The strength of the electric field at that point and the force would this charge experiences at that point will be 4.587 N/C and 12.38 N.
What is the electric field strength?The electric field strength is defined as the ratio of electric force to charge.
Given data;
q₁ = 5.4 C
F₁ is the electric force in case1
E is the electric field =?
F₂ is the electric force in case 2
q₂ is the charge 2
The strength of the electric field at that point is;
F₁=Eq₁
E₁=F/q₁
E₁=25.0 N / 5.4 C
E₁=4.587 N/C
The force would this charge experience at that point when the charge is 2.7 C;
F₂=Eq₂
F₂=4.587 N/C × 2.7 C
F₂ = 12.38 N
Hence the strength of the electric field at that point and the force would this charge experiences at that point will be 4.587 N/C and 12.38 N.
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A hammer of mass m = 0.46 kg is moving horizontally at a velocity of v = 6.5 m/s when it strikes a nail and comes to rest after driving the nail a distance Δx = 1.1 cm into a board.
What is the duration of the impact, assuming the acceleration is constant during this time period, in terms of the given variables? It is not accepting numerical values
What was the average force exerted on the nail, in terms of the mass, initial velocity, and distance traveled?
What was the average force, in newtons, exerted on the nail?
The impact will last for 3.3 milliseconds, the average force applied to the nail will be [m (v² - u²)]/2s, and the average force applied to the nail will be 883.2 N, respectively.
What is force?Force is defined as the push or pulls applied to the body. Sometimes it is used to change the shape, size, and direction of the body.
Force is defined as the product of mass and acceleration. Its unit is Newton.
Given data;
Average force,F = ?
Mass,m = 0.46 kg
Acceleration,a
Final velocity,v = 0 m/sec
Initial velocity,u = 6.5 m/sec
The duration of the impact, assuming the acceleration is constant is found with the help of Newton's third equation of motion as;
v²=u²+2as
0 = (6.5)² + 2 ×a × 1.1 × 10⁻²
- 42.25 = 2 × a × 1.1 × 10⁻²
a = - 1920 m/s²
a = (v-u)/t
-1920 = (0-6.5)/t
t = 3 × 10⁻³ sec
t = 3.3 milli second
From Newton's third equation of motion;
v² = u² +2as
a = (v² - u² ) /2s
The average force exerted on the nail, in terms of the mass, initial velocity, and distance traveled is;
F = ma
F = [m (v² - u² )] /2s
The average force, in newtons, exerted on the nail is;
F = [m (v² - u² )] /2s
F= ma
Substitute the given value;
F = 0.469 × 1920
F = 883.2 N
Hence the duration of the impact, the average force exerted on the nail and the average force, in newtons, exerted on the nail will be 3.3 milliseconds, F = [m (v² - u² )] /2s and 883.2 N respectively.
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please help me there
Answer:
when switch is off no electricity will flow and then the circuit is called an open circuit
Explanation:
Electricity will not flow in open circuit
Find the magnitude of this
vector:
174 m
N
188.4 m
HELP FAST
Answer:
195.168 m
Explanation:
To find the magnitude of the vector you can use the Pythagorean Theorem since you have the height and base and the vector is really just the hypotenuse
Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
Plug values in
[tex]88.4^2+174^2=c^2[/tex]
Simplify
[tex]7814.56+30276=c^2[/tex]
Add the two values
[tex]38090.56=c^2[/tex]
Take the square root of both sides
[tex]195.168\approx195.168[/tex]
A generator produces 60 000 J of electric energy every minute. How many watts does it produce?
Answer:
[tex]1000\; {\rm W}[/tex].
Explanation:
Joule is a unit for work, while watt is a unit for power- the rate at which work is being done. Divide work by time to find power.
By definition, one watt is equivalent to one joule-per-second. In other words: [tex]1\; {\rm W} = 1\; {\rm J \cdot s^{-1}}[/tex]. Note that the unit of time in this question is "minute", not second.
