Forces with magnitudes of v = 135 newtons and u = 280 newtons act on a hook (see figure). The angle between the two forces is 45°. Find the direction and magnitude of the resultant of these forces. (Hint: Write the vector representing each force in component form, then add the vectors. Round your answers to two decimal places.)
Answers
To find the resultant force we will first find the component force of the forces given, to do this, we need to remember that any vector can be express in component form by:
[tex]\begin{gathered} \vec{v}= \\ \text{ where } \\ v\text{ is the magnitude } \\ \theta\text{ is the angle of the vector with respect to the positive x-axis.} \end{gathered}[/tex]For force u we notice that its magnitude is 280 N and its angle is zero, then we have:
[tex]\begin{gathered} \vec{u}=<280\cos0,280\sin0> \\ \vec{u}=<280,0> \end{gathered}[/tex]For force v we know that its magnitude is 135 N and its angle is 45°, then we have:
[tex]\begin{gathered} \vec{v}=<135\cos45,135\sin45> \\ \vec{v}=<95.46,95.46> \end{gathered}[/tex]Now that we have both vectors in component form we add them to get the resultant in component form:
[tex]\begin{gathered} \vec{F}=\vec{u}+\vec{v} \\ \vec{F}=<280,0>+<95.46,95.46> \\ \vec{F}=<375.46,95.46> \end{gathered}[/tex]Once we have the resultant force in component form we can find its magnitude and direction if we remember that they are given by:
[tex]\begin{gathered} F=\sqrt{F_x+F_y} \\ \theta=\tan^{-1}(\frac{F_y}{F_x}) \end{gathered}[/tex]Plugging the values we found for the components we have:
[tex]\begin{gathered} F=\sqrt{375.46^2+95.46^2} \\ F=387.41 \end{gathered}[/tex]and
[tex]\begin{gathered} \theta=\tan^{-1}(\frac{95.46}{375.46}) \\ \theta=14.27 \end{gathered}[/tex]Therefore, the magnitude of the resultant force is 387.41 N and the direction is 14.27°
Related Questions
one steel ball and one aluminum ball are the same size but the steel ball weighs twice as much as the other. the balls are dropped from the roof of a single-story building at the same instant of time. the time it takes the balls to reach the ground below will be:
Answers
It is same for both the balls. Due to the fact that balls fall freely regardless of their weight, both metallic balls take the same amount of time to reach the ground.
When two identically sized objects are dropped from a certain height, they will fall with gravitational acceleration (g). The weight of the objects will not affect how long it takes them to reach the ground. The density of the medium in which an object is dropped affects how long it takes for each object to travel there. Due to the influence of gravity and the same medium, we can therefore infer that both metal balls will take the same amount of time to reach the ground (air). Experiments have been conducted in vacuum rooms and show that when the balls are released from the top of the store, the acceleration of attraction to the floor is gravity and it has a value of 9.8 meters/square second regardless of its weight.
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A tennis ball moves 22 meters southward, then 12 meters northward, then 16 meters southward, and finally 34 meters northward
Answers
The resultant displacement of the tennis ball is 8 m northward.
What is displacement?
The displacement of an object is the change in the position of the object. The displacement of an object describes the shortest point between the final and initial position of an object.
The displacement of the tennis ball is calculated as follows;
d = (12 m north + 34 m north) - (22 m south + 16 m south)
d = (46 m north) - (38 m south)
d = 8 m northward
Thus, the resultant displacement of the tennis ball for the given motion is 8 m northward.
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The compete question is below:
A tennis ball moves 22 meters southward, then 12 meters northward, then 16 meters southward, and finally 34 meters northward. find the resultant displacement of the tennis ball.
After every movement in north and south direction multiple times, the displacement of the tennis ball is 8 meters in north direction.
What is displacement?The definition of displacement is the modification of an object's position. It has a direction and magnitude and is a vector quantity. It is shown as an arrow that travels from the initial location to the conclusion.
