v ≈ (3.28512, 20.74146) (3.28512, 20.74146)
In trigonometry, what is a vector?
Vectors can be used to depict motion between points in the coordinate plane. A vector is just a line segment in a specified location with an arrow designating its length and direction. The vectors in the following
Detailed explanationv = 21 (cos (81°), sin (81°))
components for v (3.28512, 20.74146) (x, y)
Authors use different notations. You can write the vector as...
(r, θ) = (21, 81°)
r∠θ = 21∠81°
21 cis 81° = r cis
v = 21·e^(i·9π/20)
(x, y) ≈ (3.28512, 20.74146) (3.28512, 20.74146)
v = 3.28512i +20.74146j Maybe this is the vector notation you're looking for (i and j are unit vectors in the x- and y-directions, respectively)
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Given a metal loop of wire with an area of 400 square centimeters and a magnetic field of 0.0875 Tesla through it. If the magnetic field is constant everywhere through the loop then which of these is the magnetic flux through the loop in SI units? [4. Define magnetic flux] 0.00350 0.0140 286
We will have that the value will be:
[tex]\Phi=(0.04m^2)(0.0875T)\Rightarrow\Phi=0.00350m^2T[/tex]a hydraulic lift requires a minimum effort force of 14.4N to lift a patient of a mass 82kg .How much is the effort piston area if the resistance piston has an area of 1.2m²
The output force of a hydraulic lift is given by:
[tex]F_2=\frac{A_2}{A_1}F_1[/tex]In this case we need to lift a patient of mass 82 kg, that means that the lifting force has to be equal to:
[tex]F_2=82\cdot9.8=803.6[/tex]Now that we know that we plug the values given, in this case we have:
[tex]\begin{gathered} 803.6=\frac{1.2}{A_1}(14.4) \\ A_1=\frac{1.2}{803.6}(14.4) \\ A_1=0.022 \end{gathered}[/tex]Therefore the area of the effort piston is 0.022 squared meters (rounded to three decimal).
a javelin is thrown at 28.5m/s from flat ground at a 43.2 degree angle. How long does it take to reach its maximum height? IN SECONDS
The time taken for the javelin thrown at 28.5 m/s from flat ground at a 43.2 degree angle to reach the maximum height is 2.0 s
How do I determine the time taken to reach the maximum height?From projectile motion, we understand that the time taken to reach maximum height is given as:
t = uSineθ / g
Where
t is the time to reach maximum heightu is the initial velocity θ is the angle of projectiong is acceleration due to gravityNow, using the above formua, we can obtain the time taken for the javelin to reach the maximum height as follow:
Initial velocity (u) = 28.5 m/s
Angle of projection (θ) = 43.2 degrees
Acceleration due to gravity (g) = 9.8 m/s²
Time taken to reach the peak (t) = ?
t = uSineθ / g
t = (28.5 × Sine 43.2) / 9.8
t = 2.0 s
Thus, the time taken to reach maximum height is 2.0 s
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The speed of sound traveling through a dense material is 600 m/s. If the wavelength is 15.0 m, what is the frequency of this sound?9,000 Hz80 Hz0.0025 Hz40 Hz
W0e are asked to determine the frequency of a sound given its velocity and wavelength. To do that we will use the following formula:
[tex]v=\lambda f[/tex]Where:
[tex]\begin{gathered} v=\text{ velocity} \\ \lambda=\text{ wavelength} \\ f=\text{ frequency} \end{gathered}[/tex]Now, we solve for the frequency by dividing both sides by the wavelength.
[tex]\frac{v}{\lambda}=f[/tex]Now, we substitute the values:
[tex]\frac{600\frac{m}{s}}{15m}=f[/tex]Solving the operations:
[tex]40Hz=f[/tex]Therefore, the frequency is 40 Hz.
can you help me with this ap physics class from my school
We know that the components of any vector along the x and y axes are given by:
[tex]\begin{gathered} v_x=v\cos\theta \\ v_y=v\sin\theta \\ \text{ where:} \\ v\text{ is the magnitude of the vector.} \\ \theta\text{ is the angle from the }x\text{ axis to the vector. } \end{gathered}[/tex]In this case we know the tha magnitude of the vector is 6.96 m/s; we also know that the angle from the x-axis to the vector is 51.5° (the sum of angles θ and the 26.5° angle); then we have:
[tex]\begin{gathered} v_x=6.96\cos51.5=4.33 \\ v_y=6.96\sin51.5=5.45 \end{gathered}[/tex]Therefore, the components of the vector are:
[tex]\begin{gathered} v_x=4.33 \\ v_y=5.45 \end{gathered}[/tex]A vector is 148 m long and
points in a -96.3 degree
direction.