Apply unit conversion and ensure that the unit of time is "second":
[tex]\begin{aligned} 1\; \text{minute} &= 1\; \text{minute} \times \frac{60\; {\rm s}}{1\; \text{minute}} = 60\; {\rm s}\end{aligned}[/tex].
The power of this generator would thus be:
[tex]\begin{aligned} \text{power} &= \frac{\text{work}}{\text{time}} \\ &= \frac{60\, 000\; {\rm J}}{60\; {\rm s}} \\ &= 1\, 000\; {\rm W} \end{aligned}[/tex].
how does the electric force vary with distance
Calculate
(
4.2
×
10
5
)
(
4.0
×
10
−
9
)
cm
2
.
Answer:
13671
Explanation:
You are raising up a big bucket of water from a 25.9 m deep well. The combined mass of the water and the bucket is 13.9 kg. The bucket is attached to a heavy duty steel chain. The mass of the chain is 19.3 kg.
1. How much work do you perform during the lifting process?
2. If it takes 1.75 minutes for you to raise the bucket of water out of the well, then what was your average power?
Answer:
Wb = 13.9 kg * 25.9 m * 9.8 m/s^2 = 3530 Joules
(work required to remove bucket)
Center of mass of chain = 25.9 / 2 = 12.95 m height of CM of chain
Wc = 12.95 * 19.3 * 9.8 = 2450 Joules
(work required to remove chain)
Total work = 3530 + 2450 = 5980 Joules
P = W / t = 5980 J / 105 sec = 57 J/s = 57 Watts
1. Objective observations do not include
2. Observations can capture a child's
3. It's important to use observations because they provide
growth.
or
happen
4. Understanding a child's
and
5. After writing an observation, you can use the
milestones a child has accomplished
6. To make sure an observation is objective you can ask yourself, "Did I capture
happened?"
7. One of the ways you can capture your observations is through
8
and
that define child
helps you accurately interpret an observation.
of child development to understand what
what
or
are ways to count specific skills or behaviors and determine when they
9
and
are ways to organize observation data.
10. The federal law which ensures that all children and family education information is confidential
is called
Objective observations do not include bias or opinions.
Observations can capture a child's strengths and weaknesses
What is an Objective Observation?This refers to the types of observation that is done through the senses through what we see, touch, feel, hear, smell, and taste.
Hence, we can see that objective observation is important because they provide insight into the strengths and needs of a child.
One of the ways you can capture your observations is through note-taking.
The federal law which ensures that all children and family education information is confidential is called The Family Educational Rights and Privacy Act (FERPA)
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A seagull flies at a velocity of 9.00 m/s straight into the wind.
(a) If it takes the bird 18.0 min to travel 6.00 km relative to the earth, what is the velocity of the wind?
m/s
(b) If the bird turns around and flies with the wind, how long will he take to return 6.00 km?
s
(c) Discuss how the wind affects the total round-trip time compared to what it would be with no wind.
a)If it takes the bird 18.0 minutes to fly 6 km away from the earth, the wind's speed will be 4 m/s.
b) The bird would need 7 minutes and 42 seconds to fly back 6 kilometers if he turned around and flew with the wind.
c)Compared to the 133.33 seconds it would take without the wind, the overall round-trip time is affected by the wind.
What is velocity?The change of distance with respect to time is defined as speed. Speed is a scalar quantity. It is a time-based component. Its unit is m/sec.
