Answer:
D
Explanation:
F = G m1 m2 / r^2 now double r
F = G m1m1/ (2r)^2
F = 1/4 G m1m2/r^2 <===== this is 1/4 of the original
a generator uses loops of area 0.239 m^2, rotating 373 rad/s in a 0.0639 t magnetic field. how many loops must the coil have to generate a maximum emf of 2500 v?
The loops must the coil have to generate a maximum emf of 2500 will be 439.
What is the faraday law of electromagnetic induction?According to Faraday's law of electromagnetic induction, the rate of change of magnetic flux linked with the coil is responsible for generating emf in the coil resulting in the flow of amount of current.
Given data;
Area,A = 0.239 m²
Angular velocity,ω=373 rad/sec
Magnetic field,B=0.0639 T
Maximum emf,E= 2500V
The formula for the maximum induced voltage is;
E{max} = N × B × A × ω
2500 = N × 0.639 × 0.0239 × 373
N = 438.66
N = 439 \ turns
Hence, loops must the coil have to generate a maximum emf of 2500 will be 439.
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Answer: 11392.99
Explanation: I had the same problem and here are the steps:
Values:
N (Number of loops) = 2000
A (area) = 0.239
ω (angular velocity) = 373
B (magnitude) = 0.0639
ε = NABω
= (2000)(0.239)(373)(0.0639)
ε = 11392.99 (FINAL ANSWER)
A hydrogen bond forms by the electrostatic interaction of opposite charges in two molecules. If
the bond length is 2x10 -10 m and the magnitude of the charges involved is
approximately 1.60x10 -20C, what is the force between the molecules involved in the bond?
The force between the molecules involved in the bond is 6. 426 *10^-11 Newton
How to determine the force
Using the formula:
F = K[q1 x q2]/D^2
where K is coulombs constant =9 *10 ^9 Nm^2/C^2.
q1 and q2 = charges = 1.60x10 -20C
d = distance between the charges = 2x10 -10 m
Substitute the values into the formula
F = [tex]9 * 10^9\frac{ 1.60*10^ -20 * 1.60 *10^ -20}{2x10^ -10^{2} }[/tex]
F = [tex]9 *10^9\frac{2. 856* 10^-40}{4* 10^-20}[/tex]
F = [tex]9* 10^9 * 7. 14* 10^-21[/tex]
F = [tex]6. 426 * 10^-11[/tex] Newton
Thus, the force between the molecules involved in the bond is 6. 426 *10^-11 Newton
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what is the radius of the 5th orbital in hydrogen?
Answer: 1.32 x 10^-9 m
Explanation:
The formula for the radius of nth orbital is:
[tex]r_{n}=\frac{n^{2}}{Z} \times 0.528 \text { Angstorms }[/tex]
For hydrogen, Z= 1, so we have:
[tex]$$\begin{aligned}r_{n} &=5^{2} \times 0.528 \text { Angstorm } \\&=13.2 \text { Angstorms } \\&=13.2 \times 10^{-10} \mathrm{~m} \\&=1.32 \times 10^{-9} \mathrm{~m}\end{aligned}$$[/tex]
Answer: 1.32*10^-9
Explanation: I had the same question and here's what I got:
rn = n2(r1)
n = 5
r = 5.29*10^-11
rn = n^2(r1)
= 5^2(5.29*10^-11)
r = 1.32*10^-9
Estimate the gravitational force of attraction between two people sitting side by side on a park bench. How does this force compare with the gravitational force exerted on each of them by the Earth
Weight is compared with the gravitational force exerted on each of them by the Earth.
What is Newton's law of gravitation?Newton's law of gravity states that each particle having mass in the universe attracts each other particle with a force known as the gravitational force.
The gravitational force is proportional to the product of the masses of the two bodies and inversely proportional to the square of their distance.
When mass increases and distance reduces, gravity rises. Gravity also lowers when the distance between two points grows and the mass decreases.
The gravitational force is balanced by weight;
[tex]\rm F = W \\\\ G\frac{mM}{r^2} =mg[/tex]
Hence, weight is compared with the gravitational force exerted on each of them by the Earth.
