When Velma’s rocket is moving with 0.75c speed and observing the tip of the laser beam to move away from him at speed c, then Velma should observe this laser beam to move past her at a speed of 0.25C.
What is a Rocket?A rocket is a vehicle that accelerates without using the air around it by using jet propulsion. A rocket engine's reaction to high-speed exhaust is what gives it power. A rocket can fly in the vacuum of space because its engines are totally powered by fuel carried inside the craft.
What is a laser beam?A laser is a device that produces light using an optical amplification technique based on the electromagnetic radiation's stimulated emission.
According to the predictions of Einstein's relativity time dilates in a gravitational field which results in the above outcome.
Hence, when Velma’s rocket is moving with 0.75c speed and observing the tip of the laser beam to move away from him at speed c, then Velma should observe this laser beam to move past her at a speed of 0.25C
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Two pure tones are sounded together and a particular beat frequency is heard. What happens to the beat frequency if the frequency of one of the tones is increased?.
Since it is unclear which of the two frequencies is being raised, the beat frequency will rise if the frequency of the higher-frequency note is raised. On the other hand, if the frequency of the lower frequency note is raised, the beat frequency decreases.
what is frequency?
A recurring event's frequency is measured by how many times it occurs in a unit of time. To emphasize distinctions with spatial and angular frequencies, respectively, it is also sometimes referred to as ordinary frequency or temporal frequency.
Frequency is an essential property for characterizing the temporal rate of change found in oscillatory and periodic phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light, in science and engineering.
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Since it is unclear which of the two frequencies is being raised, the beat frequency will rise if the frequency of the higher-frequency note is raised. On the other hand, if the frequency of the lower frequency note is raised, the beat frequency decreases.
What is frequency?
A recurring event's frequency is measured by how many times it occurs in a unit of time. To emphasize distinctions with spatial and angular frequencies, respectively, it is also sometimes referred to as ordinary frequency or temporal frequency.
Frequency is an essential property for characterizing the temporal rate of change found in oscillatory and periodic phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light, in science and engineering.
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what is the magnitude of the acceleration of a skydiver who is currently falling at one-fifth his eventual terminal speed?
G = 9.81 m/s2 is the acceleration caused by gravity. The skydiver's acceleration, who is currently descending at a speed that is one-fifth of his ultimate terminal speed, is 3.5316.
What is an explain acceleration?Acceleration: the rate at which the speed and direction of a moving object vary over time. A object and item moving straight forward is propelled when it increases or depreciates.
Is zero acceleration possible?Acceleration is a component of velocity profile. As a result, velocity must remain constant if accelerations are zero. That constant, however, might be anything, such as 5 m/s. Additionally, zero acceleration is indicated if the speed is zero .
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how fast will an electron be traveling after being ejected from the electron gun if the voltage is set to 500 v? for full credit: (1) show your work, (2) show explicitly how the units simplify, and (3) express your answer as a percentage of the speed of light. attach a separate sheet of paper if needed.
The speed of the electron ejected from the electron gun is 13.25 x 10^6 m/s
How do you define electrostatic force?
The attraction or repulsion between particles that electrostatic forces produce is due to their electric charges. In honour of French physicist Charles-Augustin de Coulomb, who first characterized the force in 1785, this force is also known as the Coulomb force or Coulomb interaction.Using Coulomb's law, one may determine the strength or force of the attraction or repulsion between two charged bodies:
F = kq1q2/r2
In this case, F is the force, k is the proportionality factor, q1 and q2 are two electric charges, and r is the separation between their centres.
Let us assum that the electron from the electron gun is ejected and accelerated in a vacuum.
Therefore if we neglect the gravitational force we see that the entire electrical potential energy is changed into kinetic energy.
According to the given informations:
Ki = initial kinetic energy of the electron = 0
Kf = final kinetic energy of the electron = mv^2/2
Ui = initial potential energy of the electron = qV
Uf = final potential energy of the electron = 0.
From the law of Conservation of energy we know,
Ki + Ui = Kf + Uf.
Putting the values we have,
0 + qV = mv^2/2 +0
qV = mv^2/2
Solving the above equation we find v,
v = √2qV/m
= √ 2 x
= √2 (−1.60×10^−19C) (−500J/C) / 9.11×1^−31kg−
= √175.6 x 10^12
= 13.25 x 10^6 m/s
Hence, the speed of the electron is 13.25 x 10^6 m/s
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you are trying to open a door that is stuck by pulling on the doorknob in a direction perpendicular to the door. if you instead tie a rope to the doorknob and then continue to pull in the same direction (i.e., perpendicular to the door) with the same force, how does the torque you exert on the door change?
