Answer:
Determining planetary laws of motion
Explanation
Kepler worked for Tycho Brahe who was recording planetary motion for 20 years. After Brahe's demise Kepler inherited those records of planetary motion. After analyzing those records he put forth the three laws of planetary motion.
Law of Orbits: Every planet in our solar system move in elliptical orbit with sun at one focus It is also called the law of Ellipses
Law of Areas: The imaginary line drawn between the planet and sun will sweep out equal areas in equal period
Law of periods: The square of the time period of the planet is directly proportional to the cube of the semi major axis of the orbit. It is also called the law of Harmonies
Johannes Kepler is known for determining the planetary laws of motion in astronomy. Therefore option 2 is correct.
"determining planetary laws of motion," is the correct answer. Johannes Kepler was a German astronomer and mathematician who made significant contributions to our understanding of the motion of planets.
His three laws of planetary motion, known as Kepler's laws, revolutionized the field of astronomy and laid the foundation for Isaac Newton's later work on universal gravitation.
Kepler's first law, known as the law of ellipses, states that planets orbit the Sun in elliptical paths, with the Sun at one of the foci of the ellipse. This challenged the prevailing notion that planetary orbits were perfect circles.
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1. Calculate the work done in raising 120 lb to a height of 15.0 ft. Find the work done in raising 250 g a distance of 215 cm.
2. A screw jack has a handle of radius 36 in and thread pitch of .25in. Calculate the IMA of the jack
PLEASE HELP ME
Answer:
1. 1800 lb ft, 5.27 J
2. 905
Explanation:
1. Work is the change in energy.
W = mgh
W = (120 lb) (15 ft)
W = 1800 lb ft
W = mgh
W = (0.250 kg) (9.8 m/s²) (2.15 m)
W = 5.27 J
2. The IMA (ideal mechanical advantage) of a screw is the circumference of the screw divided by the pitch.
IMA = 2πr / p
The IMA of a handle (lever) is the circumference of the handle divided by the circumference of the screw.
IMA = 2πR / 2πr
The total IMA is the product:
IMA = (2πR / 2πr) (2πr / p)
IMA = 2πR / p
IMA = 2π (36) / (0.25)
IMA = 905
A circular loop of flexible iron wire has an initial circumference of 167 cm, but its circumference is decreasing at a constant rate of 15.0 cm/s due to a tangential pull on the wire. The loop is in a constant uniform magnetic field of magnitude 0.500 T, which is oriented perpendicular to the plane of the loop. Assume that you are facing the loop and that the magnetic field points into the loop.A) Find the magnitude of the emf E induced in the loop after exactly 8.00 s has passed since the circumference of the loop started to decrease.B) Find the direction of the induced current in the loop as viewed looking along the direction of the magnetic field. (Clockwise or Counterclockwise?)
Answer:
Part a)
[tex]EMF = 5.6 \times 10^{-3} V[/tex]
Part b)
Since the radius is decreasing so induced current will increase the flux through the coil
So it would be clockwise in direction
Explanation:
As we know that magnetic flux linked with the coil is given as
[tex]\phi = \pi r^2 B[/tex]
now the rate of change in flux is given as
[tex]\frac{d\phi}{dt} = 2\pi r \frac{dr}{dt} B[/tex]
now we know that circumference is decreasing at rate of 15 cm/s
so here we know the length of circumference as
[tex]C = 2\pi r[/tex]
So rate of change in circumference is
[tex]\frac{dC}{dt} = 2\pi \frac{dr}{dt}[/tex]
[tex]\frac{1}{2\pi}(15 cm) = \frac{dr}{dt}[/tex]
final length of circumference at t = 8 s
[tex]C = 167 - (15)(8) = 47[/tex]
Part a)
Now the induced EMF is given as
[tex]EMF = (2\pi r)(\frac{1}{2\pi})(0.15)(0.5)[/tex]
[tex]EMF = (0.47)(\frac{1}{2\pi})(0.15)(0.5)[/tex]
[tex]EMF = 5.6 \times 10^{-3} V[/tex]
Part b)
Since the radius is decreasing so induced current will increase the flux through the coil
So it would be clockwise in direction
The problem is solved using Faraday's Law of Electromagnetic Induction: the induced emf equals to the change in magnetic flux divided by change in time. Then, Lenz's law is used to determine the direction of the induced current.
Explanation:The problem you're dealing with is an application of Faraday's Law of Electromagnetic Induction. This law states that the electromotive force (or emf) induced in a circuit is equivalent to the rate of change of magnetic flux through that circuit.
For Part A, you know that the rate of change of the circumference is constant and you can convert that to a rate of change of radius (since circumference = 2πr). Using these formulas, you can determine the rate of change of area as πr(dr/dt), where dr/dt is the rate of change of radius. The induced emf is proportional to the rate of change of magnetic flux, which is the product of magnetic field strength and area. Thus, induced emf equals to (change in flux/change in time), or -Bπr(dr/dt).
For part B, you apply Lenz's law, which states that the direction of induced current is such that the magnetic field due to it opposes the change in the initial magnetic field. Since the field is getting smaller (since the loop is contracting), then the current will act in such a way as to try to keep the size of the field the same. This means going in the counterclockwise direction.