The given data in the problem is
A seagull flies at a velocity,[tex]\rm v_{SA} = 9 \ m/sec[/tex]
The time the bird takes,t=18.0 min
The distance traveled relative to the earth = 6.00 km
a)
The seagull's relative velocity with reference to the ground as;
[tex]\rm v_{sg} = \frac{6.00 \times 10^3 \ m }{(20 min) \times \frac{60 s }{1 \ min}} \\\\ v_{sg}= 5.00 \ m/sec[/tex]
Air velocity with reference to the ground is;
[tex]\rm v_{AG}= v_{SG}-v_{SA} \\\\ v_{AG} = 5.00 \ m/sec - 9.00 \ m/sec \\\\ v_{AG} = -4.00 \ m/sec[/tex]
b)
If the bird turns around and flies with the wind, The time will he take to return 6.00 km is;
[tex]\rm v_{SG}=v_{SA}+v_{AG} \\\\ v_{SG}=-900 \ m/sec +(-4.00 \ m/sec) \\\\ v_{SG}= -13.00 \ m/sec[/tex]
The time the bird takes;
[tex]\rm t = \frac{x_{SG}}{v_{SG}} \\\\ t = \frac{6.00 \times 10^3 \ m }{13.00 \ m/sec } \\\\ t = 462 m/sec \\\\ t = 7 \ min \ and \ 42 \ sec[/tex]
c)\
The total round-trip time compared to what it would be with no wind. is;
[tex]\rm t = 20 \ min( \frac{60 \ sec }{1 \ min} )+ 462 \ sec \\\\ t = 1200 \ sec +6 462 \ ec \\\\ t= 1662 \ sec[/tex]
The time for the round trip is;
[tex]\rm t = \frac{12 \times 10^ 3 }{ 9 \ m/sec } \\\\ t = 1333.33 \ sec[/tex]
Hence the wind's speed, the time bird would need to fly back the total round-trip time will be 4 m/s, 7 minutes and 42 seconds and 1333.33 sec.
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Emma is the sole earning member of her family. She wants to study further but is forced to give up on her dreams to support her family. Which of the following ideas explains Emma's behavior?
Answer:
jsjdhfhdhsjeyeushshshdhfjfjfhfj
Explanation:
a
The theory that helps to explain Emma's actions will is Determinism. Option C is corect.
What is determinism?The idea is that all of our actions are the result of some uncontrollable internal or external force or cause.
Similar to the scenario given above, Emma's decision to abandon her studies was driven by an external factor—the fact that she is the family's sole provider of income, over which she has no influence.
The theory that helps to explain Emma's actions will is Determinism.
Hence option C is corect.
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Which expression is equivalent to 6(a - 3)?
Answer:
it's 6a - 18
Explanation:
because 6 is multiplied witk a and -3
A figure skater glides along a circular path of radius 6.70 m. If she coasts around one half of the circle, find the following.
(a)her distance (in m) from the starting location
(b)the length (in m) of the path she skated
(a) Her distance from the starting location is 21.05 m.
(b) The length of the path she skated is 21.05 m.
Distance of the skater from the starting positionThe distance around a complete circular path is calculated as 2πr.
The distance for a half circle is calculated as ¹/₂ x 2πr = πr
Distance from the starting location = π x 6.7 m = 21.05 m
The length of the path she skated is the same as her distance from the starting location = 21.05 m.
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Annie is considering two different coach journeys from Bristol to Birmingham.
Journey A takes 2 hours and does not stop. The shortest distance by road between the wo coach stations is 143 km, most of which s on the motorway where the speed limit is 31m/s (70 mph).
Journey B costs only half as much, but it takes 3 hours 15 minutes and stops at 5 other towns on the way. This journey is 160 km long, and most of it is on country roads with a speed limit of 22 m/s (50 mph). The speed limit in towns the coach passes through is 13 m/s (30 mph).
Calculate the average speed for each journey in m/s. Think carefully about the units you need to use in your calculations.
The average speed in the first case is 19.86 m/s and the average speed in the second case is 13.67 m/s.