The torque about the center of mass is the same as in a direction perpendicular to the door.
What is torque?The rotational equivalent of a force in physics and mechanics is called torque. Depending on the subject matter, it may also be referred to as the moment, moment of force, rotational force, or turning effect. torque symbolizes a force's ability to cause a change in the body's rotational motion around center of mass. The idea was developed as a result of Archimedes' studies on the application of levers. Similar to how a linear force pushes or pulls an object, torque is a twist about a particular axis. The ratio of the force's magnitude to the angle at which the force's line of action is perpendicular to the axis of rotation is known as the torque.
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situation where middle polarizer is rotated. suppose the middle polarizer is rotated at 100 revolutions per minute. how many times per minute will you observe the light change from bright (max intensity) to dark (min intensity)? this effect, although not normally done with mechanical rotation, is the basis for making optical modulators that are used in high-speed digital communication systems. can you please explain? thanks
When middle polarizer is rotated rotated at 100 revolutions per minute we can take following steps into consideration-
Weight the 20gm of sugar and dissolve the whole of it in 60cc of distilled water and filter the solution by keeping the filter paper in a funnel in clean beaker. We can add distilled water to make the volume of solution equal to 100 cc. This 20% solution i.e. 0.20gm/cc.Now take 50 cc of 20% solution in measuring cylinder and add 50cc distilled water to form 10% solution. Pour it in beaker labeled as 10% solution.Now take 50cc of 10% solution and add 50cc of distilled water in it to form 5% solution.This effect although not normally done with mechanical rotation, is the basis for making optical modulators that are used in high-speed digital communication systems by inserting the thermometer in solution and note down the temperature.
Remove the caps of polarimeter glass tube and measure the length of tube.
Setting up of sodium source in front of slit will be placed at the principal focus of lens of polarimeter.
[tex]Rotation=\alpha =\frac{\beta }{y}[/tex]
β is the mean angle of rotation and y means length of polarimeter tube in decimeter.
[tex]y=\frac{len. of polarimeter}{10}[/tex]
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Complete combustion of 1.0 metric ton ofcoal (assuming purecarbon) to gaseous carbon dioxide release 3.3x10¹⁰ j of heat. Convert this energy to (a) kilojoules; (b) kilocalories
Complete combustion of 1.0 metric ton of coal (assuming pure carbon) to gaseous carbon dioxide release 3.3x10¹⁰ j of heat. a) energy converted into kilojoules will be 3.3 * [tex]10^{7}[/tex] kJ
b) energy converted into kilocalories will be 7.882 * [tex]10^{6}[/tex] kcal
Heat released = 3.3x10¹⁰ j
a) 1 J = [tex]10^{-3}[/tex] kJ
3.3x10¹⁰ j = 3.3x10¹⁰ * [tex]10^{-3}[/tex] = 3.3 * [tex]10^{7}[/tex] kJ
b) 1J = 0.23885 = 2.3885 * [tex]10^{-4}[/tex] kcal
3.3x10¹⁰ j = 3.3x10¹⁰ * 2.3885 * [tex]10^{-4}[/tex] = 7.882 * [tex]10^{6}[/tex] kcal
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A solar-powered car has a kinetic energy of 110250 J. Its mass is 180 kg. Work out how fast the car is travelling
Answer:
Speed = 126 km/h
Explanation:
Given:
Wk = 110250 J - Kinetic energy of the car
m = 180 kg - Mass
________________
V - ? Speed
Wk = m·V² / 2
V = √ (2·W/m)
V = √ (2·110250 / 180) = 35 m/s or V ≈ 126 km/h
Why do telescopes have to have a good motorized drive system to move them quickly and smoothly?.
Telescopes have to have a good motorized drive system to move them quickly and smoothly so that they can continue to point at the object being observed.
Astronomers use a telescope to observe distant things. Curved mirrors are used by the majority of telescopes, including all large telescopes, to collect and concentrate light from the night sky. The original telescopes employed lenses, which were curved pieces of clear glass, to focus light. The ability of an optical telescope to gather light is its most crucial ability. This capability is solely dependent on the telescope's aperture, or the diameter of the clear objective.