Find the x-component of the
vector.
The x-component of the vector is determined as -16.24 m.
What is the x-component of a vector?
The x-component of a vector is the vector component measured along x - direction. It is the vector acting in the x-coordinate.
The magnitude of x -component of a vector is given by the following formula as shown below;
Vₓ = V cosθ
where;
Vₓ is the x - component of the vectorV is the magnitude of the vector = 148 mθ is the angle of the vector = -96.3 degreesVₓ = 148 m x cos(-96.3)
Vₓ = -16.24 m
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Answer:
Y= -147
X= -16.24
Explanation:
The potential energy for a mass on a spring is proportional to the square of which of these quantities?
A. mass
B. frequency
C. displacement
E. period displacement velocity
Answer:
C. Displacement
Explanation:
Please help!!
Question in the picture
Set of equation which is true for the situation is
c) 2SA = SB and 2BA=BB
What is pressure?
Force applied perpendicular to the surface of an object per unit area is called pressure
SI unit of pressure is one newton per square meter (N/m2).
Given, length = 3 foot, width= 1 foot and height = 1 foot
1foot = 0.305m
Volume of tank A = 3*0.305*0.305*0.305
= 0.085
density of water= 1000kg/m^3
Pressure= 1000kg/m^3 *gravity * height
=1000kg/m^3 * 9.8 m/s^2* 0.305
=2989 N
Force exerted by water at bottom= P * A
= 2989*0.085
=254.065 Nm^2
similarly, for tank B
Given ,length = 6 foot, width =1 foot and height= 1foot
Volume of tank B = 6*0.305*0.305*0.305
=0.17
pressure= 1000kg/m^3 * 9.8m/s^2 * 0.305
= 2989 N
Force exerted by water at bottom = P*A
= 2989 * 0.17
=508.13 Nm^2
Hence proved that pressure exerted by tank B is twice that of tank A.
And same goes for pressure exerted on the side of the tank.
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A 100 kg man and 50 kg woman on ice
skates stand facing each other. If the
woman pushes the man backwards so that
his final speed is 1 m/s, at what speed
does she recoil?
Answer:
First you must find the kinetic energy that aman use to push her;So you can find the speed that she recoil
An electron moves between the ends of a 9.00 volt battery. How much work is done on the electron? A)0.78 x10^-15 J B)9.00 x10^-17 J C)1.44 x10^-18 J D)25.0 x 10^-20 J E)15.3 x 10^-20 J
When an electron moves between the ends of a 9.00-volt battery, the work done on the electron is 1.44 * 10⁻¹⁸ Jouoles; option C
What is the work done on an electron?The work done in moving an electron between two points is defined as the product of the potential difference between the points and the charge on an electron.
Mathematically;
Work done = ΔV * qwhere;
ΔV is the potential difference between the points
q is the charge on the electron.
The potential difference between the two points is the work done in moving a unit positive charge from one point to the other in the circuit.
The charge, q on an electron is 1.609 * 10⁻¹⁹ Coulombs.
For the given electron that moves between the ends of a 9.00-volt battery;
ΔV = 9.000 Volts
q = 1.609 * 10⁻¹⁹ Coulombs
Work done = 9.000 * 1.609 * 10⁻¹⁹
Work done = 1.44 * 10⁻¹⁸ Jouoles
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If Hubble's constant had a value of 95 km/s/Mpc, what would be the age of the Universe?
The age of the Universe is 13.8 ± 0.1 billion years.
What is Hubble's constant?The ‘hubble constant, h0’ is used to determine the size of the universe. It is a measurement that is used in describing the universe's expansion. It was a constant introduced by Edwin Hubble. He found out that the farther the distance of the galaxies from the Earth, the faster they would appear to be moving.
