Answer:W hen the car suddenly stops due to either braking or crashing, inertia will force the passengers or any other objects to keep moving forward. And since the force of inertia increases with the speed, the motion can varied from a light erk to a more serious crash.
Explanation:
a pendulum with a length of 1 m, is taken to a planet, where its period is 2 s. the acceleration due to gravity on the other planet is most nearly –use the formula where the period is squared and solve for g. g
The acceleration due to gravity on the other planet is most nearly 0.25 m/s².
Equation :As it is given the length of the pendulum is 1 m
So, the time period is 2s
Now the given are putting in the formula of acceleration
a = Δv / Δt
a = d/t / Δt
So,
a = 1/2 / 2
a = 0.25 m/s²
Hence, the acceleration due to gravity on the other planet is most nearly 0.25 m/s².
Gravity :The force that pulls objects toward the center of a planet or other body is called gravity. All of the planets are kept in orbit around the sun by gravity. The amount of mass between you and the Earth's center determines how much gravity there is because the material that makes up the Earth's interior is not uniform.
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During Piaget's sensorimotor stage, children acquire a
1) theory of mind.
2) concept of conservation.
3)sense of object permanence.
4) capacity for abstract reasoning
3) sense of object permanence is the condition that the children acquire during the Piaget's sensorimotor stage and is identified during the conscious interaction.
What is the sensorimotor development theory proposed by Piaget?The sensorimotor stage, according to Piaget’s theory of cognitive development, lasts during the first two years of a child’s existence. Your youngster will learn: to repeat enjoyable behaviors throughout this stage.
To consciously interact with objects and investigate their surroundings. To plan actions in order to accomplish a given objective.
What is Piaget’s conservation concept?The Swiss psychologist Jean Piaget was the first to examine conservation as a logical reasoning skill in young children.
To put it simply, being able to preserve means understanding that a quantity remains unchanged when changed (by being stretched, cut, elongated, spread out, shrunk, poured, etc.)
Stage of SensorimotorAccording to Piaget, infants are only conscious of what is directly in front of them during the early stages.
They concentrate on what they are doing, what they observe, and their bodily interactions with the surroundings. They are continually conducting experiments because they are unsure of how things during sensorimotor stage will react.
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A 7. 50g-bullet has a speed of 555 m/s as it leaves the muzzle of a rifle. If the barrel of the rifle is 0. 950 m, what is the average force exerted on the bullet by the ammunition?.
The average force exerted on the bullet by the ammunition is 1215.88N
From the question above, It is given that,
Mass of the bullet, m = 7.50 g
Initial speed of the bullet, u = 0
Final speed of the bullet, v = 555 m/s
We need to find the force exerted on the bullet while it was traveling down the 0.950m length of the barrel of the rifle. Let:
a is the acceleration of the bullet. So,
v² - u² = 2ad
v² = 2ad
a = v²/2d
a = 555²/2*0.950
a = 162118.42m/s²
Let F be the force exerted. It is given by:
F = Ma
F = 7.5 * 10⁻³ * 162118.42
F = 1215.88N
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F = 1590.87 N
So, the constant force exerted on the bullet is 1590.87 N. Hence, this is the required solution.
romeo (75.0 kg) entertains juliet (57.0 kg) by playing his guitar from the rear of their boat at rest in still water, 2.70 m away from juliet, who is in the front of the boat. after the serenade, juliet carefully moves to the rear of the boat (away from shore) to plant a kiss on romeo's cheek. what if? if the lovers both walk toward each other and meet at the center of the boat, how far (in m) and in what direction does the boat now move?
If the lovers both walk toward each other and meet at the center of the boat, at 0.725m and since romeo has greatest mass of the boat moves towards him away from the shore.
Calculating the system's center of mass should come first
X_{CM}=\sum_{n=1}^{n}\frac{X_n*M_n}{M_n}
Romeo, Juliet, and the boat's masses are multiplied by each coordinate's x value, and the result is then divided by the sum of all the masses.referring to Juliet's position as an example.
X_{CM}=\frac{57Kg\times0m+75Kg\times 2.7m+75kg\times1.35m}{57kg+75kg+75kg}
X_{CM}=\frac{307.395kg.m}{207kg}=1.485m
When internal forces are in play, the center of mass remains constant.