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The following equation shows the position of a particle in time t, x=at2i + btj where t is in second and x is in meter. A=2m/s2, b=1m/s. Find
A, the average velocity of the particle in the time interval t₁=2sec and t₂=3sec
B, the velocity and acceleration at any time t.
C, the average acceleration in the time interval given in part (a)
will give brilliance
A. The average velocity of the particle in the time interval t₁=2sec and t₂=3sec is 4 i m/s.
B. The velocity and acceleration at any time t is 4t i +1 j and 4i.
C. The average acceleration in the time interval given in part (a) is 4
What is acceleration?Acceleration can be defined as the rate change of velocity with time.
acceleration a = (Δv) / (Δt)
Given the following equation shows the position of a particle in time t, x=at² i + bt j
where t is in second and x is in meter. a=2m/s², b=1m/s.
A. Velocity is time rate of change of displacement.
V = dx/dt
V = d/dt (2t² i + 1t j)
V = 4t i +1 j
Velocity in time interval,
At t₁=2sec , V₂= 4x2 i + 1 j = 8 i + 1 j
At t₂=3sec, V₃ = 4x3 i + 1 j = 12 i + 1 j
Average velocity in time interval t₁=2sec and t₂=3sec is
, V₃ - V₂ = (12 i + 1 j) - ( 8 i + 1 j )
Average velocity = 4 i
B. Velocity at time t, is
V(t) = V = 4t i +1 j
Acceleration a = dV/dt
a(t) = d/dt (4t i +1 j)
a(t) = 4 i +0 j
C. Average acceleration in time interval t₁=2sec and t₂=3sec is
a = 4 m/s²
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3. Sarah is a world-class diver in the women's 3-m springboard competition. Her height
h (in metres), above the water t seconds after she leaves the board is given by
h = -4.9t2 + 8.8t + 3. How long is Sarah in the air before she reaches the water?
Make sure to round your answer to the nearest tenth.
Answer:
2011, 2013, 2016 Alberta Education
Answer:
1.163 seconds
Explanation:
see the attached. solve the quadratic equation.
When a cold alcohol thermometer is placed in a hot liquid, the column of alcohol goes down slightly before going up. Explain why.
Answer:
See below
Explanation:
When a cold alcohol thermometer is placed in a hot liquid, the following takes place.The glass of thermometer expands because of the heat so the column of alcohol goes down.After some time, the heat travels to alcohol and then alcohol expands.So, Reason why alcohol goes down first:Alcohol first goes slightly down because of the expansion of the glass of thermometer before doing up.
[tex]\rule[225]{225}{2}[/tex]
What is the monthly (30 days) energy cost (in
$) of leaving a 40-W bulb on continuously if
electricity costs 21¢ per kWh? Round final
answer to the nearest cent.
Explanation:
Power= 40 W
cost=21¢/kWh
t=1 month=30 days = 720h
Energy= power*time
E= 40W* 720h = 28800kWh
Cost= Energy*rate
cost= 28800kWh*21¢/kWh
cost=604800¢
What does the first law of thermodynamics state about energy?
The first law states that the internal energy change of that system is given by Q − W . Since added heat increases the internal energy of a system, Q is positive when added to the system and negative when removed from the system.
1) 40 coloumbs of charge flow in 10 seconds. What is the current?
[tex]\large\boxed{Formula: I= \frac{Q}{t}}[/tex]
Note that:I: CurrentQ: Charge t: TimeSolution:Current is the flow of electrons around a circuit.SI unit of current is Amperes or Amps Symbol is ( A )Let's solve!
The formula is given above.
Let's substitute the values according to the formula.
We'll have to divide the measure of charge by the given time.
[tex]I= \frac{40}{10}[/tex]
Final answer:
[tex]\large\boxed{= 4 \: Amps \: (A)}[/tex]
Hence, the current is 4 amps.
Lesson 1, What is Physical Science.
Write an expository essay explain the difference between scientific knowledge and other kinds of science, include ideas regarding:
1) the scientific method.
2) true science versus false science.
3) examples of what scientists study and do not study.
4) what is required for a scientist to consider an idea to be true.
Physical science explains the physical world and not supernatural events and an idea is considered true by science if it can be observed, explained and reproduced by others.