One of the most important numbers in cosmology Hubble's constant because it is needed to estimate the size and age of the universe which is 13.8 ± 0.1 billion years.
The age of the universe using Hubble's constant which is 13.8 ± 0.1 billion years.
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A 150 pound man runs up a stairway 20 feet above ground level in 15s. How much work did the man do?
Given:
h = height = 20 ft = 6.096 m
m = 150 pound = 68.0389 kg
time = 15 s
g= 9.8 m/s^2
Potential energy = mgh = (68.0389 ) (9.8 ) (6.096 ) = 4,064.7 J
Work done = 4,064.7 J
I need helppp
What is the force applied to the small piston,f,in Lb that is required to deliver a working force,F, of 1000 lb? The area of the small piston,a, is 0.1963 sq in. and the area of the large piston,A, is 6.28 sq in.
The area of the small piston, a, is 0.1963 sq in. and the area of the large piston, A, is 6.28 sq in. The force applied to the small piston (f)= 31.21 lb that is required to deliver a working force (F)= 1000 lb
What is force?Force is a physical quantity that means if some kind of external or internal affair is happen on a object and the object is move a bit that means a force is act on it. Its a vector quantity.
How can we calculate the force?To calculate the force of the small piston f we are using the formula,
p=P
Or, f/a=F/A
Here we are given,
a= The area of the small piston = 0.1963 sq in
A= The area of the big piston = 6.28 sq in.
F= The force of the big piston = 1000 lb.
We have to calculate the force of the small piston = f
Now we put the values in above equation we get,
f / a = F / A
Or, f = a F/A
Or, f = [tex]\frac{0.1963 \times 1000}{6.28}[/tex]
Or, f = 31.21 lb
Now from the calculation we can say that, The force applied to the small piston (f)= 31.21 lb
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The question is in the attached image:)
No count number what time of the 12 months it's far, the northern and the southern hemisphere will usually revel in a season contrary to the other.
Therefore, if the northern hemisphere has the summer time, then the southern hemisphere will revel in the wintry weather season. When we are saying contrary we additionally suggest that once it's far spring season in the northern hemisphere, then it's far autumn season in the southern hemisphere.
The most important motive for this phenomenon is the lean of the earth on its axis. Since the earth is tilted slightly, one of the hemispheres will usually get hold of greater and direct rays from the solar. It approach that once the earth is tilted in the direction of the solar, then the northern hemisphere gets direct solar rays that are skilled through us because the summer time.
During this time the southern hemisphere stories the wintry weather season. This phenomenon maintains alternating because the planet revolves across the sun. This summer time lasts for 1/2 of a 12 months, or instead 1/2 of a revolution.
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In your readings you learned that “correlation does not imply causality.” Which of the following is the best interpretation of this statement?
A. Just because there is a relationship between two behaviors does not mean that one causes the other
B. Many factors influence the relationship between two behaviors.
C. A relationship between two behaviors does not mean that one or both behaviors are testable.
D. Correlated behaviors are the result of operational conditioning.
SOMEONE PLEASE HELP!
Just because there is a relationship between two behaviors does not mean that one causes the other. Option A.
Natural observation is a research method that observes objects in their natural environment. This approach is commonly used by psychologists and other social scientists. It is a process of deep reflection, questioning, and evidence evaluation. A study in which researchers look for relationships between people's demographic neighborhood and their level of prejudice.
Psychologists use this because it is the most objective method known to produce reliable insights. The science of behavior and mental processes. It attempts to describe and explain aspects of human thinking feeling perception and behavior. Naturalistic observation is a method of observation that involves observing people's behavior in environments in which they normally occur. Laboratory Observation observing behavior in a more artificial environment focusing on a small number of carefully defined behaviors.
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a car accelerates from rest at 7.8 meters per second squared. how much time does it need to attain a speed of 6 meters per second?
Answer:
v = u + at
Explanation:
initial velocity = u = 0
acceleration of the car = a = 7.8 m/s^2
time taken to reach a speed of, v = 6 m/s
hence,
6 = 0 + 7.8 x t
t = 6/7.8
t = 0.77 s
A lamp draws 0.50 A from a 120 V generator. (a) How much power does the generator deliver to the lamp? (b)How much electric energy does the lamp convert to light and heat in a period of 5.0 minutes?