According to the question, the tennis ball moves 22 meters in south direction then it moves towards north and travels for 12 meters again it turns to south and covers 16 meters and at last it covers 34 meters in the north direction.
d = (12 m + 34 m ) north direction - (22 m + 16 m ) south direction
d = 8 meters in north direction.
Hence, the total displacement done by the tennis ball is 8 meters in the north direction.
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after driving a portion of the route, the taptap is fully loaded with a total of 27 people including the driver, with an average mass of 70 kgkg per person. in addition, there are three 15- kgkg goats, five 3- kgkg chickens, and a total of 25 kgkg of bananas on their way to the market. assume that the springs have somehow not yet compressed to their maximum amount. how much are the springs compressed? enter the compression numerically in meters using two significant figures. view available hint(s)
Answers
When something, like a spring, is stretched, the added length is referred to as its extension.According to Hooke's law, as long as the limit of proportionality is not crossed, a spring's extension is directly proportionate to the force exerted.
Solve the problem ?
The ends of an extension spring connect to two devices.The hooks and loops on the extension springs store and compress energy.An extension spring delivers return force to connected mechanisms via hooks or loops.The no-load position is where tightly wrapped extension springs normally rest. Total mass refers to the combined weight of the shell, its structural and support equipment, and the heaviest load that may be conveyed.The spring's compression at the specified weight is 0.80cm.
"Your inquiry is incomplete because it appears to be lacking the information below,"
The taptap's spring has a k value of 2.4 104 N/m.
the settings provided;
Each of the 27 people weighs 69 kg.
Each of the three goats weighs 15 kg.
Each of the five hens weighs 3 kg.
The weight of the bananas is 25 kg
The taptap's total mass, which includes every passenger, is computed as;
the people's combined mass is 27 x 70 or 1960 kg.
The goats' combined mass is 3 x 15 =45 kg.
The birds' combined mass is equal to 5 x 3 = 15 kg.
The bananas weigh a total of 25 kilograms
The extension of the spring
= 1960×9.8/2.4×104
= 19208/24000
= 0.80 cm
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A 4 coulombs charged particle experiences an electric force of 200 N when placed at point P in an electric field. The magnitude of the electric field at point P is :
a) 5 N/C
b) 800 N/C
c) 0.02 N/C
d) 50 N/C
Answers
(d) 50N/C
The magnitude of the electric field at point 'P' is 50N/C.
It is derived from the basic concepts of Electrostatics. Coulomb's Law is the basis of relations in Electrostatics. It resembles Newton's Law of Gravitation.
Using the relation between Electric force, charge, and Electric field:
F = qE
F = 200N; q = 4C200 = (4)E
E = 50N/C
It is widely used in the calculation of Electric Force and Electric Field. The S.I. Unit of the Electric Force is Newton. The S.I. Unit of the Electric Field is N/C. The S.I. Unit of charge is Coulomb.
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two power lines, each 300 m in length, run parallel to each other with a separation of 23 cm . part a if the lines carry parallel currents of 130 a , what is the magnitude of the magnetic force each exerts on the other? express your answer using two significant figures.
Answers
The magnitude of the magnetic force each exerts on the other is 4.41 N.
The magnitude of the magnetic force depends on the current through the wire, the length of the wire, and the radius of separation. It can be written as
F = μ₀ . I1 . I2 . L / (2π . a)
where F is a magnetic force, μ₀ is vacuum permeability (4π x 10¯⁷ H/m), I1 and I2 is current through the wire, L is the length of the wire and a is the radius of the wire.
From the question above, the given parameters are
L = 300 m
a = 23 cm = 0.23 m
I1 = I2 = 130 A
By substituting the parameters, we can calculate the magnetic force
F = μ₀ . I1 . I2 . L / (2π . a)
F = 4π x 10¯⁷ . 130 . 130 . 300 / (2π . 0.23)
F = 4.41 N
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How far could you speed walk in 90 seconds based on your speed for the 10 meter trail
Answers
Answer:
Explanation:
Given,
Time ( t ) = 90 seconds
Distance ( d ) = 10 meter
To find : Speed ( v ) = ?