After the maneuver, the center of mass shifts in relation to the back of the boat, but it stays at the same distance from the shore.
X_{CM}=\frac{75\times1.35m+(75kg+57kg)\times2.70m}{207kg}=
X_{CM}=\frac{457.65}{207kg}=2.210m
The boat moves toward the shore with this displacement.
0.725m
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In the free-body diagram, the magnitude of the normal force is 35 N, the friction force is 15 N, and the net force is 70 N. What is the magnitude of the applied force? Explain how you came to your answer in one to two sentences.
The applied force on the object is 85 N. This answer was obtained by considering forces acting in horizontal direction.
Also the concept of net force by Newton's second law of motion was used to obtain the applied force (85 N).
What is applied force?The applied force on an object is the external force applied or exerted on an object.
The applied force on the object is determined by calculating the net force on the using Newton's second law of motion.
F(net) = F(app) - F(fric)
where;
F(net) is the net forceF(app) is the applied forceF(fric) is the frictional force70 N = F(app) - 15 N
F(app) = 70 N + 15 N
F(app) = 85 N
Thus, we can conclude that the applied force must be obtained from the forces acting on horizontal direction since force of friction exits only when an object is in horizontal motion.
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The law of superposition states that in an undeformed sequence of sedimentary rocks the oldest rocks will be at the bottom while the youngest will be on top. Notice the word undeformed in the last sentence: that means the naturally occurring rock layers are somehow altered, causing confusion or gaps in the geologic record. Changes to the rock strata can occur due to a variety of geologic events. Which geologic event is INCORRECTLY identified?
A) D. Intrusion of magma at Earth's surface.
B) B. Folding of layers due to compression.
C) C. Unconformity showing erosion and deposition.
D) A. Faulting due to stress and fracture.
The geologic event that is incorrectly identified is option A) D. Intrusion of magma at Earth's surface.
What is the law of superposition about?According to the Law of Superposition, the oldest rocks will be at the bottom and the youngest at the top of a sequence of sedimentary strata that has not undergone any deformation.
If you were to imagine a river dumping sand into an ocean, the sand would eventually pour out onto the ocean floor and settle on top of the seafloor. After the seafloor's sand had already been laid down, this sand was added.
Note that the events are as follows:
Subsidence and deposit layer Folding of layers as a result of compression.Unconformity showing erosion as well as deposition.Faulting as a result of stress and fracture.Therefore, option A is incorrectly labeled because it is one that is supposed to be labeled as subsidence and deposit layer of geologic event.
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the following statements are related to household circuits and electrical safety. determine whether each statement is true or false. hint (a) circuit breakers are wired in series with the outlets they protect. true false (b) a circuit breaker rated at 20 a provides a constant current of 20 a to each outlet in the circuit. true false (c) three-wire electrical cords help prevent dangerous electrical shocks by grounding the case of a device. true false
(a) This is true since a circuit breaker is linked in series with the electric device in order to interrupt the circuit if the current flow exceeds a predetermined (rated) limit.
(b) False, because the circuit breaker only permits the maximum current that has been rated for it; when the circuit exceeds that limit, it is broken. There's no issue with continuous current.
(c) The earthing terminal is present.
Circuit breakers: what are they?A circuit breaker is a type of electrical switch used to guard against short circuits, overloads, and over currents that could harm an electrical circuit. Its primary purpose is to halt current flow when protective relays identify a defect.
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must have an opening of sufficient size to allow free movement of water at the bottom of the tank and movement of air at the top during rapid filling or unloading
During dump site operations, the tank baffles must have an opening of sufficient size to allow free movement of water at the bottom of the tank and movement of air at the top during rapid filling or unloading.
What is a land filling?Land filling can be defined as a biological method that is typically adopted for the effective and efficient treatment of waste products (garbage).
The types of land filling.Generally speaking, there are different types of land filling and these include the following:
Green waste landfills.Municipal solid waste landfills.Hazardous waste landfills. Industrial waste landfills. Dumping waste landfills.In conclusion, the dumping waste landfill involves the dumping of solid waste products (garbage) into the landfill site through the use of trucks.