The formula of average speed is
average speed = total distance / total time
In first case
total distance is 143 km which is also 143000 m
and total time is 2 hours which is also 7200 seconds
so average speed = ( 143000 / 7200 ) m/s
average speed = 19.86 m/s
In second case
total distance is 160 km which is also 160000 m
and total time is 3 hours and 15 minutes which is also 11700 seconds
so average speed = ( 160000 / 11700 ) m/s
average speed = 13.67 m/s
So to conclude with we have find the the average speed in both cases by dividing total distance by total time and in first case we have got our answer as 19.86 m/s and in second case we have got 13.67 m/s.
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What states the purpose of an experiment
Answer:
The purpose of an experiment is to test out your hypothesis. If your hypothesis is correct, then it is a theory that could work every single time the experiment has been performed by scientists.
Adults sometimes lump all "screen time" together—social media, music videos, games and so on. Is this valid, or are there distinct differences among different types?
Answer:
it’s all time on the Screen so it should be counted as one thing they are different things that you have different timelines for each category
Since everything is happening at once on the screen, even though there are distinct events with separate timings for each category, it should all be considered one item.
What are social media ?Websites and programs that place a high value on community involvement, content sharing, collaboration, and social interaction are referred to as social media. Social media is used by people to interact and communicate with their friends, family, and other groups.
Why is social media so important?It is a helpful tool for talking with individuals locally and internationally as well as for generating, sharing, and spreading information. Social media has the power to influence consumer buying decisions via reviews, marketing, and marketing tactics.
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28. An electron with a speed of 4.0 x 10° m/s enters a uniform magnetic field of magnitude 0.040 T at an angle of 35 degrees to the magnetic field lines. The electron will follow a helical path. a) Determine the radius of the helical path. b) How far forward will the electron have moved after completing one circle?
The radius of the helical path and the period of the electron are 3. 26* 10^-10m and 8.94*10^-10m respectively.
How to determine the radiusUsing the formula:
r = [tex]\frac{mvsin \alpha }{Bq}[/tex]
m = 9.109 × 10-31 kg
α = 35°
B = 0. 040 T
q = 1.6 × 10-19 C
Substitute values into the formula
[tex]r = \frac{9. 109 * 10^-31 * 4.0 * 10^0 * sin 35}{0. 040 * 1.6 * 10^-19 }[/tex]
[tex]r = \frac{2. 089 * 10^-30}{6. 4* 10^-21}[/tex]
[tex]r = 3. 26 * 10^-10[/tex] m
b. [tex]T = \frac{2\pi m}{qB}[/tex]
[tex]T = \frac{2 * 3.142 * 9.109 *10^-31}{1.6* 10^-19* 0.040}[/tex]
[tex]T = \frac{5. 72* 10^-30}{6. 4* 10^-21}[/tex]
[tex]T = 8. 94* 10^-10[/tex]
Therefore, the radius of the helical path and the period of the electron are 3. 26* 10^-10m and 8.94*10^-10m respectively.
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What is causing her to resist a change in her lack of motion? Answer asap
Answer:
uduehdhehshdhdhdhdegsgshe
Explanation:
a
I don’t not get anything to do with this question
Answer:
C
Explanation:
Mechanical energy = kintetic energy + grav potential energy
ME = KE + GPE <==== re-arrange
GPE = ME - KE <==== KE = 1/2 m v^2
GPE = ME - 1/2 mv^2
(a) Calculate the tension in a vertical strand of spiderweb if a spider of mass 5.00 ✕ 10-5 kg hangs motionless on it.
N
(b) Calculate the tension in a horizontal strand of spiderweb if the same spider sits motionless in the middle of it much like the tightrope walker in Figure 4.13. The strand sags at an angle of 10.0° below the horizontal.
N
Compare this with the tension in the vertical strand (find their ratio).
(tension in horizontal strand / tension in vertical strand)
a)The tension in the vertical strand will be 0.00049 N.
b))The tension in the horizontal strand will be 0.001284 N.
c)The ratio of tension in the horizontal strand to the tension in the vertical strand will be 2.62.
What is tension force?
The tension force is described as the force transferred through a rope, string, or wire as it is pulled by opposing forces.