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A ball is dropped and begins bouncing. On the first bounce, the ball travels 3 feet. Each consecutive bounce is 1/8 the distance of the previous bounce. What is the total distance that the ball travels? Round to the nearest hundredth.
Answer:
Total distance covered equals [tex]\frac{48}{7}feet[/tex]
Explanation:
The situation is represented in the attached figure
Distance in first bounce = [tex]d_{1}=2\times 3ft[/tex]
Distance in second bounce =[tex]d_{2}=2\times \frac{3}{8}ft[/tex]
Distance in third bounce=[tex]d_{3}=2\times \frac{3}{8^{2}}ft[/tex]
Thus the total distance covered = [tex]d_{1}+d_{2}+d_{3}+...[/tex]
Applying values we get
Total distance covered = [tex]2\times 3+2\times \frac{3}{8}+2\times \frac{3}{8^{2}}+2\times \frac{3}{8^{3}}+....\\\\=6(1+\frac{1}{8}+\frac{1}{8^{2}}+\frac{1}{8^{3}}+...)[/tex]
Summing the infinite geometric series we get total distance covered as[tex]S_{\infty }=\frac{a}{1-r}[/tex]
[tex]D=6(\frac{1}{1-\frac{1}{8}})\\\\D=\frac{48}{7}feet[/tex]
An object cannot remain at rest unless which of the following holds?
a. The net force acting on it is zero.
b. The net force acting on it is constant and nonzero.
c. There are no forces at all acting on it.
d. There is only one force acting on it.
Answer:
a. The net force acting on it is zero.
An object can remain at rest if the net force acting on it is zero (a) OR there are no forces at all acting on it (c).
In Part H, you discovered that the luminosity of a light bulb increases if the current increases. The rate at which electric potential energy is converted into heat depends on the current flowing through the bulb and the voltage across the bulb. This energy is supplied by the battery. Mathematically, the luminosity P of the light bulb is given by P=ΔVI, where ΔV is the voltage across the bulb and I is the current.What happens to the luminosity of the light bulb if the voltage of the battery is doubled? (Note that the PhET simulation does not display a numerical value for the luminosity, so you should use the relationship between the luminosity, the voltage across the bulb, and the current.)
Doubling the battery voltage applied to a light bulb will result in nearly quadrupling its power, assuming the bulb's resistance remains constant, due to the power being proportional to the square of the voltage (P = V²/R).
Explanation:The luminosity of a light bulb, which can be thought of as its power output, is directly proportional to the electric potential energy converted into light and heat. The relationship between power (P), voltage (V), and current (I) is given by P = ΔVI, where ΔV represents the voltage across the bulb, and I represents the current flowing through it. When we discuss this relationship in terms of resistance (R), we can also express power as P = V²/R. According to this formula, doubling the voltage while keeping the resistance constant will result in a near quadrupling of power because the voltage is squared in the expression.
For example, a 25-W bulb designed to operate at a certain voltage would have its power increased nearly to 100 W if the voltage is doubled, assuming the resistance remains constant. However, in actual practice, the resistance of a bulb increases with temperature; thus, although the power increase is substantial, it is not exactly quadrupled.
Energy transformations that involve one transformation from one type of energy to another are called...............transformations.
Answer:
It is called single transformation
Answer:
Single transformation
Explanation:
Energy can neither be created nor be destroyed, it can only covert from one form to another. Sometimes, to get a work done one form of energy only require to be transformed into another form then it is known as single transformation.
For Example, cell phone transforming electrical energy into electromagnetic energy that makes it's working feasible.
Moving vehicle converting chemical energy to kinetic energy.
A 160-N child sits on a light swing and is pulled back and held with a horizontal force of 100 N. The magnitude of the tension force of each of the two supporting ropes is A : 190 N B : 120 N C : 60 N D : 94 N
The tension in each rope supporting the child on the swing can be calculated by summing the forces (weight of the child and the pulling force) and dividing by 2, because the force is being equally distributed among the ropes due to the symmetry of the situation. This gives a tension of approximately 130N in each rope. The closest answer to this is B: 120N.
Explanation:This problem relates to forces and tension. As the child is at rest, the total net force on the child is zero. This means that the sum of the upward forces (tension in the ropes) is equal to the downward forces (the weight of the child and the horizontal force pulling him backwards).
The weight of the child can be calculated using the formula Weight = m*g, where m is the mass and g is the acceleration due to gravity. In this case, the weight of the child is 160 N. As for the horizontal pull, it is given as 100N.
The combination of these two forces is then equally distributed across the two ropes holding the swing, due to the symmetry of the situation. Therefore, we sum the forces (160N for weight and 100N for pull) and divide by 2 to find the tension in each rope.
The calculation is, therefore, (160N + 100N) / 2 = 130N.
The answer closest to this value is B: 120N. Without more precise numbers, we choose the closest value.
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The primary coil of a transformer contains 100 turns; the secondary has 200 turns. The primary coil is connected to a size aa battery that supplies a constant voltage of 1.5 volts. What voltage would be measured across the secondary coil?