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Complete Question:
During dump site operations, the _____ must have an opening of sufficient size to allow free movement of water at the bottom of the tank and movement of air at the top during rapid filling or unloading.
suppose a uniform slender rod has length l and mass m . the moment of inertia of the rod about about an axis that is perpendicular to the rod and that passes through its center of mass is given by icm
The moment of inertia of the rod with respect to a parallel axis through one end of the rod is Ml^2/3
To calculate inertia, according to the parallel axis theorem:
[tex]I=I_{cm}+Md^{2}[/tex]
Where,
I is the inertia from an axis that is at distance d from the center of mass and Icm is the inertia when the axis passes through the center of mass.
The distance d = l/2
Now to calculate inertia
[tex]I=I_{cm}+Md^{2}[/tex]
[tex]I=\frac{Ml^{2}}{12} + M\frac{1}{2}\\I=\frac{Ml^{2}}{12}+\frac{Ml^{2}}{4}\\I=\frac{Ml^{2}+3Ml^{2}}{12}\\I=\frac{Ml^{2}}{3}[/tex]
The moment of inertia of the rod with respect to a parallel axis through one end of the rod is Ml^2/3.
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A baseball is thrown horizontally off a cliff with a velocity of 15.9 m/s. It lands 35.9 meters away. Assuming that gravity is 9.8 m/s2, how high (dy) is the cliff?
The height of the cliff, given that the baseball landed 35.9 m away is 25.03 m
How to determine the timeFirst, we shall determine the time taken for the baseball to land. This can be obtained as follow:
Horizontal velocity (u) = 15.9 m/sHorizontal distance (s) = 35.9 mTime (t) =?s = ut
35.9 = 15.9 × t
Divide both sides by 15.9
t = 35.9 / 15.9
t = 2.26 s
How to determine the height of the cliffWe can obtain the height of the cliff as follow:
Acceleration due to gravity (g) = 9.8 m/s²Time (t) = 2.26 sHeight (h) =?h = ½gt²
h = ½ × 9.8 × 2.26²
h = ½ × 9.8 × 5.1076
h = 25.03 m
Thus, we can conclude that the cliff is 25.03 m high
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a baseball is thrown straight upwards from the ground and undergoes a free fall motion as it rises towards its highest point. What changes , if any ,would be observed of the velocity and the acceleration of the baseball as it rises towards its highest point?
The baseball thrown upwards will experience change in its velocity while its acceleration will be constant.
What is upward motion?Upward motion is a type of motion in which an object moves upwards against force of gravity.
During the upward motion of an object, its vertical velocity decreases as the object moves upwards due to opposing force of gravity. The velocity of the object eventually becomes zero when the object reaches maximum height.
As the object begins to move downwards, the velocity begins the increase and eventually become maximum before the object hits the ground.
The acceleration of the object during the upward motion is always point downwards and does not change.
Thus, we can conclude that if an object moving upwards, its velocity will change while the acceleration will not change.
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A person on a cruise ship is doing laps on the promenade deck. On one portion of the track the person is moving north with a speed of 3.9 ms relative to the ship. The ship moves east with a speed of 12 ms relative to the water.
The resultant speed of the person on the cruise ship is 12.62 m/s.
What is resultant speed?The resultant speed of an object is the single speed which can effectively represent two or more speed of the object.
The magnitude of the resultant speed of the person on a cruise ship is calculated as follows;
Vr² = Va² + Vb²
where;
Vr is the resultant speed of the personVa is the speed of the person to the northVb is the speed of the person to the eastSubstitute the value of the north speed and east speed to determine the resultant speed of the person on the ship.
Vr = √Va² + Vb²
Vr = √[(3.9 m/s)² + (12 m/s)² ]
Vr = 12.62 m/s
Thus, for a person on a cruise ship is doing laps on the promenade deck at a speed of 3.9 m/s to the north and the speed of the ship 12 m/s to the east, the resultant speed is 12.62 m/s.