The telescope has a motorized drive mechanism that drives it smoothly from east to west at precisely the same rate that Earth is rotating from west to east in order to maintain the telescope's pointing at the object being seen because Earth is revolving.
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The energy flux from the sun has a peak value of around 1500 W/m2, and solar cells are around
15% efficient. Estimate the area needed to satisfy US energy needs using solar cells, using the
estimates that there are about 350 million people in the US and that we use an average of 90
kW/person. Also assume that there are about 6 hours of "peak" sunlight per day. Answer in square
kilometers (do not put units in your answer, however).
Answer:
Power required = 3.5E8 * 9.0E4 = 3.2E13 (watts)
Power supplied = 1.5E3 * .15 * 3600 * 6 (watts / m^2) * A
= 1.5E3* .15 * 3600 * 6 = 4.9E6 * A
A = 3.2 / 4.9 * E7 = 3.2 / 4.9 * 10 = 6.5 km*2 (1 km^2 = 10E6 m^2)
Note: 1 W = 1 J / sec 1 kw = 1000 W
The area needed to satisfy US energy needs using solar cells 6.5 km²
What is energy?Energy is the ability or capability to do tasks, such as the ability to move an item (of a certain mass) by exerting force. Energy can exist in many different forms, including electrical, mechanical, chemical, thermal, or nuclear, and it can change its form.
Power required = 3.5E8 * 9.0E4 = 3.2E13 (watts)
Power supplied = 1.5E3 * .15 * 3600 * 6 (watts / m^2) * A
= 1.5E3* .15 * 3600 * 6 = 4.9E6 * A
A = 3.2 / 4.9 * E7 = 3.2 / 4.9 * 10
= 6.5 km*2
The area needed to satisfy US energy needs using solar cells 6.5 km².
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A certain car is capable of accelerating at a rate of 0. 60 m/s2. How long does it take for this car to go from a speed of 55 mi/h to a speed of 60 mi/h?.
The time taken for a car that can accelerate at a rate of 0.6 m / s² to go from a speed of 55 mi/h to a speed of 60 mi/h is 3.68 s
a = ( v - u ) / t
a = Acceleration
v = Final velocity
u = Initial velocity
t = Time
a = 0.6 m / s²
v = 60 mi / h = 26.8 m / s
u = 55 mi / h = 24.59 m / s
t = ( v - u ) / a
t = ( 26.8 - 24.59 ) / 0.6
t = 3.68 s
Acceleration is the rate of change of velocity with respect to time. If the final speed is greater than the initial speed it is called as acceleration and if the final speed is lesser than the initial speed it is called as deceleration.
Therefore, the time taken for this car is 3.68 s
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What is concave lens?
Answer:
Diverging Lens.
Explanation:
Concave lenses have at least one surface curved inside. A concave lens is also known as a diverging lens because it is shaped round inwards at the centre and bulges outwards through the edges, making the light diverge. They are used to treat myopia as they make faraway objects look smaller than they are.
determine the current magnitude and direction of flow in each of the three branches of the circuit below.
The current magnitude in each of the three branches of the circuit below are 1.25 A, 0.924 A and 0.31 A respectively
According to Ohm's law,
V = I R
V = Voltage
I = Current
R = Resistance
In loop 1,
33 I1 + 76 ( I1 - I2 ) - 48 + 20 ( I1 - I2 ) = 22
129 I1 - 96 I2 = 70 → ( 1 )
In loop 2,
76 ( I1 - I2 ) + 51 I1 + 8.5 + 42 I2 + 20 ( I1 - I2 ) = 0
- 96 I1 + 189 I2 = 56.5
I1 = ( 189 I2 - 56.5 ) / 96 → ( 2 )
Sub ( 2 ) in ( 1 ),
129 ( 189 I2 - 56.5 ) / 96 - 96 I2 = 70
( 24381 I2 - 7288.5 ) / 96 = 96 I2 + 70
24381 I2 - 7288.5 = 9216 I2 + 6720
15165 I2 = 14008.5
I2 = 0.924 A
I1 = ( 189 * 0.924 - 56.5 ) / 96
I1 = 1.25 A
I3 = I1 - I2
I3 = 1.25 - 0.924
I3 = 0.31 A
Therefore, the current magnitude in each of the three branches of the circuit below are:
I1 = 1.25 AI2 = 0.924 AI3 = 0.31 AThe given question is incomplete. The complete question is:
Determine the current magnitude and direction of flow in each of the three branches of the circuit below. The circuit is shown in the image attached.