What is physical science?
Physical science is a systematic study of the of the physical world and phenomena based on observation and experiments.
The scientific method involves:
observation and questionshypothesisexperimentsresults and further experimentstheories and lawsScience explains the physical world and not supernatural events.
Science studies physical phenomena such as the stars, the planets, living things, etc.
Science do not study about angels or demons or supernatural events.
An idea is considered true by science if it can be observed, explained and reproduced by others.
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Metals are used in many products because of the characteristic properties that most metals have.
Which product
requires the high luster of metals in order to work?
O mirrors
O pots and pans
O food wrap
O circuit boards
a) Mirrors
Mirror requires the high luster of metals in order to work.
What causes the highest luster of a metal?When light shine on to the surface of a metal, its electrons absorb small amounts of energy and become excited into one of its many empty orbitals.
The electrons immediately fall back down to lower energy levels and emit light.
This process is responsible for the high luster of metals.
Here,
Mirrors have metal coating on its back side, because of high reflective property , high lustrous mirror is preferred . When metal is more lustrous, the less light reflect into it and bounces back.
Coating one side of a piece of glass with shiny metals can turn it into a mirror, reflecting light coming toward it.
Window glass can reflect only eight percent of light hitting it, while mirrors can reflect 95 percent of light hitting them.
The glass in a mirror is usually coated with a layer of silver or aluminum.
Mirrors are shiny because when photons (rays of light) coming from an object , it strike the smooth surface of a mirror, then they bounce back at the same angle. Our eyes see these reflected photons as a mirror image.
Therefore,
Mirror requires the high luster of metals in order to work.
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Answer:A) mirrors
Explanation:
In a hydraulic lift whose input line has a cross-sectional area of 1.00 cm² and whose output line has
a cross-sectional area of 22.0 cm², what is the largest mass (kg) that can be lifted by an input force
of 200. N?
By using Newton's Second law of motion, the largest mass that can be lifted by this input force is equal to 2,244 kg.
How to calculate the largest mass?Based on the information provided, we can logically deduce that the output to input force ratio is equal to 22:1. This ultimately implies that, the input force is equal to 1000 N, which would result in an output force of 22,000 N.
Next, we would calculate the largest mass by using Newton's Second law of motion:
Mass = Force/Acceleration
Mass = 22,000/9.8
Mass = 2,244 kg.
Note: Acceleration due to gravity is equal to 9.8 m/s².
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A local municipality placed an advert in the local newspaper for a competition of local high schools to participate to build a security system in the community hall to avoid vandalism and break ins
We will use the design process to meet the requirements of the competition by the given explained in the main answer.
What is the competition?The initiative was taken by two or more parties operating independently to win the business of a third party by competing to hire contractors on the best terms possible.
The complete question is
"A local businessperson placed an advert in the local newspaper for a competition for girls only from different schools to participate in the competition. The competition is about drawing ideas for a shopping complex for the local community. Girls from the different schools are excited about the competition. you are a group of boys in the local schools who saw the advert and feel it is unfair for you to be excluded from the competition.
consider yourself as one of the learners in the local schools.
Explain why the project should be given to boys also who have better skills for this project than the girls do.
1.2 think about the design process skills, investigates, design, make, evaluate and communicate."
Explain how you will use the design process to meet the requirements of the competition.
[ 1.1 ]Boys should also be given the project because some of them have more artistic talent than girls do when it comes to sketching designs for local shopping centers.
Boys can also present a clear picture of how local communities can expand their shopping options.
For instance, they can encourage local merchants to offer seasonal items because doing so will benefit their businesses.
They can also suggest that retailers encourage customers to bring a friend to participate in competitions, which will be highly regarded.
[1.2] In order to fulfill the needs of the competition, I would make sure to explore how a shopping center for the neighborhood functions, for instance, by making sure I am aware of the strategies one may use to enhance his or her firm in the neighborhood.
In order to win the competition, I would make sure that I was confident in what I was saying and that I was audible enough to be heard during the competition.
Finally, I would make sure I met the competition's conditions by staying on-topic and solely addressing the issues raised in the advertisement
Hence will use the design process to meet the requirements of the competition.