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The complete question is below:
person on a cruise ship is doing laps on the promenade deck. On one portion of the track the person is moving north with a speed of 3.9 ms relative to the ship. The ship moves east with a speed of 12 ms relative to the water. Find the resultant speed of the person
A student writes an expression for the momentum (P) of of mass (m), with total energy (E) and considering the body duration of time (t) as P = √2 mE/t Check it's correctness on dimensional analysis.
Answer:
The expression written for the momenum of a body is dimensionally incorrect.
Explanation:
P = momentum, m = mass, E = Energy & t = time Now, we know: Dimensional formula of momentum (p) = [MLT-1] Dimensional formula of mass (m) = [M] Dimensional formula of Energy (E) = [ML2T-2] Dimensional formula of time (t) = [T] Here, Dimensional formula of LHS = [MLT-1] And, Dimensional formula of RHS = 2/M212T-21 [T] -=√2 M²LT 3]=[MLT/2] [2 is constant] 2[M] [MLT-21 [T] Since the dimensional formula of LHS # dimensional formula of RHS. [MILT-1] [MLT-3/2] hence the given relation is dimensionly incorrect
A roller coaster car, 500 kg, starting at a point 80 m above the lowest point of the track. The car travels from 8 m·s -1 down the steep track. There is no friction.
9.1 What is the total energy of the roller coaster car at the top of the track?
9.2 What is the total energy of the system at the base of the rollercoaster
track?
9.3 What is the velocity of the car at a height of 30 m from
the base of the roller coaster track?
9.4 What is the velocity of the car at the base of the roller coaster track?
The total energy of the roller coaster car at the top of the track is 392,000 J.
The total energy of the system at the base of the rollercoaster track is 392,000 J.
The velocity of the car at a height 30 m above the base is 25.53 m/s.
The velocity of the car at the base of the roller coaster track is 40.4 m/s.
What is the total energy of the roller coaster car?
The total energy of the roller coaster car at the top of the track is calculated as follows;
P.E = mgh
where;
m is mass of the carg is acceleration due to gravityh is heightP.E = (500 kg) x (9.8 m/s²) x (80 m)
P.E = 392,000 J
Based on the law of conservation of energy, the total energy of the rollercoaster at the top of the track is the same as that at the bottom of the track.
Thus, total energy of the system at the base of the rollercoaster track = 392,000 J.
The velocity of the car at a height 30 m above the base is calculated as follows;
v² = u² + 2gh
v² = (8)² + 2(9.8)(30)
v² = 652
v = √652
v = 25.53 m/s
The velocity of the car at the base of the roller coaster track is calculated as follows;
v² = u² + 2gh
v² = (8)² + 2(9.8)(80)
v² = 1632
v = √1632
v = 40.4 m/s
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A material through which electrons can move easily is a what
Answer:
Electrical conductors
three people pull simultaneously on a stubborn donkey. jack pulls directly ahead of the donkey with a force of 98.3 n, jill pulls with 62.5 n in a direction 45° to the left, and jane pulls in a direction 45° to the right with 117 n . (since the donkey is involved with such uncoordinated people, who can blame it for being stubborn?)
Jane and Jill are stubborn because they have opposite force directions.
We need to know about force resultant to solve this problem. The force resultant is the total net force applied to the object according to the direction. It can be written as
R = F1 + F2 + ... + Fn
where R is force resultant (net force)
From the question above, we know that
F Jack = 98.3 N
F Jill = 62.5 N
F Jane = 117 N
Assume that the direction
Jack = east
Jill = north east
Jane = south east
The Force to the north direction is
F Jill y = Fjill . cos45
F Jill y = 62.5 . √2/2
F Jane y = -F Jane . cos45
F Jane y = -117 . √2/2
Jane and Jill are stubborn because they have opposite directions.
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The magnitude of the net force the people exert on the donkey is 239 N.
Net force :
[tex]F_{n}[/tex]= [tex]F_{1}+F_{2} +F_{3}[/tex]
Now finding the x and y components of the forces F2 and F3,
[tex]F_{x}[/tex] = F1 + F2cos45°+F3sin45°
[tex]F_{x}[/tex] = 98.5 + 69.3 ×√2/2 + 125 ×√2/2
[tex]F_{x}=235.9N[/tex]
[tex]F_{y}[/tex] = -F2sin45°+F3sin45°
= −69.3 ×√2/2+ 125 ×√2/2
[tex]F_{y}[/tex] = 39.4 N
Now find the magnitude
[tex]F_{n}[/tex] = √235.9^2+39.4^2 = 239 N
The magnitude of the net force the people exert on the donkey is 239 N.