Formula : -
v = d/t
v = 10/90
v = 1/9 m/s ( meters per second )
Hence,
1/9 m/s is the speed walk in 90 seconds for the 10 meter trail.
a 2.6 m diameter penstock carries water at a velocity of 7m/s to an 80% efficient hydroelectricity generation facility in west virginia that produces 12 mw. another 2.275 m diameter penstock carries water at a velocity of 3 m/s to a 74% efficient hydroelectric generation facility in arkansas that produces 9 mw. what is the ratio of the heads of arkansas' reservoir to west virginia's reservoir?
Answers
The ratio of the heads of arkansas' reservoir to west virginia's reservoir is 1813 : 1120
Consider the West virginia reservoir,
To calculate the head of the virginia reservoir, we will use
φ = P / nρgh ...(1)
where φ is the flow rate, P is the power generated, n is efficiency, ρ is the density of water, g is the acceleration due to gravity and h is the head.
Given that flow rate is 7 m/s, power generated is 12 mw, 80% is the efficiency.
We know that density of water is 1000 [tex]kg/m^{3}[/tex] and acceleration due to gravity is 9.8 [tex]m/s^{2}[/tex]
By using equation (1)
h = P / φnρg
h = [tex]\frac{12}{7 * \frac{80}{100} * 1000*9.8 }[/tex]
h = 13440
Similarly, the head of the arkansas reservoir will be
Given that flow rate is 3 m/s, power generated is 9 mw, 74% is the efficiency.
h = P / φnρg
h = [tex]\frac{9}{3 * \frac{74}{100} * 1000*9.8 }[/tex]
h = 21756
Now, the ratio of the heads of arkansas' reservoir to west virginia's reservoir is
= (heads of arkansas) / (head of the virginia)
= 21756 / 13440
= 1813 : 1120
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Select the correct answer from each drop-down menu. earth's rotation causes the cycle of . if earth began to spin a little bit faster .
Answers
now assume that a satellite of mass mmm is orbiting the earth at a distance rrr from the center of the earth with speed vevev e . a satellite of mass 2m2m2m is orbiting mars, also at a distance rrr from the center of mars, with a speed vmvmv m . what is the ratio tmte
Answers
The ratio between centripetal force of satellite b and satellite a is 2vm²/ ve².
We need to know about centripetal force to solve this problem. When an object moves in a circular motion, the object is experiencing centripetal force. The magnitude of centripetal force is
Fc = m . v²/R
where Fc is the centripetal force, m is mass, v is velocity and R is the radius.
From the question, we know that
ma = m
mb = 2m
va = ve
vb = vm
ra = rb = r
Find the centripetal force ratio
Fcb / Fca = (mb . vb²/Rb) / (ma . va²/Ra)
Fcb / Fca = (2m . vm²/r) / (m . ve²/r)
Fcb / Fca = 2 . vm²/ ve²
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Which answer best describes "displacement"?
A. Displacement is a vector quality showing total length of an area traveled by a particular object.
B. Displacement is a scalar quantity which accounts for how far away an object is after a period of time has elapsed from its initial starting point.
C. Displacement is a scalar quality showing total length of an area traveled by a particular object.
D. Displacement is neither a vector nor scalar quantity, which accounts for how far away an object is after a period of time has elapsed from its initial starting point.
Answers
Answer: The answer is the letter
A
Explanation:
Because displacement Its a vector and the letter A says than displacement is a vector quality showing total length of an area traveled by a particular object.
Answer:
(Question 1) Which answer best describes displacement?
(Answer) Displacement is a vector quality showing total length of an area traveled by a particular object.
(Question 2) Kelley is playing pool and hits the cue into the nine ball, which is directly in the center of the pool table. The nine ball travels a total of 7 meters before stopping, 1 meter to the left of the initial starting point of the nine ball. Which sentence reflects the correct statement regarding distance and displacement when considering the motion of the nine ball?
(Answer) The nine ball traveled a distance of 7 meters and was displaced by 1 meter.
(Question 3) What is velocity?
