease and the air was pumped out, the sphere contained a vacuum and could not be pulled apart by teams of horses.
It is important to use the correct drying tempture because it prevents shrinkage and will not damage the garment.
True or False
Answer:
fjowe
Explanation:
kbegtrf3g4ef j3kq4ef 3w4beysrf2w4er8f6ywgbaebf7v2wy4egdwa4i6e5
a 250 mH coil of negligible resistance is connected to an AC circuit in which as effective current of 5 mA is flowing. if the frequency is 850Hz, find the inductive reactance
Answer:
the inductive reactance of the coil is 1335.35 Ω
Explanation:
Given;
inductance of the coil, L = 250 mH = 0.25 H
effective current through the coil, I = 5 mA
frequency of the coil, f = 850 Hz
The inductive reactance of the coil is calculated as;
[tex]X_l = \omega L = 2\pi f L\\\\X_l = 2\pi \times 850 \times 0.25\\\\X_l = 1335.35 \ ohms[/tex]
Therefore, the inductive reactance of the coil is 1335.35 Ω
What is the thinnest soap film (excluding the case of zero thickness) that appears black when illuminated with light with a wavelength of 555 nmnm
Answer:
The minimum thickness of soap film is [tex]2.086\times 10^{-7} m[/tex].
Explanation:
wavelength = 555 nm
refractive index, n = 1.33
For the destructive interference,
the thickness is given by
[tex]t =\frac{m \lambda }{2 n}[/tex]
Here, m is the order, n is the refractive index and [tex]\lambda[/tex] is the wavelength.
For minimum thickness, m = 1
So the thickness is
[tex]t =\frac{1 \times 555\times 10^{-9} }{2 \times 1.33}\\\\t = 2.086\times 10^{-7} m[/tex]
4.Upthrust doesnt depend on the following Physical quantity?
volume of body
density of body
mass of body
acceleration due to gravity
Answer:
C: Mass of body
Explanation:
Upthrust is defined as the upward force that a liquid will exert on a body floating atop it.
Now, Formula for upthrust is;
Upthrust = density of liquid × volume of the body × acceleration due to gravity.
From the formula, we can see that upthrust depends on density, volume and acceleration due to gravity.
Thus, looking at the options, the one that doesn't apply is mass of body.
With the frequency set at the mid-point of the slider and the amplitude set at the mid-point of the slider, approximately how many grid marks is the wavelength of the wave (use the pause button and step button as you need to in order to get a good measure, and round to the nearest whole grid mark)?
If the amplitude is increased the wavelength:___________.
a. decreases
b. stays the same
c. increases
Answer:
correct answer is b
Explanation:
The frequency of a wave depends on the properties of medium density and the elasticity properties change the amplitude depends on the energy carried by the wave, that is, the amplitude is proportional to the height of the wave (oscillation).
Consequently the amplitude of independent of the frequency because it depends on different factors.
Therefore when changing the amplitude the wavelength remains constant
the correct answer is b
Which nucleus completes the following equation?
Answer:
Option D. ²⁰⁸₈₄Po
Explanation:
From the question given above, the following data were obtained:
²¹²₈₆Rn —> ⁴₂He + ?
Let the unknown be ⁿₓD. Thus, the equation becomes:
²¹²₈₆Rn —> ⁴₂He + ⁿₓD
Next, we shall determine n, x and D. This can be obtained as follow:
212 = 4 + n
Collect like terms
212 – 4 = n
208 = n
n = 208
86 = 2 + x
Collect like terms
86 – 2 = x
84 = x
x = 84
ⁿₓD => ²⁰⁸₈₄D = > ²⁰⁸₈₄Po
²¹²₈₆Rn —> ⁴₂He + ²⁰⁸₈₄Po
Thus, option D gives the correct answer to the question.
A rubber ball is shot straight up from the ground with a speed of 12 m/s. Simultaneously, a second identical rubber ball is dropped from rest exactly 7 m directly above the first ball. At what height (in m) do the two balls collide?
Answer:
6.17 m
Explanation:
We are given that
Initial speed of rubber ball, u=12 m/s
Total height, h=7 m
Initial speed of second ball, u'=0
We have to find the height at which the two balls collide.
Let first rubber ball and second ball strikes after t time.