Final answer:
Assuming an AC source for illustration, a transformer with a primary coil of 100 turns connected to a 1.5 V source and a secondary coil of 200 turns would yield a voltage of 3.0 V across the secondary coil, calculated by the turns ratio and input voltage.
Explanation:
The question pertains to the operation of a transformer, which is a device that uses electromagnetic induction to change the voltage levels between circuits. A transformer consists of a primary coil and a secondary coil wound around a common core. When an alternating current (AC) flows through the primary coil, it creates a changing magnetic field, which induces a voltage across the secondary coil. The voltage induced in the secondary coil is related to the voltage in the primary coil by the ratio of the number of turns in each coil.
For a step-up transformer, the voltage is increased from the primary to the secondary coil. The relationship can be denoted as Vp/Vs = Np/Ns, where Vp and Vs are the voltages in the primary and secondary coils, respectively, and Np and Ns are the number of turns in the primary and secondary coils, respectively. Since this question refers to a direct current (DC) source (a size AA battery) which would not work effectively with a transformer, let's consider it as an AC source for the purpose of explanation.
If we apply the formula Vs = (Ns/Np) * Vp, where Vp is 1.5 volts, Np is 100 turns, and Ns is 200 turns, we get:
Vs = (200/100) * 1.5 V
Vs = 2 * 1.5 V
Vs = 3.0 V
The voltage across the secondary coil would theoretically measure 3.0 volts if the system operated with an AC input and perfect efficiency.
A block is given an initial velocity of 4.90 m/s up a frictionless 20.5° incline. How far up the incline does the block slide before coming to rest?
Answer:
7.0 m
Explanation:
We can solve the problem by using the work-energy theorem, which states that the work done on the block is equal to the block's change in kinetic energy:
[tex]W=K_f - K_i[/tex]
where:
W is the work done (by gravity, since it is the only force acting on the block)
[tex]K_i[/tex] is the initial kinetic energy
[tex]K_f = 0[/tex] is the final kinetic energy, which is zero since the block comes to a stop
The work done by gravity against the block is:
[tex]W=-(mgsin \theta) d[/tex]
where
m is the mass of the block
g = 9.8 m/s^2 is the acceleration due to gravity
[tex]\theta=20.5^{\circ}[/tex] is the angle of the incline
[tex](mg sin \theta)[/tex] is the component of the force of gravity that acts along the plane parallel to the incline, and the negative sign is due to the fact that this force acts opposite to the displacement of the block, d
d is the displacement of the block
Instead, the initial kinetic energy is
[tex]K_i = \frac{1}{2}mv^2[/tex]
where
v = 4.90 m/s is the initial speed of the block
Substituting everything into the first equation, we can solve to find d, the displacement covered by the block up the incline:
[tex]-mgsin \theta d = -\frac{1}{2}mv^2\\d = \frac{v^2}{g sin \theta}=\frac{(4.90)^2}{(9.8)(sin 20.5^{\circ})}=7.0 m[/tex]
Final answer:
To find how far a block slides up an incline given an initial velocity and angle, we use energy conservation and kinematic equations, considering the acceleration due to gravity and the incline's angle.
Explanation:
The question involves calculating the distance a block slides up a frictionless incline given an initial velocity, making use of concepts from kinematics and energy conservation in physics. Using the energy conservation principle, the initial kinetic energy of the block is converted into potential energy at the highest point of its trajectory on the incline. Given an initial velocity of 4.90 m/s and an incline angle of 20.5°, we can calculate the distance using the formula v^2 = u^2 + 2as, where v is the final velocity (0 m/s at the highest point), u is the initial velocity, a is the acceleration (negative due to gravity acting opposite to the motion), and s is the distance travelled. The acceleration component along the incline can be calculated as a = -g*sin(θ), where g is the acceleration due to gravity (9.81 m/s²) and θ is the incline angle. Hence, the distance s can be found by rearranging the formula. This approach demonstrates the application of kinematic equations and the concept of work-energy theorem in solving problems related to motion on an incline.
What is the greatest distance an image can be located behind a convex spherical mirror?
Answer:
Maximum distance of image from mirror is equal to focal length of the mirror
Explanation:
As we know by the equation of mirror we have
[tex]\frac{1}{d_i} + \frac{1}{d_o} = \frac{1}{f}[/tex]
here we know for convex mirror
object position is always negative as it will be placed behind the mirror always
while the focal length of the convex mirror is always taken positive
So here we have
[tex]\frac{1}{d_i} + \frac{1}{-d_o} = \frac{1}{f}[/tex]
[tex]\frac{1}{d_i} = \frac{1}{d_o} + \frac{1}{f}[/tex]
so here maximum value of image distance is equal to focal length of the mirror
The rate (in mg carbon/m3/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function P = 90I I2 + I + 9 where I is the light intensity (measured in thousands of foot-candles). For what light intensity is P a maximum?