Given:
The lamp draws the current is
[tex]I=0.50\text{ A}[/tex]The voltage supplied by the generator is
[tex]V=120\text{ V}[/tex]The time for which energy converted is
[tex]\begin{gathered} t=5\text{ min} \\ t=5\times60\text{ s} \\ t=300\text{ s} \end{gathered}[/tex]Explanation:
(a)
The power delivered by the generator is given by
[tex]P=VI[/tex]Plugging all the values in the above equation, we get
[tex]\begin{gathered} P=120\text{ V}\times0.50\text{ A} \\ P=60\text{ watt} \end{gathered}[/tex]The power delivered by the generator is
[tex]60\text{ watt}[/tex](b)
Energy is converted by the electric lamp is given by
[tex]E=Pt[/tex]Plugging all the values in the above relation, we get
[tex]\begin{gathered} E=60\text{ watt}\times300\text{ s} \\ E=18000\text{ J} \end{gathered}[/tex]Thus, the electric energy convert by the lamp is
[tex]18000\text{ J}[/tex]an optical instrument consist of two lenses .if the object distance for lens 1 is 12cm then the image distance is 36cm.if the height of the object for lens 2 is 5cm then the image height is 2.5cm. evaluate the combined magnification of the two lenses
The magnification of first lens can be given as,
[tex]m_1=-\frac{v_1}{u_1}[/tex]Here, m1 is the magnification of first lens, v1 is the distance of image from first lens and u1 is the distance of object from first lens.
Substitute the known values in the equation,
[tex]\begin{gathered} m_1=-\frac{36\text{ cm}}{12\text{ cm}} \\ =-3 \end{gathered}[/tex]The magnification of second lens can be given as,
[tex]m_2=-\frac{v_2}{u_2}[/tex]Here, m2 is the magnification of second lens, v2 is the distance of image from second lens and u2 is the distance of object from second lens.
Substitute the known values in the equation,
[tex]\begin{gathered} m_2=-\frac{2.5\text{ cm}}{5\text{ cm}} \\ =-0.5 \end{gathered}[/tex]The combined magnification of two lenses can be given as,
[tex]m=m_1m_2[/tex]Substitute the known values,
[tex]\begin{gathered} m=(-3)(-0.5) \\ =1.5 \end{gathered}[/tex]Thus, the combined magnification of two lenses is 1.5.
A rectangular coil of dimensions 5.40cm x 8.50cm consists of 25 turns of wire. The
coil carries a current of 15.0mA.
(a) Calculate the magnitude of its magnetic moment [5]
(b) Suppose a magnetic field of magnitude 0.35T is applied parallel to the plane of
the loop. What is the magnitude of the torque acting on the loop? [5]
(c) Calculate the magnitude of the torque on the coil when 0.35T magnetic field
makes angles of 600 and 00 with μ. [5]
(d) Show that the units A.m2.T Reduce to N.m. [
A. Magnetic moment will be 17.212*[tex]10^{-4} A-m^{2}[/tex].
B. Torque will be 6.024* [tex]10^{-4} N-m[/tex]
C. 9f B = 35 make angle 60°
then T = 25 × 15,×10³× (5.40x8.50) ×10 × 0.35 Sm 60°
5.22x[tex]10^{-4}[/tex] n-m
of ∅ = 0° t = 0 ∵ sm0 = 0
As it is a Torque NIAB
= Am². Tesla
= N-3.
Rectangular coils have four sides and slightly rounded edges and are generally cheaper to manufacture. Importantly they cannot handle radial forces more effectively than their circular counterparts and most lose their rectangular shape during short circuits. A rectangular coil carrying current is placed in a uniform magnetic field. The direction in which the spool is difficult to rotate.
The motor works on the principle that when a rectangular coil is placed in a magnetic field and an electric current is applied, a force acts on the coil, causing it to rotate continuously. A toroidal transformer is a type of electrical transformer that consists of a toroidal or annular core. Its primary and secondary windings are wound across the surface of the torus core and separated by insulating material. This configuration minimizes flux leakage.
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If a car accelerated from 55 mi/hr to 16 mi/hr. in 3.2s how far did the car go while it was accelerating?