(Answer) Velocity is a vector quantity that tells the distance an object has traveled over a period of time.
(Question 4) Imagine a time-position graph where the velocity of an object is constant. What will be observed on the graph concerning the slope of the line segment as well as the velocity of the object?
(Answer) The slope of the line is equal to zero and the object will be stationary.
(Question 5) Select the option that best summarizes the reason for the use of position-time graphs when studying physical science.
(Answer) The position-time graphs show the relationship between the position of an object (shown on the y-axis) and the time (shown on the x-axis) to show velocity.
Explanation:
just did the quick check, UwU enjoy
Whoever answers asap gets marked Brainliest! A hockey puck with a mass of 0.12 kg is traveling across the ice at a velocity of 150 m/s downfield. What is the momentum of the hockey puck?
P = 18 N
P = 18 kg * m/s
P = 8 * 10 - 4 kg * m/s
M = 18 kg * m/s
Answers
Answer:
Explanation:
Momentum = m * v = .12 * 150 = 18 kg m/s
complete the table=x =0 2 3 4 6 8 y=30 27 24
Answers
Answer: (x=1 y=30) (x=2 y=27) (x=3 y=24) (x=4 y=21) (x=5 y=18) (x=6 y=15) (x=7 y=12) (x=8 y=9) (x=9 y=6) (x=10 y=3) etc its going down by 3 so 30-3=27 27-3=24 24-3=21 etc
hope i helped
Explanation:
A meteorite is found to contain two isotopes of element x, x-12, and x-14. Experimental analysis determined 95% of the element is isotope x-12, whereas 5% of the element is isotope x-14. What is the average atomic mass of element x?.
Answers
Considering the definition isotopes and atomic mass of an element, the average atomic mass of element x is 12.1
Definition of isotopeThe same chemical element can have the same atomic numbers, but the number of neutrons is different. These atoms are called isotopes of the element.
Definition of atomic massThe atomic masses of chemical elements are calculated as the weighted average of the masses of the different isotopes of each element, taking into account the relative abundance of each of them.
Atomic mass of the element in this caseIn this case, you know:
Isotope x-12 is 95% abundant (the atomic mass is 12).Isotope x-14 is 5% abundant (the atomic mass is 14).The average mass of the element x can be calculated as:
average mass of element x=12 amu×0.95 + 14 amu×0.05
average mass of element x= 12.1 amu
Finally, the atomic mass of the element x is 12.1.
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what is the velocity (in m/s) of a 925 kg car initially moving at 29.5 m/s, just after it hits a 145 kg deer initially running at 12.5 m/s in the same direction? assume the deer remains on the car. (enter the magnitude.)
Answers
The velocity after the collision is 27.19 m/s
What is the law of conservation of momentum?For a collision between Object 1 and Object 2 in an isolated system, the total momentum of the two objects before collision equals the total momentum of the two objects after collision. That is, the momentum lost from object 1 is equal to the momentum gained from object 2 (a constant or unchanging value). It can be stated by following equation:
Pₙ = mₙvₙ
mₙvₙ = m₁v₁ + m₂v₂
Where, Pₙ = final momentum
mₙ = total mass of the system
vₙ = final velocity of the system
For the given case,
Since, mₙvₙ = m₁v₁ + m₂v₂
(m₁ + m₂)vₙ = m₁v₁ + m₂v₂
(925 + 145)vₙ = (925 × 29.5) + (145 × 12.5)
1070 vₙ = 27287.5 + 1812.5
1070 vₙ = 29100
vₙ = [tex]\frac{29100}{1070}[/tex]
vₙ = 27.19 m/s
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name two powers of the president
Answers
Answer:
The President can issue executive orders, which direct executive officers or clarify and further existing laws.
The President also has the power to extend pardons and clemencies for federal crimes.
Explanation:
9. a supply plane needs to drop a package of food to scientists working on a glacier inalaska. the plane flies 100 m above the glacier at a speed of 150 m/s. how far short of the target should it drop the package?
Answers
[tex]X=150m/s * 4.518s =677.63m[/tex] far short of the target it will drop the package.