Answer:
At light intensity I = 3, is P a maximum
Explanation:
Given:
[tex]P=\frac{90I}{I^2+I+9}[/tex]
now differentiating the above equation with respect to Intensity 'I' we get
[tex]\frac{dp}{dI}=\frac{(I^2+I+9).\frac{d(90I)}{dI}-90I.\frac{d((I^2+I+9)}{dI}}{(I^2+I+9)^2}[/tex]
or
[tex]\frac{dp}{dI}=\frac{(I^2+I+9).90-90I.(2I+1)}{(I^2+I+9)^2}[/tex]
or
[tex]\frac{dp}{dI}=\frac{90I^2+90I+810)-(180I^2+90I)}{(I^2+I+9)^2}[/tex]
or
[tex]\frac{dp}{dI}=\frac{-90I^2+810)}{(I^2+I+9)^2}[/tex]
Now for the maxima [tex]\frac{dP}{dI}=0[/tex]
thus,
[tex]0=\frac{-90I^2+810)}{(I^2+I+9)^2}[/tex]
or
[tex]-90I^2+810=0[/tex]
or
[tex]I^2=\frac{810}{90}[/tex]
or
[tex]I^2=9[/tex]
or
I = 3
thus, for the value of intensity I = 3, the P is maximum
at I = 3
[tex]P=\frac{90\times3}{3^2+3+9}[/tex]
or
[tex]P=\frac{270}{21}[/tex]
or
[tex]P=12.85[/tex]
Green light has a frequency of about 6.00×1014s−1. What is the energy of a photon of green light?
Answer: [tex]3.97(10)^{-19}J[/tex]
Explanation:
The energy [tex]E[/tex] of a photon is given by:
[tex]E=h\nu[/tex] (1)
Where:
[tex]h=6.626(10)^{-34}\frac{m^{2}kg}{s}[/tex] is the Planck constant
[tex]\nu=6(10)^{14}s^{-1}[/tex] is the frequency of green light
Solving (1):
[tex]E=(6.626(10)^{-34}\frac{m^{2}kg}{s})(6(10)^{14}s^{-1})[/tex] (2)
[tex]E=3.9756(10)^{-19}\frac{m^{2}kg}{s^{2}}=3.9756(10)^{-19}J[/tex] (3)
1. What is the name given to the total possibility of sound frequencies
2. What is the difference between a single musical note and another note at twice the frequency of the first?
3. What exactly is the relationship of sound to the distance between the source and reciver?
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HELP ASAP PLEASE DUE TOMORROW
I really need help somebody....anybody
Explanation:
1. The entire span of possible sound waves is called the acoustic spectrum. It is subdivided into infrasonic sounds, audible sounds, and ultrasonic sounds.
2. The difference between a musical note and another note at twice the frequency is called an octave.
3. Sound intensity varies with the inverse square of distance.
The possibility of sound frequencies is called the sound spectrum. Notes at double the frequency are an octave higher, and the perception of sound varies with distance from the source.
Explanation:The total possibility of sound frequencies is referred to as the sound spectrum. The difference between a single musical note and another note at twice the frequency of the first is known as an octave in music. The note that is twice the frequency appears higher in pitch.
The relationship of sound to the distance between the source and receiver affects the perceived loudness of the sound. This is due to the way sound waves spread out and weaken as they travel away from the source. As a result, the further somebody is from the source of the sound, the quieter it will appear.
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A spherical iron ball 10 in. in diameter is coated with a layer of ice of uniform thickness. If the ice melts at a rate of 15 in cubed Over min, how fast is the thickness of the ice decreasing when it is 3 in thick?
Answer:
Decreasing rate of thickness when x=3 in is [tex]\dfrac{dx}{dt}= -7.28\times 10^{-3} in/min[/tex]
Explanation:
Lets assume that thickness of ice over the spherical iron ball =x
So radius diameter of Sphere=5+x in
Inner radius=5 in
So volume V=[tex]\dfrac{4}{3}\pi [(5+x )^3-5^3][/tex]
V=[tex]\dfrac{4}{3}\pi [x^3+75x^2+15x][/tex]
Now given that ice melts rate=[tex] 15in^3/min[/tex]
[tex]\dfrac{dV}{dt}= -15in^3/min[/tex]
[tex]\dfrac{dV}{dt}=\dfrac{4}{3}\pi [3x^2+150x+15]\dfrac{dx}{dt}[/tex]
When x=3 in [tex]\dfrac{dV}{dt}= -15in^3/min[/tex]
[tex]-15=\dfrac{4}{3}\pi [3\times 3^2+150\times 3+15]\dfrac{dx}{dt}[/tex]
[tex]\dfrac{dx}{dt}= -7.28\times 10^{-3} in/min[/tex]
So decreasing rate of thickness when x=3 in is [tex]\dfrac{dx}{dt}= -7.28\times 10^{-3} in/min[/tex]
A rock is suspended by a light string. When the rock is in air, the tension in the string is 43.8 N . When the rock is totally immersed in water, the tension is 31.3 N . When the rock is totally immersed in an unknown liquid, the tension is 18.3 N .