Given data;
Mass of spiderweb = 5.00 ✕ 10⁻⁵ kg
The tension in a horizontal strand of a spiderweb, Tₓ
The tension in a vertical strand of a spiderweb, Tₐ
The angle at which the strand sags, Θ = 10.0°
R is the ratio of tension in the horizontal strand to the tension in the vertical strand
a)
From the FBD,
The tension in the vertical strand is equal to the weight of the spider;
Tₐ = W
Tₐ = mg
Tₐ= 5 x 10⁻⁵ kg x 9.8 m / s²
Tₐ= 0.00049 N.
(b)
The super's total vertical forces are zero since it is not moving the value of the tension in the horizontal strand;
Tₓ = mg/( 2sinΘ)
Tₓ = 5 x 10⁻⁵ kg x 9.8 m /s² / ( 2 sin 11° )
Tₓ= 0.001284 N.
c)
R is the tension in the vertical strand divided by the tension in the horizontal strand.
R= Tₐ / Tₓ
R= 0.001284 N / 0.00049 N
R= 2.62
Hence, the tension in a vertical strand of a spiderweb, the tension in a horizontal strand of a spiderweb, and the ratio of tension in the horizontal strand to the tension in the vertical strand will be 0.00049 N, 0.001284 N, and 2.62 respectively.
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A tennis player tosses a tennis ball straight up and then catches it after 2.07 s at the same height as the point of release.
(a) What is the acceleration of the ball while it is in flight?
magnitude
m/s2
direction
upward
(b) What is the velocity of the ball when it reaches its maximum height?
magnitude ms
direction
downward
magnitude in zero
(c) Find the initial velocity of the ball.
m/s upward
(d) Find the maximum height it reaches.
m
(a) The ball will accelerate at a speed of 9.81 m/s² while it is in flight.
(b) The ball will be moving at a speed of 0 m/sec when it reaches its highest point.
(c) The ball's initial upward velocity is 20.30 m/s.
(d) It will reach a maximum height of 21.0 m.
What is speed?Speed is defined as the change in distance with regard to time. A scalar quantity, speed. It is a temporal element, m/sec is its unit.
The information provided in the issue is;
u is the fall's beginning speed in m/sec;
h is the fall's distance
g is the fall's acceleration or 9.81 m/sec²
a. The ball's speed while in flight is equal to the acceleration caused by gravity, which is 9.81 m/s².
b. When the ball reaches its highest point, its velocity will be zero.
c. The ball's starting velocity is;
v=u-gt
0=u-gt
u=gt
u=9.81 m/s² × 2.07 sec
u=20.30 m/s
d. The formula is used to determine the highest height it can reach.
[tex]\rm u^2 = - 2gh \\\\ (20.30)^2 = -2 \times (-9.8) \times h \\\\ 412.09 = 19.6 \times h\\\\ h = 412.09/19.6\\\\ h = 21.00 m[/tex]
As a result, the ball's greatest height, beginning velocity, and acceleration are all 9.81 meters per second, zero meters per second, 20.30 meters per second, and 21 meters accordingly.
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What is the magnitude of the displacement?
A) 20 m
What is called magnitude of displacement?
The magnitude of displacement is defined as the shortest distance between the initial and final position of the object.
For a particle in motion, the magnitude is either less than or equal to the distance travelled.
Also,
Velocity is simply defined as the rate of change of displacement with time.
Mathematically, it can be expressed as:
Velocity = displacement / time
According to the question,
The following data were obtained:
Time = 5 s
Velocity = 4 m/s
Displacement =?
Velocity = displacement / time
4 = d / 5
D = 4 × 5
D= 20 m
Hence,
20 m is the magnitude of the displacement of the object after it travelled for five seconds.
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Sally and Sam are in a spaceship that comes to within 18,000 km of the asteroid Ceres. Determine the force Sally experiences, in N, due to the presence of the asteroid. The mass of the asteroid is 8.7 1020 kg and the mass of Sally is 80 kg. For calculation purposes, assume the two objects to be point masses.