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The larger the frequency of a photon of light, the _______ the energy of the photon.
The larger the frequency of a photon of light, the lower the energy of the photon.
The energy of a photon is proportional to its electromagnetic frequency. The energy of a photon depends on its wavelength in such a way that its energy is inversely proportional to its wavelength. The higher the frequency of photon energy, the greater its energy.
The energy carried by a single photon is referred to as photon energy. The amount of energy is proportional to the electromagnetic frequency of the photon and thus inversely proportional to the wavelength. The higher the frequency of a photon, the greater its energy. The longer the wavelength of a photon, the lower its energy. Frequency is defined as the number of complete wavelengths in a given unit of time. The frequency and energy (E) of a wavelength decrease as its size increases.
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A certain liquid sample has a volume of 14. 7 ml and a mass of 22. 8 grams. Calculate the density.
The density of the liquid sample is 1.52 g/ml.
Density is the substance's mass consistent with the unit of quantity. The symbol most customarily used for density is ρ, despite the fact that the Latin letter D can also be used. Density is the size of ways tightly a cloth is packed together. it's far defined as the mass consistent with unit quantity.
ρ = m/V, wherein ρ is the density, m is the mass of the item and V is the quantity of the object.
Calculation:-
Density = mass/volume
= 22.8/14.7 g/ml
= 1.52 g/ml
The density is of two types, one is absolute density, and the alternative is relative density. Relative density is also called unique gravity, which is the ratio of the density of a material to the density of a reference material. typically, the reference fabric is water.
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A ball has a mass of 50g and is revolving at the end of a string in a circle with a radius of 40cm. The Ball moves with a speed of 2.5m/s, or one revolution per second. What is the horizontal component of the tension needed to produce this acceleration (in N)?
0.781 N is the horizontal component of the tension needed to produce this acceleration.
F=ma
T=ma
m= mass=0.05
a= centripetal acceleration =15.6
T=ma
T=0.05×15.6
T=0.781 N
When pressures on opposing ends are tugging on a rope, thread, wire, or something similar, tension is a contact force communicated through it. For instance, the rope attaching a tire swing to a limb of a tree is under strain. Gravity pulls the rope downward, while the upward pull is caused by a branch that is resisting the rope's tug tension, which is just a pulling force. A slack rope has no tension when one pushes on it. As a result, in a free-body diagram, the force of tension must always be shown in the direction that the string is pulling the item.
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When the current in the wire is decreasing the oppose magnitude of the magnetic flux in the loops is _____. Increasing support Induced currents in the loops and the forces exerted on them are directed so they _____ this change
When the current in the wire is decreasing the oppose magnitude of the magnetic flux in the loops is Decreasing. Increasing support Induced currents in the loops and the forces exerted on them are directed so they Oppose this change.
The above statement was proved in Ampere's Circuital Law. According to the law the Current induced is directly proportional to the magnetic flux in the loops. So increasing the current would definitely oppose the change of decreasing the current.
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a force of 20 n is directed at an angle of 609 above the x-avis. a second force of 20 n is directed at an angle of 60 below the x-axis. what is the vector sum of these toro forces?
20 N , in +x direction is the vector sum of these Toro forces.
What is force?The word "force" has a specific meaning in science. At this level, calling a force a push or a pull is entirely appropriate. A force is not something an object "has in it" or that it "contains." One thing experiences a force from another. There are both living things and non-living objects in the concept of a force.Force is used to describe a body's tendency to modify or change its state as a result of an external cause. When force is applied, the body can also alter its size, shape, and direction. kicking a ball, pushing and pulling on the door, or kneading dough are a few examples. The newton, abbreviated N, is the SI unit of force.To learn more about forces from the given link :
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Two rods are made of the same kind of steel and have the same diameter. A force of magnitude F is applied to each end of each rod. Compared to the rod of length L, the rod of length 2L has
Compared to the rod of length L, the rod of length 2L has The same stress and same strain.