The cargo while it was accelerating at a distance of 0.602 meters.
Acceleration is the name we give to any system wherein the speed changes. on the grounds that speed is a pace and a direction, there are only two approaches so that you can boost up.
Velocity is the rate of change of displacement. Acceleration is the price of alternate velocity. velocity is a vector quantity because it consists of both significance and direction. Acceleration is likewise a vector quantity as it's far simply the charge of alternate velocity.
initial velocity = 55 m/hr
= 55/60× 60 m/sec
= 0.0152 m/sec
final velocity = 16 mi/hr
= 16/3600
= 0.0044 m/sec
time = 3.2 sec
V = u - at
a = ( U - V )/t
= (0.0152 - 0.0044)/t
= 0.0108 m/sec²
S = ut + 1/2at²
= 0.0152 × 3.2 sec + 1/2 × 0.0108 m/sec² × (3.2)²
= 0.0486 + 0.553
= 0.602 meter.
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Jerry is riding his motorcycle at a speed of 45 m/s. He accelerates at a speed of -8 m/s² for 4seconds. How fast will he be going
Given
Initial speed, u=45 m/s
Acceleration
[tex]a=-\frac{8m}{s^2}[/tex]Time taken, t=4 sec
To find
The final speed
Explanation
Let the speed he be going in be v
Thus,
[tex]\begin{gathered} a=\frac{v-u}{t} \\ \Rightarrow-8=\frac{v-45}{4} \\ \Rightarrow-32+45=v \\ \Rightarrow v=13\text{ m/s} \end{gathered}[/tex]Conclusion
The velocity he is going in is 13 m/s.
A satellite orbiting Earth at an orbital radius r has a velocity v. Which represents the velocity if the satellite is moved to an orbital radius of 5r?(1 point)
The equation which represent the velocity, if the satellite is moved to an orbital radius of 5r is V = V/[tex]\sqrt\\5[/tex].
What is Orbital velocity?Orbital velocity or orbital speed is the minimum velocity a body must maintain to stay in an orbit. Due to the inertia of a moving body, the body has the tendency to move on in a straight path.
It is given that the radius is 5r
To find out the equation which represent the velocity if the satellite is moved to an orbital radius of 5r.
Mathematically, the orbital velocity is calculated by the formula:
V = [tex]\sqrt{GM}[/tex]/r
where, V = orbital velocity,
G = gravitational constant
M = mass of a satellite
r = radius
Substituting the value of r in this equation, we have:
V = [tex]\sqrt{GM}[/tex]/r
V = 1/ [tex]\sqrt{5}[/tex] × [tex]\sqrt{GM}[/tex]/r
V = [tex]\sqrt{GM}[/tex]/r
Therefore,
V = 1/ [tex]\sqrt{5}[/tex] × V
V = V/[tex]\sqrt{5}[/tex]
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my opponent will say that recycling is in an issue here but that's just because they don't care about the sea turtles or other marine life affected by plastic in the ocean what is a logical fallacy
Three point charges are located along the x-axis: q1 = +5.0 μC is at 20 cm, q2 = +4.0 μC is at 0 cm, and q3 = +10.0 μC is at –30 cm. What is the net electrostatic force on q2? 0.50 N to the left 500 N to the right 0.50 N to the right 8.5 N to the left
The correct answer is option C, 0.50 N to the left.
Given,
The charges,
q₁=5×10⁻⁶ C
q₂=4.0×10⁻⁶ C
q₃=10.0×10⁻⁶ C
The distance between the 1st charge and the second charge, r₁=20 cm=0.20 m
The distance between 2nd charge and the 3 rd charge, r₂=30 cm=0.30 m
As all the charges have the same sign, the nature of the force is repulsive. Thus the force applied by the q₂ is directed to the left. And the force applied by the charge q₃ is pointed to the right.