The force Sally experiences, in N, due to the presence of the asteroid is 0.0143 N.
Force experienced by Sally
F = Gm1m2/R²
where;
G is universal gravitation constantm1 is mass of asteroidm2 is mass of SallyR is the distance between Sally and SamF = (6.67 x 10⁻¹¹ x 80 x 8.7 x 10²⁰)/(18,000,000)²
F = 0.0143 N
Thus, the force Sally experiences, in N, due to the presence of the asteroid is 0.0143 N.
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A 520 Hz tone is sounded at the same time as a 516 Hz tone. What is the beat frequency?
A 520 Hz tone is sounded at the same time as a 516 Hz tone now the beat frequency is 4 Hz.
What is a frequency?The pace of direction changes in current per second is known as frequency. It is expressed in hertz (Hz), a unit of measurement that is used internationally. One hertz is equal to one cycle per second. One hertz (Hz) is equivalent to one cycle per second. A complete alternating current or voltage wave is referred to as a cycle.
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WHATS THE CORRECT ANSWER ANSWER ASAP
Answer:
speed and velocity
Explanation:
Three strings, attached to the sides of a rectangular frame, are tied together by a knot as shown in the figure. The magnitude of the tension in the string labeled C is 56.3 N.
Calculate the magnitude of the tension in the string marked A. (You'll need to get the various positions from the graph. The ends of the strings are exactly on one of the tic marks.)
331.35 N is incorrect.
The magnitude of the tension in the string marked A and B is mathematically given as
A = 52.5 N
What is the magnitude of the tension in the string marked A?Generally, the equation for is mathematically given as
The angle at A is...
[tex]tan\theta = 3/8[/tex]
When below the negative x
B= tan\phi
[tex]tan\phi = 5/4[/tex]
When below the negative x
C=
[tex]tan \rho = 1/6[/tex]
Hence, considering the Horizontal components
74.9cos(9.46) = A*cos(20.6) + B*cos(51.3)
A = 78.9 - 0.668B
Hence, considering the Vertical components
74.9*sin(9.46) + Asin(20.6) = Bsin(51.3)
40.07 = 1.015B
B = 39.5 N
In conclusion, Sub the value of B is the equation of A
A = 78.9 - 0.668B
Sub
A = 78.9 - 0.668( 39.5 N)
A = 52.5 N
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An open bed truck is moving at 20 m/s and comes to a stop. A 100 kg crate sitting in the back of the truck remains at rest in the truck bed. How much work was done by friction to keep the crate from moving
as the truck came to a stop?
[?] J
The work done was done by friction to keep the crate from moving as the truck came to a stop is 20,000 J.
Work done by friction to prevent the crate from moving
The work done is determined by applying the principle of conservation of energy.
W = K.E
W = ¹/₂mv²
where;
m is mass of cratev is speed of the crate with respect to the truck = 20 m/sW = ¹/₂(100)(20²)
W = 20,000 J
Thus, the work done was done by friction to keep the crate from moving as the truck came to a stop is 20,000 J.
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A rocket starting from its launch pad is subjected to a uniform acceleration of 100 meters/second2. Determine the time needed to reach the final velocity of 1,000 meters/second.
Answer:
10s
Explanation:
Acceleration is a measure of a rate of change of velocity, or in other words, a measure of how quickly the velocity is changing.
If acceleration is constant, then the velocity is changing by a constant amount.
With an acceleration of 100 m/s^2, starting from the launching pad (and thus, an initial velocity of zero), we can calculate how long it will take to reach a final velocity of 1000m/s with the following formula:
[tex]v=at+v_o[/tex] where "v" is the final velocity at some later time "t", "a" is the constant acceleration, and "v" sub-zero is the initial velocity.