How far short of the target should it drop the package?First we can find the total time in order to reach the ground using the following kinematic formula:
[tex]y_{f} =y_{i}+v_{iy}+ \frac{1}{2} gt^{2}[/tex]
And replacing we have:
[tex]-100 =0+0- \frac{1}{2} (9.8)t^{2}[/tex]
And solving for t we got:
[tex]t=\sqrt{ \frac{2* (-100)}{-9.8} }=4.518 s[/tex]
And now we can find the final distance on the x axis using the formula:
[tex]D = Vxt[/tex]
The velocity on x not changes and is the same plane speed [tex]Vx=150m/s[/tex] , if we replace we got:
[tex]X=150m/s * 4.518s =677.63m[/tex]
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Use this diagram to calculate the magnitude of the block's acceleration.
A. 0.50 m/s2
B. 2.0 m/s2
C. 9.8 m/s2
D. 32 m/s2
Answers
The mass of the block is 4 kg and the force applied on the block is 8 N. So, the acceleration of the block will be 2 m/s².
What is acceleration?The rate at which an object's velocity varies with respect to time is referred to as acceleration in mechanics. accelerations' magnitude as a vector. Depending on which way the net force is pulling on an object, it will accelerate in that direction.
Acceleration has a magnitude and a direction, making it a vector quantity. Vessel quantities include velocity as well. The definition of acceleration is the change in the vector of velocity over a time interval divided by the time interval.
According to the question, the given values are :
Block mass, m = 4 kg
Force applied on the block, f = 8 N
[tex]Force = mass *acceleration[/tex]
a = 8/4
a = 2m/s².
Hence, the acceleration of the block will be 2m/s².
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A man is pulling on a rope with a force of 44 N
directed at an angle of 63◦
to the horizontal.
What is the x-component of this force?
Answer in units of N.
Answers
Answer:
20 N
Explanation:
Vertical component will be 44 sin 63
HORIZONTAL component is 44 cos 63 N = 19.97 =~ 20 N
How is the amplitude of a
longitudinal wave measured?
A. the distance between two rarefactions
B. the distance between two compressions
C. It is measured by how close together or spread
apart the compressions and rarefactions are.
Answers
Compressions
Explanation:
A longitudinal wave is a wave in which the direction of propagation of the wave and the direction of the displacement of the particles of the wave are parallel.
As the wave propagates, the particles do not move, but, oscillate back and forth about their equilibrium position, and there are thus regions of high pressure called compressions and regions of low pressure called rarefactions.
The amplitude is thus the distance between successive compressions.
Instructions:Draw a speed graph in the box that matches thefollowing scenario:A runner jogged 40m at a slow pace for 40seconds. She then stopped for 40 seconds to gea drink of water. After that, she sped up and ran60m more in 20 seconds.Tip:y axis - total of 100 mx axis - total of 100 s
Answers
Given data:
1) Runner jogged 40 m at a slow pace for 40 sec.
2) Stopped for 40 sec.
3) Again funs for 60 m in 20 sec.
a pellet gun fires ten 3.0 g pellets per second with a speed of 400 m/s. the pellets are stopped by a rigid wall. what is the magnitude of the average force on the wall from the stream of pellets?
Answers
Explanation
The speed of the block when it has moved a distance of 0.0150 m from it's initial position is 0.32 m/s .
When a spring is compressed by a force F, the potential energy is stored on it.
If the spring is released, the potential energy turns into kinetic energy.
The object is replaced by the call-back force which occurs on the spring F' = K.∆x
K= 815 N/m
∆x= 0.0190 m
F' = 815.0.019 = 15.8 N
Ff= k.m.g
Ff = 0.35 . 2.55. 9.81 = 8.76 N friction force acceleration of object is-
a= F' - Ff/m
V^2 = 2.a . displacement
V^2 = 2.264. 0.0200.
V^2 = 0.1056
V=√0.1056.