Answer:
Density of unknown liquid is [tex]2047 kg/m^3[/tex]
Explanation:
When rock is suspended in air then the weight of the rock is counter balanced by the tension force in the string
So here we have
[tex]T = mg = 43.8 N[/tex]
now when the rock is immersed in water then the tension in the string is and buoyancy force due to water is counter balanced by the weight of the object
so here we have
[tex]T_1 + F_b = mg[/tex]
[tex]31.3 + F_b = 43.8[/tex]
[tex]F_b = 43.8 - 31.3 = 12.5 N[/tex]
now we have
[tex](1000)V(9.81) = 12.5[/tex]
[tex]V = 1.27 \times 10^{-3} m^3[/tex]
now when the rock is immersed into other liquid then we have
[tex]T_2 + F_b' = mg[/tex]
[tex]18.3 + F_b' = 43.8[/tex]
[tex]F_b' = 25.5 N[/tex]
now we have
[tex]\rho(1.27 \times 10^{-3})(9.81) = 25.5[/tex]
[tex]\rho = 2047 kg/m^3[/tex]
Seema knows the mass of a basketball. What other information is needed to find the ball’s potential energy?
Potential energy can be found using this formula:
PE= m * g * h
where:
PE= potential energy
m=mass
g=gravitational acceleration constant (9.8 m/s^2)
h= height
So your answer is height because you also use the gravitational constant.
Answer:
We know, U = m * g * h
So, seema needs the value of g & h
In short, Your Answer would be Option C) acceleration due to gravity and the height the ball reaches
Explanation:
Let R be the distance between the cylinder and the center of the turntable. Now assume that the cylinder is moved to a new location R/2 from the center of the turntable. Which of the following statements accurately describe the motion of the cylinder at the new location? Check all that apply.1.The speed of the cylinder has decreased.2. The speed of the cylinder has increased.3. The magnitude of the acceleration of the cylinder has decreased.4. The magnitude of the acceleration of the cylinder has increased.5. The speed and the acceleration of the cylinder have not changed.
Answer:
The speed of the cylinder has decreased
Explanation:
Given data:
Distance between the center of the turn table and the cylinder = R
Distance between the center of the turn table and the cylinder when it is moved to a new point, R' = R/2
the tangential velocity in circular motion is given as:
[tex]V=\frac{2\pi R}{T}[/tex]
where T is the time
now for R = R' = R/2
the new velocity V' comes as:
[tex]V'=\frac{2\pi \frac{R}{2}}{T}[/tex]
or
[tex]V'=\frac{\pi R}{T}[/tex]
thus the velocity becomes half or we can say the velocity decreases
Now, the acceleration (a) in circular motion is given as:
a = V²/R
now for
R = R' = R/2
the velocity V' = V/2
thus,
new acceleration a' comes as:
[tex]a = \frac{(\frac{V}{2})^2}{R/2}[/tex]
or
[tex]a'=\frac{V^2}{2R}[/tex]
thus,
the acceleration decreases by 2 times
The statement that accurately describes the motion of the cylinder at the new location is : ( 1 ) and ( 3 )
The speed of the cylinder has decreased ( 1 )The magnitude of the acceleration of the cylinder has decreased ( 3 )Given data :
Distance between cylinder and center of the turn table = R
Distance between cylinder and turntable when moved = R/2
where ;
Tangential Velocity/speed = [tex]\frac{2\pi R}{T}[/tex]
R = distance between objects
T = time
∴ The initial Tangential velocity of the cylinder at rest ( V ) = [tex]\frac{2\pi R}{T}[/tex] ----- ( 1 )
while the
Tangential velocity/speed of the cylinder when it moves ( V' ) = [tex]\frac{2\pi R/2}{T}[/tex]
= [tex]\frac{\pi R}{T}[/tex] ----- ( 2 )
Therefore comparing equations ( 1 ) and ( 2 ) the speed of the cylinder has decreased as the cylinder moves from R to R/2 .
Also Given that Tangential acceleration = v² / R .
Since velocity decreases after the cylinder moves, the magnitude of the acceleration of the cylinder will decrease as well.
Hence we can conclude that the acceleration and speed of the cylinder has decreased with the movement of the cylinder.
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Given that the electromagnetic force is far stronger than gravity on a per-particle basis, why doesn't the electromagnetic force dominate the interactions of large objects like planets, stars, and galaxies?
Explanation:
The electro magnetic force is given by
F = [tex]\frac{k.q_{1}.q_{2}}{r^{2}}[/tex]
where [tex]q_{1}[/tex] and [tex]q_{2}[/tex] are charged particles
k =Coulombs constant
r = distance between two charges
And gravitational force is given by
F = [tex]\frac{G.m_{1}.m_{2}}{r^{2}}[/tex]
where [tex]m_{1}[/tex] and [tex]m_{2}[/tex] are masses
G =Garvitation constant
r = distance between two masses
Now since the planets, stars and galaxies are electrically neutral, therefore they have zero electrical charge and so electro magnetic forces have no affect on these planets, stars and heavenly bodies.
Whereas the masses of the heavenly bodies are very large, so they are largely affected by the gravitational force since Gravitational force is directly proportional to the product of the masses of a body.
Therefore, though the electromagnetic force is stronger than the gravitational force, the electromagnetic force does not dominate the forces in the heavenly bodies as they as not electrically charged.