Since we know that Tensile Stress is determined by the relation :
Tensile Stress = [tex]\frac{F}{A}[/tex]
Where F is the force applied and A is the circular area, which will definitely remain same for both of the rods as they have same diameter.
aslo the Tensile Strain, which is dependent on the young's modulus and stress which would remain same for both of the rods as the material used is same and the stress is alo the same.
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The reason that most seti programs choose to listen at microwave radio frequencies is that.
The reason that most SETI programs choose to listen at microwave radio frequencies is that sending information is via microwaves is the most efficient way.
What is a microwave?Microwave radiation has wavelengths between one metre and one millimeter, which correspond to frequencies between 300 MHz and 300 GHz, respectively.
What is a radio frequency?In the frequency range between about 20 kHz and about 300 GHz, radio frequency is the rate at which an alternating electric current or voltage, a magnetic, electric, or electromagnetic field, or a mechanical system, oscillates.
The most energy-efficient method of sending information is via microwaves. Because of this, the majority of SETI programmes opt to listen at microwave radio frequencies.
Hence , the reason that most SETI programs choose to listen at microwave radio frequencies is that sending information is via microwaves is the most efficient way.
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The Earth moves in a nearly perfect circle around the Sun. Assume the speed stays
constant. Is Earth accelerating?
Answer:
yes
Explanation:yes
Answer:
Yes
Explanation:
Earth is accelerated around the sun
A ball is dropped from rest from a height of 1.88 m. How long does it take to strike the ground? (use g = 10 m/s2)
A. 0.43 seconds
B. 0.38 seconds
C. 0.61 seconds
D. 0.19 seconds
It will take the ball 0.61 second of time to strike the ground. Option C is the right answer.
Motion Under GravityThe motion of an object under gravity is the object' s vertical motion under the influence of acceleration due to gravity.
Given that a ball is dropped from rest from a height of 1.88 m. Since the ball was dropped,
Initial velocity u = 0The height h = 1.88 mAcceleration due to gravity g = 10 m/s²Time t = ?How long it takes, that is, the time taken to strike the ground can be calculated by using the formula
h = ut + 1/2gt²
Substitute all the parameters into the formula
1.88 = 0 + 1/2 × 10 × t²
1.88 = 5t²
t² = 1.88/5
t² = 0.376
t = √0.376
t = 0.61 s
Therefore, the time taken for the ball to strike the ground is 0.61 s
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summarize the energy transformations that occur when a tennis racket hits a tennis ball.
Answer:
See explanation...
Explanation:
the kinetic energy of the moving tennis racket is converted (not transformed) to the kinetic energy of the tennis ball.
Since not much description is given here, I didn't include the potential energy of the tennis ball. But in normal cases, the kinetic energy of the tennis ball would be converted to potential energy of the ball, and it falls back down after some time (because of gravity) and slows down due to friction on earth- kinetic energy is converted to heat energy because of friction.
other types of energy are not stated since they can be negligible.
alice prevents on object from intersecting with another object. that is two objects cannot occupy the same space. true or false
All matter has volume but also impenetrability because it occupies space, and two objects cannot occupy a same space at the same time.
What matters is this?An object that occupies space and has inertia is said to be matter, which is composed of numerous types of particles. The different kinds of particles each get a unique mass and size, according to the fundamentals of current physics. The electron, proton, and neutron are three of the most prevalent instances of material particles.
What are matter's characteristics, exactly?Anything with mass and physical space is considered matter. Matter underlies everything that you can see and touch. The three primary types of matter are gases, liquids, and solids. It also possesses qualities that can be expressed through conductivity, magnetism, solubility, density, etc.
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Who was awarded the highest-ever rank in the u. S. Armed forces? george patton douglas macarthur george washington dwight d. Eisenhower.
He attained the rank of military officer during the combat on the Western Front in World War I and was once more nominated for a Medal.
How do you define forces?The pushing or push on a phalanx item alters its speed. An unseen factor is an agent that possesses the power to change the resting or traveling position of a body. It has a direction as well as a quantity.
What kind of force is it?Contact forces and non-forces are two different kinds of forces. Nuclear force, gravitational force, frictional force, magnetic force, electrostatic force, spring force, and others are a few examples of forces.
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Hi! Can someone help me figure out the Fg(N) column? I don't know how to plug my information into the formula.
The gravitational force (Fg) for the first column is 1.96 x 10⁷ N.
The gravitational force (Fg) for the second column is 2.48 x 10⁷ N.