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Aude slipped on ice going 7.6 m/s .What was her velocity before she hit the wal?
Answer:
Define universal gravitational constant. Why is newton's law of gravitation called universal law?
a. The potential energy stored in the compressed spring of a dart gun, with a spring constant of 62.00 N/m, is 0.940 J. Find by how much is the spring is compressed.
b. A 0.010 kg dart is fired straight up. Find the vertical distance the dart travels from its position when the spring is compressed to its highest position.
c. The same dart is now fired horizontally from a height of 4.70 m. The dart remains in contact until the spring reaches its equilibrium position. Find the horizontal velocity of the dart at that time.
d. Find the horizontal distance from the equilibrium position at which the dart hits the ground.
a. The spring is compressed by 0.174 m.
b. The vertical distance the dart travels from its position when the spring is compressed to its highest position is 9.6 m.
c. The horizontal velocity of the dart at that time is 13.74 m/s.
d. The horizontal distance from the equilibrium position at which the dart hits the ground is 19.236 m.
What is potential energy?The energy by virtue of its position is called the potential energy.
a. Given is the potential energy stored in the compressed spring of a dart gun, with a spring constant of 62.00 N/m, is 0.940 J.
PE of spring = 1/2 kx²
Put the values, we get
P.E = 0.940 = 1/2 x 62 x²
x = 0.174 m
Thus, the spring is compressed by 0.174 m.
b. Given is a 0.010 kg dart is fired straight up.
The vertical height is find out by
0.940 J = (0.010 kg) (9.8 m/s²) h
h = 9.6 m
Thus, the vertical distance the dart travels from its position is 9.6 m
c. From the conservation of energy principle, total mechanical energy is conserved.
1/2 mv² =mgh
v = √2gh
Plug the values, we get
v = √2 x 9.8x 9.6
v = 13.74 m/s
Thus, the horizontal velocity is 13.74 m/s.
d. Time that dart spends in air, t = √2h/g
t = √(2x9.6)/9.81
t = 1.4 s
The horizontal distance from the equilibrium position at which the dart hits the ground.
Horizontal distance = (Velocity on x direction) x time
Horizontal distance = 13.74 m/s x 1.4s
Horizontal distance = 19.236 m
Thus, the horizontal distance is 19.236 m.
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The position of given object is s(t)= t^5 + cos 4t
Find the velocity and acceleration functions
Answer:
v(t)=s'(t)=5t⁴-sin(4).4, for velocity function at time t
a(t)=v'(t)=20t³, for acceleration function at time t
A box with a mass of 40 kg sits at rest on a frictionless tile floor. with your foot, you apply a 20 N force in a horizontal direction. what is the acceleration of the box?
Answer:
0.5 m/s²
Explanation:
according to Newton's second law, we are goven a relationship between force, mass and acceleration, with the formula:
F = m×a
F for force
m for mass
a for acceleration
we use the given data and get:
20 = 40×a
we find a=20/40=0.5m/s²
acceleration of the box is 20m/s^2
given
mass (m) = 40 kg
force (f) = 20n
acceleration (a) =?
we know,
f = m × a
20 = 40 × a
40 - 20 = a
20m/s^2 = a
the temprerture of an object is 40°c.what is this tempreture in farhenhite scale?
This is an exercise of thermal scales.
Data:T = 40 °C
T = °F ¿?
To convert degrees Celsius to degrees Fahrenheit, we have the formula:
[tex]\bf{^{\circ}F=\dfrac{9}{5} \ ^{\circ}C+32 \ \ \to \ \ \ Formula }[/tex]
We substitute our data into the formula.
[tex]\bf{^{\circ}F=\dfrac{9}{5} \times 40+32}[/tex]
First we divide 9/5 multiplied by 40.
[tex]\bf{=75+32}[/tex]
Add 75 plus 32
[tex]\bf{=104 \ ^{\circ}F}[/tex]
Therefore, the temperature change of 40 °C on the °F scale is equal to 104.