It is common to see birds of prey rising upward on thermals. The paths they take may be spiral-like. You can model the spiral motion as uniform circular motion combined with a constant upward velocity. Assume a bird completes a circle of radius 6.00m every 5.00s and rises vertically at a rate of 3.00m/s.
1. Find the speed of the bird relative to the ground.
2. Find the magnitude of the bird's acceleration.
3. Find the direction of the bird's acceleration.
4. Find the angle between the bird's velocity vector and the horizontal.
1. 8.11 m/s
In order to find the speed of the bird, we need to combine both the horizontal and the vertical component of its velocity.
The horizontal component is equal to the tangential velocity of the circular motion of the bird. We have:
r = 6.00 m radius of the circle
T = 5.00 s period of the circular motion
So the tangential velocity (=horizontal component of the velocity) is
[tex]v_x=\frac{2\pi r}{T}=\frac{2\pi (6.00 m)}{5.00 s}=7.54 m/s[/tex]
The vertical component of the velocity is given by the problem
[tex]v_y = 3.00 m/s[/tex]
So the speed of the bird is the magnitude of its velocity:
[tex]v=\sqrt{v_x^2 + v_y^2}=\sqrt{(7.54 m/s)^2+(3.00 m/s)^2}=8.11 m/s[/tex]
2. 9.48 m/s^2
The only component of the acceleration of the bird is the one that determine the circular motion in the horizontal plane - so it is the centripetal acceleration.
The centripetal acceleration of the bird is given by:
[tex]a=\frac{v_x^2}{r}[/tex]
where
[tex]v_x = 7.54 m/s[/tex] is the tangential velocity of the bird
r = 6.00 m is the radius of the circular trajectory
Substituting,
[tex]a=\frac{(7.54 m/s)^2}{6.00 m}=9.48 m/s^2[/tex]
3. Towards the centre of the circle
The bird is moving upward at constant velocity and in a straight line, so there is no component of the acceleration in the vertical direction.
In the horizontal plane, however, the bird is moving in a uniform circular motion: this means that the tangential acceleration is zero, while there is a centripetal acceleration (calculated in the previous part of the exercise). The direction of the centripetal acceleration is always towards the centre of the circular trajectory: so, the acceleration of the bird has exactly the same direction as the centripetal acceleration, i.e. towards the centre of the circle.
4. [tex]21.7^{\circ}[/tex]
We said that the components of the velocity of the bird are:
[tex]v_x = 7.54 m/s[/tex] in the horizontal direction
[tex]v_y = 3.00 m/s[/tex] in the vertical direction
So we can find the angle of the velocity with the horizontal by using the equation:
[tex]\theta = tan^{-1} (\frac{v_y}{v_x})[/tex]
Substituting the values in, we find
[tex]\theta = tan^{-1} (\frac{3.00 m/s}{7.54 m/s})=21.7^{\circ}[/tex]
If an object is propelled upward from a height of 128 feet at an initial velocity of 112 feet per second, then its height h after t seconds is given by the equation h equals negative 16 t squared plus 112 t plus 128. After how many seconds does the object hit the ground? Round to the nearest tenth of a second.
Explanation:
The equation of motion of an object is given by :
[tex]h(t)=-16t^2+112t+128[/tex]
Where
t is the time in seconds
We need to find the time when the object hits the ground. When the object hits the ground, h(t) = 0
So,
[tex]-16t^2+112t+128=0[/tex]
[tex]-t^2+7t+8=0[/tex]
On solving above equation using online calculator, t = 8 seconds. So, the object hit the ground after 8 seconds. Hence, this is the required solution.
Suppose that the angular separation of two stars is 0.1 arcseconds, and you photograph them with a telescope that has an angular resolution of 1 arcsecond. How will the stars appear in the photograph?
Answer: the photograph will likely show only one star.
Explanation:
Since their angular separation is smaller than the telescope's angular resolution, the picture will apparently show only one star rather than two.
The photograph will likely show only one star.
How do you find the angular distance?And their mathematical relationship is tan θ = a / d. θ ≈ a / d. Remember that the perfect circle is 2π radians = 360 degrees. The magnitude or distance of the angle can also be measured in arc minutes (60 arcs = 1 degree) or arc seconds (60 arcs = 1 arc).
RA takes values from 0 to 360 degrees, and declination takes values from -90 to +90 degrees). Next, the angular distance A between the two stars 1 and 2 in degrees is determined by the following relationship: cos (A) = sin (devil.
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The rear wheel on a clown’s bicycle has twice the radius of the front wheel. (a) When the bicycle is moving, is the linear speed at the very top of the rear wheel greater than, less than, or the same as that of the very top of the front wheel? (b) Is the angular speed of the rear wheel greater than, less than, or the same as that of the front wheel?
Answer:
a). same as
b). less than
Explanation:
a). When a bicycle is moving, the linear speed at the top of the rear wheel is same as the linear speed at the top of the front wheel. Since the clown's bicycle is a rigid body, both the wheels that is the front wheel and the rear wheel will move with the same linear speed.
b). Since we know that angular speed varies inversely to the radius of the wheel.
That is ω = 1 / r
Since the rear wheel has twice the radius of that of the front wheel, therefore real wheel will have less angular speed than the front wheel.