V= 0.32 m/s
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In the diagram below, two of the three rays used to find the image position are shown. Which of the following best describes the third (missing) ray?A.A ray incident parallel to the axis refracts outward, as if it came from the focus on the left hand side.B.A ray incident through the vertex continues through the lens without refracting.C.A ray incident parallel to the axis refracts so that it passes through the focus on the right hand side.D.A ray incident on a path that would take it through the right focus refracts parallel to the axis.
Answers
Answer:
C. A ray incident parallel to the axis refracts so that it passes through the focus on the right hand side
Explanation:
The third ray is the blue ray in the following figure
Therefore, the third ray is a ray parallel to the axis that refracts and passes through the focus of the right side.
So, the answer is:
C. A ray incident parallel to the axis refracts so that it passes through the focus on the right hand side
Hey surveyor is drawing property lines . He draws one line that is 25.0 m long and is 20° south of west.  how long is the western component of the vector he has drawn?
Answers
Answer:
23.5 m
Explanation:
25 m * cos 20 =23.5 m
A particle’s position along the x-axis is described by the functionx(t) = A t + B t2,where t is in seconds, x is in meters, and the constants A and B are given below.Randomized VariablesA = -4.9 m/sB = 6.9 m/s2q. Enter expression interms of A,B, t for the velocity of the particle as a function of time? What time will the velocity be zero?
Answers
Given,
The position function is, x(t)=At+bt²
A=-4.9 m/s
B=6.9 m/s²
The velocity is described as the rate of change if the displacement with time.
That is, the velocity is the time derivative of the displacement.
Therefore on differentiating the given function with respect to the time, we get the expression for the velocity.
i.e.,
[tex]\begin{gathered} v(t)=\frac{d(At+Bt^2)}{dt} \\ =A+2Bt \end{gathered}[/tex]Therefore the expression for the velocity is A+2Bt
To know at what time the velocity will be zero,
[tex]A+Bt=0[/tex]On simplifying the above equation,
[tex]t=\frac{-A}{B}[/tex]On substituting the known values in the above equation,
[tex]t=\frac{-(-4.9\text{ )}}{6.9}=0.71\text{ s}[/tex]Therefore the velocity will be zero at 0.71 s
A truck is traveling at a constant velocity of 30 m/s. How long will it take to travel 1000 meters?
Answers
A truck is traveling at a constant velocity of 30 m/s. It will take the time to travel 1000 meters is (t)=33.33 S.
What is velocity?The velocity means the ratio of distance and time. Mathematically it means the distance divided by time. It can be measured in m/s and cm/s.
How can we calculate the time?To calculate the time we are using thee formula here is,
S=vt
Or, t=S/v
Here we are given,
S = The covered distance of the car = 1000 m
v= The velocity of the car. = 30 m/s.
We have to calculate the time taken by truck = t
Now we put the values in the above equation, we get
t=S/v
Or, t=1000/30
Or, t=33.33 S
From the calculation we can say that, It will take the time to travel 1000 meters is (t)=33.33 S.
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an 81-kg baseball player slides into second base. the coefficient of kinetic friction between the player and the ground is 0.49. (a) what is the magnitude of the frictional force? (b) if the player comes to rest after 1.6 s, what was his initial velocity?
Answers
a) The magnitude of the frictional force= -µ mg = 0.49*81*9.8 = 389 N
b)The player comes to rest after 1.6 s, his initial velocity Vi = 7.68 m/s
Acceleration due to friction = - µ g = - 4.80 m/s^2.
V = V0 + at
V = 0
a = - 4.802 m/s^2
t = 1.6 s
V0 = V - at = 0 + 4.8*1.6 = 7.68 m/s
the acceleration of the player due to frictional force is given as
a = f/m = 388.96 /81 = 4.8 m/s2
final velocity = Vf = 0
time = t = 1.6 sec
using the formula
Vf = Vi + at (Vi = initial velocity)
Vi = Vf - at
Vi = 0 - (-4.8) (1.6) (a = -4.8 since player is slowing down)
Vi = 7.68 m/s
A force known as friction exists between two surfaces that are sliding or attempting to glide over one another. Friction, for instance, makes it challenging to push a book across the floor. The direction in which an object moves or attempts to move is always the direction in which friction operates. When anything moves faster or slower in a straight line, it is said to have been acceleration. Because the direction is constantly changing, even motion on a circle accelerates at a constant pace.