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magnetic effects involving jupiter's moon io results in an effective voltage of about 550 kv that drives a current of about 4.5 ma between io and jupiter.
Effective voltage for the Gi system
V = 550 KV = 550 * 10 3 * v
Current I = 4.5MA = 4.5 * 10 6 *
A The strength of the Lo to Jupiter current
P= VI\s= (550 * 10 ^ 3)(4.5 * 10 ^ 6)
K = Kilo = 10 3 M = Mega = 106
P = 24.75* 10 ^ 7 W
What is magnetic effects?
Moving electric charges and magnetic dipoles combine to form a magnetic field, which acts as a force field on other adjacent moving charges and magnetic dipoles. Given that it has both a magnitude and a direction, the magnetic field is a vector quantity.
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An airplane, moving at 375 ms relative to the ground, fires a missile forward at a speed of 790 m/s relative to the planewhat the speed of the relative the ground?
Answer:
1165 m/s relative to ground
Explanation:
(375 + 790 ) = 1165 m/s
particle 1 carrying -4.0 μc of charge is fixed at the origin of an xy coordinate system, particle 2 carrying 8.0 μc of charge is located on the x axis at x
The phenomenona of vectors proved.
What is vector?vector is a quantity that has two independent properties magnitude and direction.
The electric force is given by coulumb's law
F = k q₁q₂ / r²
Let's apply newtons second law in particle 3
F = F₃₁ - F₃₂
F₃₁ = k q₃q₁ / r₃₁²
F₃₂ = k q₃q₂ / r₃₂²
Let's write the values they give us
q₁ = -4.0 10⁻⁶ C
x₁ = 0
q₂ = q₃ = + 8.0 10⁻⁶ C
x₂ = 4.0 m
x₃ = -4.0 m
We look for the distances
r₃₁ = x₃ -x₁
r₃₁ = -4.0 - 0 = -4.0 m
r₃₂ = -4.0 - 4.0 = -8.0 m
Let's write the force equation
F = k q₃ (q₁ / r₃₁² + q₂ / r₃₂²)
so let's calculate
F = 8.99 10⁹ 8 10⁻⁶ (4 10-6/4 2 - 8 10-6 / 8 2)
F = 71.92 10³ (1/2 - 1/8 )10⁻⁶
F = 26.97 10-3 N
None of the charge are on the axis and therefore there are no forces on this axis.
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the current if 55C of charge pass a particular point in a circuit in 5 seconds.
The current if 55C of charge pass a particular point in a circuit in 5 seconds is 11A.
What's current?One kind of electrical charge carrier that moves as current are electrons. From negative to positive areas, current flows. The ampere is the SI unit used to measure electric current (A). One coulomb of electrical charge travelling over a given region in one second is referred to as an ampere of current.
Similar to how current is widely employed in relation to electronic circuits, voltage is also. Voltage is measured using volts (V). Similar to how current and current are related, voltage and the flow of electrons in a circuit are as well. Current is the flow of electrons, whereas voltage is the amount of force driving the flowing electrons.
At higher voltages, current flows more freely; at lower voltages, current is weaker.
Given,
Electrical charge = 55 C
Time = 5 secs
Therefore current = 55 / 5 A
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4 – Microwave Miracle Patrick believes that fish that eat food exposed to microwaves will become smarter and would be able to swim through a maze faster. He decides to perform an experiment by placing fish food in a microwave for 20 seconds. He has the fish swim through a maze and records the time it takes for each one to make it to the end. He feeds the special food to 10 fish and gives regular food to 10 others. After 1 week, he has the fish swim through the maze again and records the times for each. 1.What was Patrick’s hypothesis?
2.Which fish are in the control group?
3.What is the independent variable?
4.What is the dependent variable?