For first ball
Distance traveled by first ball in time t
[tex]S=ut-\frac{1}{2}gt^2[/tex]
Substitute the value
[tex]S=12t-\frac{1}{2}(9.8)t^2[/tex]
[tex]S=12t-4.9t^2[/tex] ...(1)
Distance traveled by second ball in time t
[tex]7-S=\frac{1}{2}(9.8)t^2[/tex]
[tex]7-S=4.9t^2[/tex] .....(2)
Using equation (2) in equation (1) we get
[tex]S=12t-(7-S)[/tex]
[tex]S=12t-7+S[/tex]
[tex]\implies 12t=7[/tex]
[tex]t=\frac{12}{7}[/tex]sec
Now, using the value of t
[tex]S=12(\frac{12}{7})-4.9(\frac{12}{7})^2[/tex]
S=6.17 m
Hence, at height 6.17 m the two balls collide .
Which of the following never cause a change in the motion of an object? O A. Net forces O B. Unbalanced forces C. Balanced forces D. Contact forces
Answer:
Hello There!!
Explanation:
The answer is C. Balanced forces.
hope this helps,have a great day!!
~Pinky~
Balanced forces never cause a change in the motion of an object. Hence, option C is correct, rest are not correct.
What is a Balanced Force?Unless another force is added, forces will always be in balance. The forces are equal, for instance, when the paper, pencil, and pen are set. Selfishly, they push and pull. However, when gravity is added, it pulls the object down, causing it to fall.
When two forces are equal in size and have the same direction, they are said to be balanced. They are thought of as being in an equilibrium state. The motion or direction of an object cannot be changed by balanced forces; instead, they maintain the object's motion at a constant speed.
A force that is exerted in one direction more than it is in the other is said to have imbalanced forces. An object's speed and/or direction change when unbalanced forces are exerting pressure on it.
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write the chemical equation of rust
ANSWER
4Fe+ 3O2 → 2Fe2O.
EXPLANATION
iron (Fe) combines with oxygen (O2) to form rust, or iron oxide (Fe2O3). The equation for this reaction is: 4Fe+ 3O2 → 2Fe2O.
A football player collides with another player. The force of the collision is
1000 kg•m/s. The collision lasts 1 second. What is the impulse?
Answer:
Impulse = 1000 Ns
Explanation:
Given the following data;
Force of collision = 1000 kg•m/s.
Time = 1 seconds
To find the impulse;
Mathematically, the impulse experienced by an object or body is given by the formula;
Impulse = force * time
Substituting into the formula, we have;
Impulse = 1000 * 1
Impulse = 1000 Ns
While an object is in projectile motion (with upward being positive) with no air resistance ct is in projectile motion (with upward being positive) with no air resistance, Group of answer choices the horizontal component of its velocity remains constant and the vertical component of its acceleration is equal to -g. the vertical component of its velocity remains constant and the vertical component of its acceleration is equal to -g the horizontal component of its velocity remains constant and the horizontal component of its acceleration is equal to -g the horizontal component of its velocity remains constant and the vertical component of its acceleration is equal to zero. the vertical component of both its velocity and its acceleration remain constant.
Answer:
The horizontal component of its velocity remains constant and the vertical component of its acceleration is equal to -g.
Explanation:
This is because, the projectile has both vertical and horizontal components of velocity. But, its vertical component of velocity changes as the object moves whereas, its horizontal component of velocity remains constant.
Also, the projectile has only vertical component of acceleration and no horizontal component of acceleration since, its horizontal component of velocity remains constant. Thus, no change in the horizontal component of velocity.
The vertical component of acceleration is equal to -g since, the weight is the only vertical force acting on it.
So, the horizontal component of its velocity remains constant and the vertical component of its acceleration is equal to -g.
FORCE AND DISPLACEMENT AT AN ANGLE A sailor pulls a boat a distance of 30.0 m along a dock using a rope that makes a 25.0° angle with the horizontal. How much work does the rope do on the boat if its tension is 255 N?
Answer: 6117.58 J
Explanation:
We know that W=Fd*cos(theta) where theta is the angle between the displacement and the force.
In this case, we are given that F=225 N, d=30 m, and theta=25 degrees.
Plugging all this in we get
W=225*30*cos(25)=6117.58 J
Work done by the rope when sailor pulls the boat in the dock is 6930.9 J
What is work ?The work is defined by the product of force and displacement. Its standard formula is,
[tex]W = F.d.Cos\alpha[/tex]
Here F is force, d is displacement and α is angle subtended by force from horizontal.
As given in the question,F = 255N, d = 30m, α = 30°
On putting in the above formulaW = 255×30×Cos30°
=7650×0.906
= 6930.9 J
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What is the kinetic energy of a 10kg object moving at 2.0m/s? *
Answer:
20J
Explanation:
[tex]KE = \frac{1}{2} mv^{2} = \frac{1}{2} (10)(2)^{2} =20J[/tex]