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The potential energy of a roller coaster is 50 joules. The kinetic energy of the same coaster is 50 joules. What is the mechanical energy of the coaster?.
Answers
A roller coaster's mechanical energy is equal to 100 Joules if its P.E. and K.E. are each 50 Joules.
As a result, the roller coaster has a mechanical energy of 100 Joules.
explanation?
50 Joules is the potential energy of a roller coaster.
A roller coaster has kinetic energy of 50 Joules.
In order to determine the roller coaster's mechanical energy:
The entire amount of potential energy (P.E.) and kinetic energy (K.E.) that an object or body possesses is known as mechanical energy.
(ME)=50+50
Mathematically, the formula for mechanical energy states that it is equal to 100 joules when the given values are substituted.
As a result, the roller coaster has a mechanical energy of 100 Joules.
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a thin, horizontal, 10-cm-diameter copper plate is charged to 3.5 nc. if the electrons are uniformly distributed on the surface, what are the strength and direction of the electric field
Answers
While negative point charges always move in the direction of the opposing electric field, positive point charges always move in the other direction. An electric field is a vector quantity. They cannot be added directly, but they can be vectorially inserted.
What are the electric field's strength and direction?A physical field called an electric field surrounds electrically charged particles and attracts or repels all other charged particles nearby. It can also refer to the physical field surrounding a system of charged particles.
While negative point charges always move in the direction of the opposing electric field, positive point charges always move in the other direction. An electric field is a vector quantity.
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a flat coil of wire consisting of 17 turns, each with an area of 50 cm2, is positioned perpendicularly to a uniform magnetic field that increases its magnitude at a constant rate from 3 t to 6 t in 2.0 s. what is the magnitude of the emf (in volts) induced in the coil? your answer should be a number with two decimal places, do not include the unit.
Answers
The magnitude of electromotive force is 0.13 volt.
We need to know about the electromotive force of induction to solve this problem. The emf induction appears when there is any change in magnetic flux. The magnitude of emf can be determined by
ε = N dΦ / dt
where N is coil turns, ε is electromotive force, dΦ is change in magnetic flux and dt is time interval.
From the question above, the parameters given are
B1 = 3T
B2 = 6T
dt = 2 s
N = 17
A = 50 cm² = 5 x 10¯³ m²
Find the change in magnetic flux
dΦ = (Φ2 - Φ1)
dΦ = (B2 . A - B1 . A)
dΦ = A (B2 - B1)
dΦ = 5 x 10¯³(6 - 3)
dΦ = 15 x 10¯³ Tm²
By substituting the given parameters, we can calculate electromotive force
ε = N . dΦ / dt
ε = 17 . 15 x 10¯³ / 2
ε = 0.13 volt
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if the speed of a car is increased by 65%, by what factor will its minimum braking distance be increased, assuming all else is the same? ignore the driver's reaction time.
Answers
If the speed of the car is increased by 65%, the stopping distance of the car will be increased by 272.25%.
Let us say, the car is moving with velocity U, the stopping time of the car is T and the stopping distance of the block is d,
Now, we should use the equation of motion,
U²-V² =2aD
Where,
U is initial velocity,
V is final velocity,
D is the stopping distance,
a is the acceleration.
We know, at the final velocity will be zero,
So,
U² = 2aD
U =√(2aD)
Now, if the speed is increased by 65%, let us say the stopping distance becomes D'.
So,
U+65%U = √(2aD')
165U/100 = √(2aD')
Now, putting U = √(2aD),
165√(2aD)/100 = √(2aD')
(1.65)²D = D'
D' = 2.7225D
Now,
∆D = D' - D/D × 100
∆D = 2.7225 × 100
∆D = 272.25%
So, the stopping distance increased by 272.25%.
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