[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Piscis04}}}}}}[/tex]
a car is traveling along a straight road at a velocity of 30m/s when its engine cuts off. For the next ten seconds, the car slows down, and its average acceleration is a1. For the next five seconds, the car slows down further at a velocity of 24m/s, and its average acceleration is a2. The ratio of the average acceleration values is a1/a2=1.5. Find the velocity of the car at the end of the initial ten-second interval.
Answer:
See below....the question is unclear....pick the answer you think they want
Explanation:
Car goes from 30 m/s to 24 m/s in 10 seconds
acceleration = change in velocity/change in time
= -6 m/s / 10 s = - 3/5 m/s^2
The wording of the question is not very good.....perhaps they meant to say that after the 5 seconds the velocity is now 24 m/s ?
a1 *10 + a2 *5 = -6 m/s
( 6 m/s is the change in velocity from 30 to 24 m/s)
a1/a2 = 1.5 so a2 = a1/1.5 (substitute this in)
10 a1 + 5 ( a1/1.5) =-6
15 a1 + 5 a1 = -9
a1 = - .45 m/s^2
The velocity of the car at the end of the initial ten-second interval, given that the car further slows down for the next five seconds, is 25.5 m/s
How to determine the velocity of the car at the end of the 10 s interval?From the first statement, we have:
Initial velocity (u₁) = 30 m/sTime (t₁) = 10 secondsVelocity at the end of 10 s (v₁) = ?v₁ = u₁ + a₁t₁
v₁ = 30 + (a₁ × 10)
v₁ = 30 + 10a₁ ......(1)
From the second statement, we have:
Time (t₂) = 5 sFinal velocity (v₂) = 24 m/sRation of acceleration (a₁/a₂) = 1.5Initial velocity (u₂) = Velocity at the end of 10 sv₂ = u₂ + a₂t₂
24 = u₂ + (a₂ × 5)
24 = u₂ + 5a₂ .......(2)
But,
u₂ = v₁ = 30 + 10a₁
Thus, we have:
24 = 30 + 10a₁ + 5a₂
But,
a₁/a₂ = 1.5
a₁ = 1.5a₂ ..... (3)
Thus, we have:
24 = 30 + 10a₁ + 5a₂
24 = 30 + 10(1.5a₂) + 5a₂
24 = 30 + 15a₂ + 5a₂
24 = 30 + 20a₂
Collect like terms
24 - 30 = 20a₂
-6 = 20a₂
Divide both sides by 20
a₂ = -6 / 20
= -0.3 m/s²
Substituting the value of a₂ into equation 3, we have
a₁ = 1.5a₂
= 1.5 × -0.3
= -0.45 m/s²
Substitute the value of a₁ into equation 1 to obtain the velocity, v₁ at the end of the initial to 10 s
v₁ = 30 + 10a₁
= 30 + (10 × -0.45)
= 30 - 4.5
= 25.5 m/s
Thus, velocity of the car at the end of the initial ten-second interval is 25.5 m/s
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A model rocket with a mass of 5 kg has a downward thrust of 100 newtons. Assuming there are no other forces acting on the rocket, what is the rocket’s acceleration upward?
a. 20 m/s2
b. 100 m/s2
c. 5 m/s2
d. 105 m/s2
Answer:
A
Explanation:
F = m * a
100 = 5 * a
a = 100/5 = 20 m/s^2
If the distance between two objects is cut in half, what happens to the
gravitational force between them?
A. It decreases to 1/2 its original magnitude.
B. It decreases to 1/4 its original magnitude.
O
C. It increases to 4 times its original magnitude.
D. It increases to 2 times its original magnitude.
Suppose the resistance of a copper wire is 1.05 N at 30°C.
Find the temperature at which the resistance becomes 1.50
Ω.
Answer:
42.9°C
Explanation:
Resistance of a conducting material is directly proportion to Temperature, that is, when being heated, their is more of collisions between the molecules of the material which as a result offers more opposition to the flow of current through it.
therefore R=kT
where R=resistance of the wire
T=Temperature
k= proportionality constant
when R=1.05 T=30°C
so k=1.05/30
k=0.035
when R=1.5 k=0.035
so T=1.5/0.035
T=42.9°C. or 43°C approximated
Three small but dense objects are located in the x-y plane as shown in the figure. The objects have the following masses: mA = 3.19 kg, mB = 2.55 kg and mC = 1.41 kg.