[tex]v=at+v_o[/tex]
[tex](1000\text{ [m/s]})=(100 \text{ } [\text{m/s}^2] )t+(0\text{ [m/s]})[/tex]
[tex]1000\text{ [m/s]}=100 \text{ } [\text{m/s}^2] *t[/tex]
[tex]\dfrac{1000\text{ [m/s]}}{100 \text{ } [\text{m/s}^2]}=\dfrac{100 \text{ } [\text{m/s}^2] *t}{100 \text{ } [\text{m/s}^2]}[/tex]
[tex]10\text{ [s]}=t[/tex]
So, it will take 10 seconds for the rocket to reach 1000m/s when starting from the launching pad, with a constant velocity of 100m/s^2.
Verification:
In this situation, it is quick to verify that 10 seconds is correct by looking at what the velocities will be each second.
Recognizing that the acceleration is [tex]a=\dfrac{100 [\frac{m}{s}]}{1[s]}[/tex], the velocity increases by 100 units [m/s] every second.
At time 0[s], the velocity is 0[m/s]
At time 1[s], the velocity is 100[m/s]
At time 2[s], the velocity is 200[m/s]
At time 3[s], the velocity is 300[m/s]
At time 4[s], the velocity is 400[m/s]
At time 5[s], the velocity is 500[m/s]
At time 6[s], the velocity is 600[m/s]
At time 7[s], the velocity is 700[m/s]
At time 8[s], the velocity is 800[m/s]
At time 9[s], the velocity is 900[m/s]
At time 10[s], the velocity is 1000[m/s]
So, indeed, after 10 seconds, the velocity reaches 1000 m/s
1kg is the mass of ……… of water in 4 degree C
(15 points) A 40.0 kg beam is attached to a wall with a hi.nge and its far end is supported by a cable. The angle between the beam and the cable is 90o. If the beam is inclined at an angle of θ = 31.0° with respect to horizontal.
1. What is the horizontal component of the force exerted by the hi.nge on the beam? (Use the `to the right' as + for the horizontal direction.)
2. What is the magnitude of the force that the beam exerts on the hi.nge?
The horizontal component of the force is 336 N
The magnitude of the force that the beam exerts on the hi_nge is 537.9 Newtons
What is the horizontal component of the force exerted by the hi_nge on the beam?The system of the beam, hi_nge and cable are in equilibrium.
The horizontal component of the force exerted by the beam is given below as:
Horizontal component of the force = mg × cos 31°
Horizontal component of the force = 40 × 9.8 × cos 31°
Horizontal component of the force = 336 Newtons
The magnitude of the force that the beam exerts on the hi_nge is given as:
F = mg × cos 31° + mg × sin 31°
F = 40 × 9.8 × cos 31° + 40 × 9.8 × sin 31°
F = 537.9 Newtons
Hence, the magnitude of the force that the beam exerts on the hi_nge is 537.9 Newtons.
In conclusion, the system of forces acting on the hi_nge and the beam are in equilibrium.
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Three ropes A, B and C are tied together in one single knot K. (See figure.)
If the tension in rope A is 65.3 N, then what is the tension in rope B?
46.17 N is incorrect.
The tension in the rope B is determined as 10.9 N.
Vertical angle of cable B
tanθ = (6 - 4)/(5 - 0)
tan θ = (2)/(5)
tan θ = 0.4
θ = arc tan(0.4) = 21.8 ⁰
Angle between B and Cθ = 21.8 ⁰ + 21.8 ⁰ = 43.6⁰
Apply cosine rule to determine the tension in rope B;
A² = B² + C² - 2BC(cos A)
B = C
A² = B² + B² - (2B²)(cos A)
A² = 2B² - 2B²(cos 43.6)
A² = 0.55B²
B² = A²/0.55
B² = 65.3/0.55
B² = 118.73
B = √(118.73)
B = 10.9 N
Thus, the tension in the rope B is determined as 10.9 N.
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