The gravitational force (Fg) for the third column is 3.24 x 10⁷ N.
The gravitational force (Fg) for the fourth column is 4.4 x 10⁷ N.
The gravitational force (Fg) for the fifth column is 6.36 x 10⁷ N.
The gravitational force (Fg) for the sixth column is 9.94 x 10⁷ N.
The gravitational force (Fg) for the seventh column is 1.77 x 10⁸ N.
What is Newton's law of universal gravitation?
Newton's law of universal gravitation states that every two objects in the universe attracts each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between the masses.
F = Gm₁m₂/r²
F = (Gm₁m₂) x 1/r²
where;
m₁ is the mass of the first objectm₂ is the mass of the second objectG is universal gravitation constantr is the distance between the two massesThe gravitational force (Fg) for the first column is calculated as;
Fg = (Gm₁m₂) x 1/r²
Fg = (6.626 x 10⁻¹¹ x 4 x 10⁹ x 6 x 10⁹) x 1/r²
Fg = 1.59 x 10⁹ x 0.0123
Fg = 1.96 x 10⁷ N
The gravitational force (Fg) for the second column is calculated as;
Fg = (Gm₁m₂) x 1/r²
Fg = 1.59 x 10⁹ x 0.0156
Fg = 2.48 x 10⁷ N
The gravitational force (Fg) for the third column is calculated as;
Fg = (Gm₁m₂) x 1/r²
Fg = 1.59 x 10⁹ x 0.0204
Fg = 3.24 x 10⁷ N
The gravitational force (Fg) for the fourth column is calculated as;
Fg = (Gm₁m₂) x 1/r²
Fg = 1.59 x 10⁹ x 0.0277
Fg = 4.4 x 10⁷ N
The gravitational force (Fg) for the fifth column is calculated as;
Fg = (Gm₁m₂) x 1/r²
Fg = 1.59 x 10⁹ x 0.0400
Fg = 6.36 x 10⁷ N
The gravitational force (Fg) for the sixth column is calculated as;
Fg = (Gm₁m₂) x 1/r²
Fg = 1.59 x 10⁹ x 0.0625
Fg = 9.94 x 10⁷ N
The gravitational force (Fg) for the seventh column is calculated as;
Fg = (Gm₁m₂) x 1/r²
Fg = 1.59 x 10⁹ x 0.1111
Fg = 1.77 x 10⁸ N
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A 100gm GOLF BALL MOVING WITH A VELOCITY OF 20m/s COLLIDES WITH A 8kg STEEL BALL AT REST. IF THE COLLISION IS ELASTIC, COMPUTE THE VELOCITIES BOTH THE BALLS AFTER COLLISION
Answer:
Golf ball ([tex]0.1\; {\rm kg}[/tex]): approximately [tex](-19.506)\; {\rm m\cdot s^{-1}}[/tex] (backwards).
Steel ball ([tex]8\; {\rm kg}[/tex]): approximately [tex]0.49383\; {\rm m\cdot s^{-1}}[/tex] (forward.)
Explanation:
Apply unit conversion and ensure that the unit of all mass are in kilograms: [tex]100\; {\rm g} = 0.1\; {\rm kg}[/tex].
In an elastic collision, both momentum [tex]p = m\, v[/tex] and kinetic energy [tex]\text{KE} = (1/2)\, m\, v^{2}[/tex] are conserved. Momentum of the two balls before the collision are:
[tex]0.1\; {\rm kg} \times 20\; {\rm m\cdot s^{-1}} = 2\; {\rm kg \cdot m \cdot s^{-1}}[/tex] for the golf ball, and [tex]8\; {\rm kg} \times 0\; {\rm m\cdot s^{-1}} = 0\; {\rm kg \cdot m\cdot s^{-1}}[/tex] for the steel ball initially at rest.Hence, the total momentum of the two balls was [tex]2\; {\rm kg \cdot m\cdot s^{-1}}[/tex] before the collision and (by conservation) will still be [tex]2\; {\rm kg \cdot m\cdot s^{-1}}\![/tex] after the collision.