5. Look at the results in the charts. What should Patrick’s conclusion be?
The term experiment has to do with the kind of study in which the effect of a dependent variable on an independent variable is undertaken and looked into in dept.
We know that in an experiment there must be an independent variable which is being monitored and changes from time to time and there is the dependent variable which changes as the independent variable changes.
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a large fan requires a torque of 260 ft-lbs to operate at 1740 rpm. what is the minimum horsepower rating of the motor to drive the fan? if the motor is 90% efficient what is minimum input power required by the motor in kw?
Large fan torque requires of 260 ft- lbs operate at 1740 RPM.
1740 RPM = 260 1b-ft N of torque
Torque 1 b. ft = Power in HP X 5252 / Speed in RPM
Power in np =260 X 1740/5252 =86.1386 HP
n= 90% =0.9
Power input = Power in np x 0.746 /n
For input power = (86.1386*0.746)/0.9
=71.4 kw.
What is torque?
The rotating equivalent of force is torque. Depending on the subject of study, it is also known as the moment, moment of force, rotating force, or turning effect. It illustrates how a force can cause a change in the body's rotational motion. Archimedes' studies on the use of levers are where the idea first emerged.
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Two point charges are separated by some distance. The first charge is positive. The second charge is negative, with a charge magnitude twice as large as that of the positive charge. Is it possible to find a place to bring a third charge in from infinity without changing the total potential energy of the system?.
No, it is not possible to bring a third charge in from infinity without changing the total potential energy of the system.
Potential energy for the first two charger is,
[tex]U=\frac{1}{4\pi E_{0} } \frac{q_{1}q_{2} }{r_{12} }[/tex]
This will change for adding a third charge no matter I it's sign, given as,
[tex]U=\frac{1}{4\pi E_{0} } [\frac{q_{1}q_{2} }{r_{12} } +\frac{q_{1}q_{3} }{r_{13} }+\frac{q_{2}q_{3} }{r_{23} }][/tex]
Hence not possible to find a place to bring a third charge in from infinity without changing the total potential energy of the system
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Name the different regions found within the electromagnetic spectrum and describe how the
are similar to and different from, one another.
The electromagnetic (EM) spectrum is the set of all EM radiation types. Electromagnetic radiation includes, for instance, radio waves from a radio station and visible light from a lightbulb in your home. Energy that flows and spreads out as it does is called radiation.
The electromagnetic spectrum is the set of frequencies of electromagnetic radiation and the related photon energies and wavelengths.
The seven regions of the electromagnetic spectrum are often arranged with wavelength decreasing and energy and frequency increasing.
X-rays,gamma rays, visible light, UV light, infrared (IR), microwaves, visible lightare a few of the common names for these energy forms.
Electromagnetic waves have a wide range of useful, everyday applications, including WiFi, cooking, kitchen appliances, eyesight, medical imaging, and cancer treatment.
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What shape is the moon's orbit around Earth?
Answer:
Elliptical Orbit
Explanation:
The Moon revolves around Earth in an elliptical orbit with a mean eccentricity of 0.0549. Thus, the Moon's center-to-center distance from Earth varies with mean values of 363,396 km at perigee to 405,504 km at apogee.
Who developed the expression for the line spectrum of hydrogen to include lines in the ultraviolet and infrared portions of the electromagnetic spectrum?.
The expression for the line spectrum of hydrogen to include lines in the ultraviolet and infrared portions of the electromagnetic spectrum was given by Johann Balmer.
It is possible to express the wavelengths of the visible hydrogen lines using a simple formula that was developed by Swiss mathematician Johann Balmer in 1885. The difference between two terms, 1/4 (written as 1/22) and the reciprocal of the square of a variable integer (1/n2), which has sequential values of 3, 4, 5, etc., yields the reciprocal wavelength (1/), which is equal to a constant (R) times the difference between the two terms.
Theodore Lyman, A.H. Pfund, F.S. Brackett, Friedrich Paschen, and Theodore Lyman are all American scientists who discovered the other four spectral line series in addition to the Balmer series. The Lyman series is in the ultraviolet, whereas the Paschen, Brackett, and Pfund series is in the infrared.