Therefore, the angular speed of the rear wheel is less than the angular speed of the front wheel.
A small 13.0-g plastic ball is tied to a very light 27.2-cm string that is attached to the vertical wall of a room (Fig. P21.65). A uniform horizontal electric field exists in this room. When the ball has been given an excess charge of -1.10 mC, you observe that it remains suspended, with the string making an angle of 17.4° with the wall. Find the magnitude and direction of the electric field in the room.
The magnitude of the electric field is found by using the components of tension in the string, related to the horizontal electric force and the vertical gravitational force, and applying trigonometry to solve for E.
Explanation:To find the magnitude and direction of the electric field, we must recognize that there are two forces acting on the plastic ball: the force of gravity and the electric force. The force of gravity acts downward and has a magnitude of mg, where m is the mass of the ball and g is the acceleration due to gravity. The electric force acts horizontally and has a magnitude of Eq, where E is the electric field strength and q is the charge on the ball.
These two forces result in a tension in the string that holds the ball in equilibrium. The electric force provides the horizontal component of this tension, and the force of gravity provides the vertical component. As the string makes an angle of 17.4° with the wall, we can use trigonometry to relate the forces. From the vertical component, we have:
Tcos(θ) = mg
And from the horizontal component, we have:
Tsin(θ) = Eq
Dividing these two equations gives us:
tan(θ) = Eq/mg
Substituting the values provides:
tan(17.4°) = E(1.10 × 10-3 C)/(0.013 kg × 9.81 m/s2)
Solving for E yields:
E = mg(tan(θ))/q
By calculating this, we can find the electric field's magnitude.
What is the maximum speed at which a car can safely travel around a circular track of radius 75.0 m if the coefficient of friction between the tire and road is 0.200?
A) 3.87 m/s
B) 12.1 m/s
C) 15.0 m/s
D) 147 m/s
Answer:
B) 12.1 m/s
Explanation:
Sum of the forces in the y direction:
∑F = ma
N − mg = 0
N = mg
Sum of the forces in the radial direction:
∑F = ma
F = m v² / r
Nμ = m v² / r
Substituting and solving for v:
mgμ = m v² / r
gμ = v² / r
v = √(gμr)
Given that μ = 0.200 and r = 75.0 m:
v = √(9.81 m/s² × 0.200 × 75.0 m)
v = 12.1 m/s
The car can turn through the circular track with a maximum speed of 12.1 m/s. Hence, option (B) is correct.
Given data:
The radius of circular track is, r = 75.0 m.
The coefficient of friction between the tire and road is, [tex]\mu = 0.200[/tex].
When the car moves around a circular track, then for safe turn through the track it is necessary to have the value of frictional force and centripetal force in a balanced amount. Therefore,
Fc = Ff
[tex]\dfrac{m \times v^{2}}{r} = \mu \times m \times g\\\\\\\dfrac{v^{2}}{r} = \mu \times g\\\\v =\sqrt{\mu \times r \times g}[/tex]
Solving as,
[tex]v =\sqrt{0.200 \times 75.0 \times 9.8}\\\\v =12.1 \;\rm m/s[/tex]
Thus, we can conclude that the car can turn through the circular track with a maximum speed of 12.1 m/s. Hence, option (B) is correct.
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A person with a mass of 15 kg is walking on a flat surface at a velocity of 5 m/s. What is the walker's momentum?
A. 3 kg-m/s
B. 0.3 kg-m/s
C. 20 kg-m/s
D. 75 kg-m/s
Answer:
d
velocity multiplied to mass
Answer:
Momentum of the person, p = 75 kg-m/s
Explanation:
It is given that,
Mass of the person, m = 15 kg
The person is moving with a velocity of, v = 5 m/s
We need to find the walker's momentum. It is equal to the product of mass and velocity with which it is moving. Mathematically, it is given by :
p = mv
[tex]p=15\ kg\times 5\ m/s[/tex]
p = 75 kg-m/s
So, the momentum of the person is 75 kg-m/s. Hence, this is the required solution.
Acceleration can be defined as the rate at which velocity ________
Acceleration is the rate of the change in velocity.
The answer would be the rate at which velocity changes.
Answer:
The speed is 20 m/s, and the direction is "downward". Acceleration is the rate of change of velocity. Usually, acceleration means the speed is changing, but not always. When an object moves in a circular path at a constant speed, it is still accelerating, because the direction of its velocity is changing.
Explanation:
The frequency of a wave is 1) A) measured in cycles per second. B) measured in hertz (Hz). C) the number of peaks passing by any point each second. D) equal to the speed of the wave divided by the wavelength of the wave. E) all of the above
The frequency of a wave is measured in hertz (Hz). Hence the correct answer is option E
Explanation:The frequency of a wave is measured in hertz (Hz). Hertz is the unit used to measure the number of waves passing by a point in one second. This means that option B) 'measured in hertz (Hz)' is the correct answer. Frequency is not equal to the speed of the wave divided by the wavelength of the wave, as stated in option D). While option C) 'the number of peaks passing by any point each second' is related to frequency, it does not encompass the entire definition. Therefore, option E) 'all of the above' is also incorrect.