Kinetic energy of the two balls before the collision are:
[tex](1/2)\times 0.1\; {\rm kg} \times (20\; {\rm m\cdot s^{-1}})^{2} = 200\; {\rm kg \cdot m^{2} \cdot s^{-2}}[/tex] for the golf ball, and[tex](1/2) \times 8\; {\rm kg} \times (0\; {\rm m\cdot s^{-1}})^{2} = 0\; {\rm kg \cdot m\cdot s^{-1}}[/tex] for the steel ball initially at rest.Thus, the total kinetic energy of the two balls will be [tex]200\; {\rm kg \cdot m^{2} \cdot s^{-2}}[/tex] before and after the collision.
Let [tex]m_{a}[/tex] and [tex]v_{a}[/tex] denote the mass and velocity of the golf ball after collision; [tex]m_{a} = 0.1\; {\rm kg}[/tex].
Let [tex]m_{b}[/tex] and [tex]v_{b}[/tex] denote the mass and velocity of the steel ball after collision; [tex]m_{b} = 8\; {\rm kg}[/tex].
Total momentum after the collision shall be [tex]2\; {\rm kg \cdot m\cdot s^{-1}}\![/tex]. Thus:
[tex]m_{a}\, v_{a} + m_{b}\, v_{b} = 2\; {\rm kg \cdot m\cdot s^{-1}}[/tex].
Total kinetic energy after the collision shall be [tex]200\; {\rm kg \cdot m^{2} \cdot s^{-2}}[/tex]. Thus:
[tex]\displaystyle \frac{1}{2} \, m_{a}\, v_{a} + \frac{1}{2}m_{b}\, v_{b} = 200\; {\rm kg \cdot m^{2}\cdot s^{-2}}[/tex].
Assume that the unit of [tex]v_{a}[/tex] and [tex]v_{b}[/tex] are both "meters per second" ([tex]{\rm m\cdot s^{-1}}[/tex].) Combine and solve this system of two equations and two variables:
[tex]\left\lbrace\begin{aligned}&0.1\, v_{a} + 8\; v_{b} = 2 \\ &\frac{1}{2}\, {v_{a}}^{2} + 4\, {v_{b}}^{2} = 200\end{aligned}\right.[/tex].
Rewrite the first equation to obtain [tex]v_{a} = 20 - 80\, v_{b}[/tex]. Substitute this equation into the second one to eliminate [tex]v_{a}[/tex]:
[tex]\displaystyle \frac{1}{2}\, (20 - 80\, v_{b})^{2} + 4\, v_{b}^{2} = 200[/tex].
Solve this equation for [tex]v_{b}[/tex]:
[tex]324\, {v_{b}}^{2} - 160\, v_{b} = 0[/tex].
There are two solutions to this quadratic equation: [tex](40 / 81)[/tex] and [tex]0[/tex]. Note that the velocity of the steel ball must be non-zero right after the collision. Hence, [tex]v_{b} \ne 0[/tex]. Therefore, the only possible value for [tex]v_{b}[/tex] will be [tex](40 / 81)\![/tex], which is approximately [tex]0.49383\; {\rm m\cdot s^{-1}}[/tex].
Substitute [tex]v_{b} = (40 / 81)[/tex] back into the first equation of the system and solve for [tex]v_{a}[/tex]: [tex]v_{a} = 20 - 80\, v_{b} \approx (-19.506)\; {\rm m\cdot s^{-1}}[/tex]. Note that the velocity of the golf ball [tex]v_{a}\![/tex] is negative since the golf ball is travelling backwards, opposite to its initial direction of motion.
In other words, the velocity right after collision will be approximately [tex](-19.506)\; {\rm m\cdot s^{-1}}[/tex] (backwards) for the golf ball and approximately [tex]0.49383\; {\rm m\cdot s^{-1}}[/tex] (forwards) for the steel ball.
Since the drag force is proportional to the square of speed, what can you do to improve your car’s gas mileage?.
Since the drag force is proportional to the square of speed, to improve your car’s gas mileage, you should drive in lower speed.
The drag force is a force experienced by an object when it is moving through a fluid. The fluid can be air, water, gas or liquid.
Some of the factors that affect the drag force are the speed of the object and its aerodynamic. The relation between drag force and velocity is given by:
F = 1/2 . CρAv²
Where:
C = drag coefficient
ρ = fluid density
A = area of the object that facing the fluid
v = velocity
Therefore, the drag force is directly proportional to the square of object's velocity, or
F ∝ v²
The power of car should overcome this drag force. The relation between power and force is given by:
P = F . v
Since F is proportional to v², then
P ∝ v³
Thus, we can conclude to use less power, which means to improve gas mileage, you should drive in lower speed.