Determine the x and the y coordinates of the center of the mass of this system. The objects are small in size, they can be treated as point masses.
x coordinate: ?
y coordinate: ?
The x and the y coordinates of the center of the mass of this system will be 43.1 m and 3.12 m respectively.
What is the center of mass?A location is established in relation to an object or set of objects in the center of mass. It is the system's average position across all of its components.
Given data;
There are three little objects that are densely spaced out in the x-y plane.;
The value of the masses
m₁=1.41 kg
m₂=2.55 kg
m₃=3.19 kg
[tex]\rm X_{cm} =\frac{ (W_1x_1 + W_2x_2 + W_3x_3)}{(W_1 + W_2 + W_3)} \\\\\ X_{cm} ==\frac{1.41 \times 2 + 2.55 \times 6 +3.19 \times 4}{1.41+2.55+3.19} \\\\ X_{cm} =4.31 \ m[/tex]
[tex]\rm Y_{cm} =\frac{ (W_1y_1 + W_2y_2 + W_3y_3)}{(W_1 + W_2 + W_3)} \\\\\ X_{cm} ==\frac{1.41 \times 2 + 2.55 \times 4 +3.19 \times 7}{1.41+2.55+3.19} \\\\ X_{cm} =3.12 \ m[/tex]
Hence, the x and the y coordinates of the center of the mass of this system will be 4.31 m and 3.12 m respectively.
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5. A uniform solid ring of mass M = 10 kg and radius R = 2 m is initially rotating in mid-air with angular speed 20 rad/s [the Before state in figure (I) below]. It is then placed in contact with a surface (assume that the surface immediately feels the full weight of the ring). (1) M Before Wi (II) wf V Ө ə Ө After Ө wf H ? (a) What kind of frictional force acts on the ring upon contact with the surface? (b) If the ring begins to roll smoothly to the right with speed v = 10 m/s after 5 seconds of contact (the After state), find the coefficient of friction corresponding to the frictional force you mentioned in (a). (c) What is the increase in the thermal energy of the ring/surface system from right before the ring contacts the surface, to when the ring starts to roll smoothly? The ring then rolls smoothly up a ramp of 0 = π/6 rad and H = 5 m [see figure (II)] (d) What is the horizontal distance, from the end of the ramp, at which the ring lands?
(a) The kind of frictional force acts on the ring upon contact with the surface is kinetic friction before rolling and afterwards it is static friction.
(b) If the ring begins to roll smoothly to the right with speed v = 10 m/s after 5 seconds of contact (the After state), the coefficient of friction corresponding to the frictional force is 0.612
(c) The increase in the thermal energy of the ring/surface system from right before the ring contacts the surface, to when the ring starts to roll smoothly is 7500 J.
(d) The horizontal distance, from the end of the ramp, at which the ring lands is 7.78 m
What is frictional force?When an object is moving on a rough surface, it experiences opposition. This opposing force is called the friction force.
Given is a uniform solid ring of mass M = 10 kg and radius R = 2 m is initially rotating in mid-air with angular speed 20 rad/s [the Before state in figure (I) below]. It is then placed in contact with a surface (assume that the surface immediately feels the full weight of the ring).
(a) The kind of frictional force acts on the ring upon contact with the surface is kinetic friction before rolling and afterwards it is static friction.
(b) angular frequency = velocity / radius
ωf = 10/2 = 5 rad/s and ωi = 20 rad/s
Angular acceleration, α = ωf - ωi /t
Put the values, we get
α = -15/5 = -3 rad/s²
Coefficient of friction, μ = a/g = rα/g
Plug the values, we get
μ = 0.612
Thus, the coefficient of friction corresponding to the frictional force is 0.612.
(c) The energy lost = heat generated
energy lost = 1/2 Iω² + 1/2 Mv²
energy lost = 1/2 MR²ω² + 1/2 Mv²
Plug the values, we get
energy lost = 7500 J
Thus, the increase in the thermal energy is 7500 J.