You have a pick-up truck that weighed 4,000 pounds when it was new. you are modifying it to increase its ground clearance. when you are finished
Based on the provided information, the correct statement is:
b. The bottom of your front bumper must not be more than 28 inches above the pavement.
The modification to increase ground clearance in the pick-up truck involves specific regulations for the front bumper height.
The statement "The bottom of your front bumper must not be more than 28 inches above the pavement" indicates a legal restriction to maintain a certain elevation for safety and compliance reasons.
This limitation aims to prevent potential hazards, such as underride collisions, and ensures that the modified truck adheres to regulatory standards. By specifying the maximum height of the front bumper, authorities aim to strike a balance between vehicle customization and road safety.
This regulation emphasizes the importance of maintaining a reasonable height for front bumpers to mitigate risks and uphold public safety standards, reflecting the broader considerations in vehicular modifications within the legal framework.
The probable question may be:
You have a pick-up truck that weighed 4,000 pounds when it was new. You are modifying it to increase its ground clearance. When you are finished
a. The bottom of your front bumper can be up to 32 inches above the pavement.
b. The bottom of your front bumper must not be more than 28 inches above the pavement.
c. You will no longer be required to have a rear bumper.
Substances A and B, initially at different temperatures, come in contact with each other and reach thermal equilibrium. The mass of substance A is twice the mass of substance B. The specific heat capacity of substance B is twice the specific heat capacity of substance A.
Which statement is true about the final temperature of the two substances once thermal equilibrium is reached?1) The final temperature will be closer to the initial temperature of substance B than substance A.2) The final temperature will be exactly midway between the initial temperatures of substances A and B.3) The final temperature will be closer to the initial temperature of substance A than substance B.
Answer: .2) The final temperature will be exactly midway between the initial temperatures of substances A and B.
Explanation:
[tex]heat_{absorbed}=heat_{released}[/tex]
As we know that,
[tex]Q=m\times c\times \Delta T=m\times c\times (T_{final}-T_{initial})[/tex]
[tex]m_A\times c_A\times (T_{final}-T_A)=-[m_B\times c_B\times (T_{final}-T_2)][/tex] .................(1)
where,
q = heat absorbed or released
[tex]m_A[/tex] = mass of A = 2x
[tex]m_B[/tex] = mass of B = x
[tex]T_{final}[/tex] = final temperature = z
[tex]T_A[/tex] = temperature of A
[tex]T_2[/tex] = temperature of B
[tex]c_A[/tex] = specific heat capacity of A = y
[tex]c_B[/tex] = specific heat capacity of B = 2y
Now put all the given values in equation (1), we get
[tex]2x\times y\times (z-T_A)=-[x\times 2y\times (z-T_B)][/tex]
[tex]2z=T_B+T_A[/tex]
[tex]z=\frac{T_B+T_A}{2}[/tex]
Therefore, the final temperature of the mixture will be exactly midway between the initial temperatures of substances A and B.
When two substances with different temperatures come into contact and reach thermal equilibrium, heat flows until they reach the same final temperature. In this case, the final temperature will be closer to the initial temperature of substance B because substance B requires more heat to raise its temperature and has a smaller mass. The specific heat capacity ratio determines the proportion of heat absorbed or released by the substances.
Explanation:When two substances at different temperatures come into contact with each other and reach thermal equilibrium, heat flows from the hotter substance to the cooler substance until they reach the same final temperature. In this case, substance A has twice the mass of substance B but substance B has twice the specific heat capacity of substance A. The specific heat capacity determines how much heat is needed to raise the temperature of a substance. Since substance B requires more heat to raise its temperature and has a smaller mass, it will be able to absorb more heat from substance A than substance A can absorb from substance B.
This means that the final temperature will be closer to the initial temperature of substance B than substance A. The specific heat capacity ratio determines the proportion of heat absorbed or released by the substances.
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A succession of 2-m long water waves on a lake goes by a piece of floating cork that bobs up and down one complete cycle each second. What is the speed of the wave?
Answer:
The speed of the wave is 2 m/s
Explanation:
It is given that,
Distance covered by water waves or the wavelength of water wave, [tex]d=2\ m[/tex]
The water waves on a lake goes by a piece of floating cork that bobs up and down one complete cycle each second, t = 1 s
The speed of the wave is equal to the distance covered divided by total time taken i.e.
[tex]v=\dfrac{d}{t}[/tex]
v = 2 m/s
So, the speed of the wave is 2 m/s. Hence, this is the required solution.
The speed of the 2-m long water waves is determined using the formula Speed = Wavelength × Frequency. With a wavelength of 2 m and a frequency of 1 Hz, the speed of the waves is 2 m/s.
The speed of a wave is calculated by multiplying its wavelength by its frequency. In the case of a 2-m long water wave and a cork bobbing up and down once every second, the frequency of the wave is 1 cycle per second (this is also known as 1 hertz).
To find the speed of the wave, we use the formula:
Speed = Wavelength × Frequency
Speed = 2 m × 1 Hz = 2 m/s
Therefore, the speed of the water waves on the lake is 2 meters per second.