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HELP HELP!!!!!!!!!!!!!!!!
Magnetic force is used in: A door catch or a latch on kitchen cabinet
and A directional compass.
Electric force is used in: Two shocks stacks together coming out of a clothes dryers and An air filter that traps dust and ion particle.
What is magnetic force?Electromagnetic force is a result of charge motion, which also produces magnetic force. We know that a moving charge creates a magnetic field around itself. In this situation, the magnetic force can be thought of as a force that results from magnetic fields interacting.
A door catch or a latch on kitchen cabinet and a directional compass are example of use of magnetic field.
Two shocks stacks together coming out of a clothes dryers and an air filter that traps dust and ion particle are example of use of etectric force.
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For a 500 gram ball traveling around a 40 cm diameter circle, calculate the angular speed of the ball if it takes 0.5 seconds to make one complete revolution. A. 1.6 π rad/s B, 0.4 π rad/s C. 4 π radis
The angular speed of the ball if it takes 0.5 seconds to make one complete revolution, is Option C. 4 π radius.
Angular speed is the velocity of the object in rotational motion. Distance traveled is represented as θ and is measured in radians. The time taken is measured in terms of seconds. therefore, the angular velocity is articulated in radians consistent with seconds or rad/s.
Angular velocity or rotational velocity, additionally called angular frequency vector, is a pseudovector illustration of how rapidly the angular function or orientation of an item modifications with time.
Calculation:-
The angluar speed ω = ΔΕ/ΔT
= (2π - 0)/0.5
= 4π radis
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The American bullfrog (Rana catesbeiana) can jump a distance of
nearly 15 times its length! If a bullfrog starts on a horizontal log and
leaps with a velocity of 4.40 m/s at an angle of 37.0° to the horizontal,
what distance can it cover?
Answer:
Approximately [tex]1.90\; {\rm m}[/tex] (assuming that [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex] and that air resistance on the bullfrog is negligible.)
Explanation:
It is given that the initial velocity [tex]u[/tex] is at an angle of [tex]\theta = 37.0^{\circ}}[/tex] above the horizontal. Therefore:
Initial vertical velocity: [tex]u_{y} = u\, \sin(\theta) \approx 2.64799\; {\rm m \cdot s^{-1}}[/tex].Initial horizontal velocity: [tex]u_{x} = u\, \cos(\theta) \approx 3.51400\; {\rm m \cdot s^{-1}}[/tex].
If air resistance on the bullfrog is negligible, final vertical velocity right before landing will be the opposite of the initial vertical velocity:
[tex]v_{y} = (-u_{y}) = (-2.64799)\; {\rm m\cdot s^{-1}}[/tex].
Change in vertical velocity:
[tex](v_{y} - u_{y}) = (-2.64799) \; {\rm m\cdot s^{-1}} - 2.64799 \; {\rm m\cdot s^{-1}} \approx (-5.29598)\; {\rm m\cdot s^{-1}}[/tex].
Vertical acceleration of the bullfrog will be [tex]a = (-g) = (-9.81)\; {\rm m\cdot s^{-2}}[/tex] while the frog is in the air. Therefore, time required for the velocity to change will be:
[tex]\begin{aligned} t &= \frac{v_{y} - u_{y}}{a_{y}} \\ &= \frac{v_{y} - u_{y}}{(-g)} \\ &\approx \frac{(-5.29598)\; {\rm m\cdot s^{-1}}}{(-9.81)\; {\rm m\cdot s^{-2}}} \\ &\approx 0.53985\; {\rm s}\end{aligned}[/tex].
If air resistance on the bullfrog is negligible, horizontal velocity will be constant: [tex]v_{x} = u_{x} \approx 3.51400\; {\rm m\cdot s^{-2}}[/tex]. After [tex]t \approx 0.53985\; {\rm s}[/tex] in the air, the horizontal displacement of the bullfrog will be:
[tex]\begin{aligned}x_{x} &= v_{x}\, t \\ &\approx 3.51400\; {\rm m\cdot s^{-1}} \times 0.53985\; {\rm s} \\ &\approx 1.90\; {\rm m} \end{aligned}[/tex].
Therefore, this bullfrog will cover a distance of approximately [tex]1.90\; {\rm m}[/tex].