(d) The horizontal distance, from the end of the ramp, at which the ring lands
s= (v- 2gH) sin2θ /g
s = (10 - 2x (-9.81)x5 ) sin (2x π/6) / 9.81
s = 7.78m
Thus, the horizontal distance is 7.78 m
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A cup of water is warmed from 21 °C to 85 °C. What is the difference between these two temperatures, in kelvins?
Answer:
337k
Explanation:
First, let us find the difference between the given two temperatures.
Difference = 85°C - 21°C
= 64°C
And now we have to write the temperature in kelvins.
To convert Celcius to Kelvins you can add 273 to the temperature in Celcius.
Let us find it now.
64°C + 273 = 337k
Therefore,
64°C ⇒ 337k
How many seconds are in 28 hours?
Answer:
1680 seconds
Explanation:
[tex]28 hrs * \frac{60 s}{1 hr} =1680s[/tex]
a. Recent studies have raised concern about 'heading' in youth soccer (i.e., hitting the ball with the head). A soccer player 'heads' a size 3 ball deflecting it by 40.0°, and keeps its speed of 13.20 m/s constant. A size 3 ball has a mass of approximately 2.000 kg. What is the magnitude of the impulse which the player must impart to the ball?
b. If the player's head has a mass of 2.90 kg, what is the magnitude of the average acceleration of the player's head during the impact. Assume that over the brief time of the impact, 30.40 ms, the player's head can be treated separately from the player's body.
a. The magnitude of the impulse which the player must impart to the ball is 17.25 kg.m/s.
b. The magnitude of average acceleration of the player's head during the impact is 195.66 m/s².
What is impulse?The change in momentum is equal to the product of impact force applied while colliding and time for that impact.
Impulse F. t = m (Vf -Vi)
where, Vf is the final velocity and Vi is the initial velocity.
Given, a soccer player 'heads' a size 3 ball deflecting it by 40.0°, and keeps its speed of 13.20 m/s constant. A size 3 ball has a mass of approximately 2.000 kg.
a. Substitute the values into the expression, we get
Impulse (x) = 2 x (13.20 - 13.20cos40°)
Impulse (x) = 3.088 kg.m/s
Impulse in y direction, is
Impulse (y) = 2 x 13.20sin40°
Impulse (y) = 16.97 kg.m/s
so, the magnitude of impulse is
I = sq rt(Ix² + Iy²)
Put the values, we get
I = 17.25 kg.m/s
Thus, the magnitude of the impulse which the player must impart to the ball is 17.25 kg.m/s
b. The player's head has a mass of 2.90 kg. The brief time of the impact, 30.40 ms,
F.t = I
Put the given values, we have
F = 17.25 / 30.40 x 10⁻³
F = 567.434 N
From the Newtons second law of motion,
F = ma
Plug the values from the question, we have
567.434 N = 2.90 x a
a = 195.66 m/s²
Thus the magnitude of average acceleration of the player's head during the impact is 195.66 m/s².
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an object is held 33.5 cm from a convex mirror. it creates a virtual image of magnification 0.253. what is the focal length of the mirror?
Answer:
Magnification= -image distance/object distance
.253=image distance/33.5
image distance= 8.48 cm
In the opposite figure, the work done by the force F to push the box upwards from the ground to the top of the inclined plane is .......... a) 300 J c) 600 J (b) 450 J d) 750 J F=100 N CamScanner Wa 3m In the opposite figure , the work done by the force F to push the box upwards from the ground to the top of the inclined plane is .......... a ) 300 J c ) 600 J ( b ) 450 J d ) 750 J F = 100 N CamScanner Wa 3m
In the opposite figure, the work done by the force F to push the box upwards from the ground to the top of the inclined plane is 600 J.Option c is correct.
What is work done?Work done is defined as the product of applied force and the distance through which the body is displaced on which the force is applied.
The displacement value from the triangle is;
[tex]\rm sin 30^0 = \frac{P}{H} \\\\ H=S =\frac{3 \ m}{sin 30^0} \\\\ S = 6\ m[/tex]
The work done is found as ;
[tex]\rm W= Fd \\\\ W = 100 \ N \times 6 \\\\ W= 600 \ J[/tex]
The force F in the opposing figure does 600 J of effort to lift the box from the ground to the top of the inclined plane.
Hence option c is correct.
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