The Rydberg formula has been used to determine the wavelengths of several spectral series that have been created from the emission spectrum of atomic hydrogen. These spectral lines that have been seen are the result of electron transitions between two energy levels within an atom. The development of quantum mechanics was greatly aided by the Rydberg formula's classification of the series. In astronomical spectroscopy, the spectral series are crucial for determining redshifts and detecting the existence of hydrogen.
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A student walked straight for 6 meters, turned, then walked straight for another 4 meters.
Without knowing how much he turned, what is the largest possible magnitude of his displacement?
Since displacement is a vector quantity, the largest possible magnitude of the student displacement will be 2 m
What is Displacement ?Displacement is the distance travel in a specific direction. It is a vector quantity. It is measured in meter.
Given that a student walked straight for 6 meters, turned, then walked straight for another 4 meters. Without knowing how much he turned, the largest possible magnitude of his displacement D will be
D = 6 - 4
D = 2 m
Therefore, the largest possible magnitude of his displacement will be 2 m
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A car moves 4 km in an easterly direction and
then turns to move 3 km in a northerly direction.
By means of a graphical approach, find the
resultant displacement of the car.
When the car moves 4km east and then turns 3km north then the resultant displacement of car will be :
5km
Explanation:Here initially the car moves 4km east , that is a straight line towards east direction with a value of 4kms (let the point be A).
then, from the point A it turns 3km towards north direction. here
North and east are perpendicular to one another.
ie, it forms 90° that means it is a right angle.
The displacement of a car is the distance between its initial and final positions.
The displacement is
S = [tex]\sqrt{3^{2} + 4^{2} }[/tex]
S = [tex]\sqrt{25}[/tex]
= 5
so the resultant displcement is 5km
the resultant graph is attached below:
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. a 7.0-kg box slides along a horizontal frictionless floor at 1.7 m/s and collides with a relatively massless spring that compresses 23 cm before the box comes to a stop. (a) how much kinetic energy does the box have before it collides with the spring? (b) calculate the work done by the spring. (c) determine the spring constant of the spring.
A. The kinetic energy of the box is 10.115 J
B. The work done by the spring is 7.889 J
C. The spring constant of the spring is 298.26 N/m
A. How to determine the kinetic energy
The kinetic energy of the box can be obatined as follow:
Mass (m) = 7 KgVelocity (v) = 1.7 m/sKinetic energy (KE) =?KE = ½mv²
KE = ½ × 7 × 1.7²
KE = 3.5 × 2.89
KE = 10.115 J
Thus, the kinetic energy is 10.115 J
B. How to determine the work done by the spring
Mass (m) = 7 KgAcceleration due to gravity (g) = 9.8 m/s²Force (F) = mg = 7 × 9.8 = 68.6 NCompression (e) = 23 cm = 23 / 100 = 0.23 mWork done (W) =?W = ½Fe
W = ½ × 68.6 × 0.23
W = 7.889 J
Thus, the work done is 7.889 J
C. How to determine the spring constant
Mass (m) = 7 KgAcceleration due to gravity (g) = 9.8 m/s²Force (F) = mg = 7 × 9.8 = 68.6 NCompression (e) = 23 cm = 23 / 100 = 0.23 mSpring constant (K) =?F = Ke
68.6 = K × 0.23
Divide both sides by 0.23
K = 68.6 / 0.23
K = 298.26 N/m
Thus, the spring constant is 298.26 N/m
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Proof homogeneity of Einstein's mass energy relation E = mc²
The homogeneity of Einstein’s mass-energy relation E = mc² can be proved by maxwell’s equation of electromagnetism.
According to maxwell’s equation of electromagnetism, light travels at a speed (c) of 3 x [tex]10^8[/tex] m/s.
The momentum(p) of electromagnetic waves is proportional to the energy(E).
So, we can write it as
p = E / c -(i)
By cross multiplication
E = pc -(ii)
As we know
From newton’s second law, momentum (p) is the product of mass (m) and velocity (v)
p = mv -(iii)
since light travels with a speed (c) of 3 x 10^8 m/s
p = mc -(iv)
From the equations (ii) and (iv)
E / c = mc
Hence,
E = mc²
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