From Coulomb's law, the net electrostatic force on q₂ is given by,
[tex]\begin{gathered} F=\frac{kq_1q_2}{r^2_1}-\frac{kq_2q_3}{r^2_2} \\ =kq_2(\frac{q_1}{r^2_1}-\frac{q_3}{r^2_2}) \end{gathered}[/tex]On substituting the knwon values,
[tex]\begin{gathered} F=9\times10^9\times4\times10^{-6}(\frac{5\times10^{-6}}{0.20^2}-\frac{10\times10^{-6}}{0.30^2}) \\ =0.5\text{ N} \end{gathered}[/tex]Thus the magnitude of the net electrostatic force on the charge q₂ is 0.5 N
As the force to the left is greater than the force to the right, the net force will be directed to the left.
Therefore the correct answer is option A, 0.50 N to the left.
Please help me understand this I go to get it
Answer:
Vx = 150 * cos 53 = 90.3 m/s horizontal speed
Vy = 150 * sin 53 = 120 m/s vertical speed
t1 = 120 / 9.8 = 12.2 sec time to reach vertical height (vy = 0 at apex)
H1 = 1/2 g t^2 = 9.8 / 2 * 12.2^2 = 729 m height risen above cliff
729 + 405 = 1134 m total height above striking point
H = 1/2 g T^2 where T is time to fall 1134 m
T = (2 * 1134 / 9.8)^1/2 = 15.2 sec
T + t1 = 15.2 + 12.2 = 27.4 sec total time in air
Sx = Vx * 27.4 = 90.3 * 27.4 = 2470 m total horizontal distance
The highest freefall jump on record is from a height of almost 38,000 m. At this height, the acceleration of gravity is slightly weaker than the accelera
of gravity on the surface of Earth. Although the skydiver used a parachute to slow himself down below a certain altitude, how would the increasing
acceleration impact his velocity and rate of displacement covered?
BIU
S2
X
Increasing his acceleration will impact his velocity and rate of displacement covered in that as the speed increases due to the increased rate of acceleration, the rate of air resistance also increases.
What is air resistance?Air resistance is a force created by air. When an item moves through the air, the force operates in the opposite direction.
When a diver descends, the force of air resistance acts to counteract the force of gravity. As the skydiver falls faster and faster, the quantity of air resistance grows until it equals the magnitude of gravity's force.
A balance of forces is achieved when the force of gravity equals the force of air resistance, and the skydiver no longer accelerates. The skydiver reaches what is known as terminal velocity.
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A helium balloon has a volume of 8.89 liters, or 0.00889 cubic meters. Air has a density of 1.29 kilograms per cubic meter, and helium has a density of 0.177 kilograms per cubic meter.a. What is the weight of the helium inside the balloon?b. What is the buoyant force exerted on the balloon?c. What is the net force on the balloon? Neglect the weight of the rubbery material that comprises the actual balloon. . How many identical balloons would be needed to lift a child of mass 24.9 kilograms?
Given:
The volume of a helium balloon: 8.89 liters or 0.00889 cubic meters
The density of helium: 0.177 kilograms per cubic meters
The density of the air: 1.29 kilograms per cubic meters
To find:
a) weight of the helium inside the balloon.
b) the buoyant force exerted on the balloon.
c) the net force on the balloon.
d) number of identical balloons needed to lift a child of mass 24.9 kilograms.
Explanation:
a)
The expression for the density of the balloon is:
[tex]Density\text{ of helium=}\frac{Mass\text{ of helium}}{Volume\text{ of helium}}[/tex]Rearrange the above expression to find the mass of the helium.
[tex]Mass\text{ of helium=Density of helium}\times Volume\text{ of helium}[/tex]Substitute the values from the given data, we get:
[tex]\begin{gathered} Mass\text{ of helium=0.177}\frac{kg}{m^3}\times0.00889\text{ m}^3 \\ Mass\text{ of helium=0.001573 kg} \end{gathered}[/tex]Thus, the mass of the helium is 0.001573 kg.
The weight of an object is the product of its mass and gravitational acceleration. Thus, the weight of helium is
[tex]\begin{gathered} Weight\text{ of helium=mass of helium}\times g \\ \end{gathered}[/tex]here, g is the acceleration due to gravity.
Substitute the values, and we get:
[tex]\begin{gathered} Weight\text{ of helium=0.001573 kg }\times9.8\text{ }\frac{m}{s^2} \\ Weight\text{ of helium=0.01542 N} \end{gathered}[/tex]The weight of helium is 0.001542 Newtons.
b)
The expression for buoyant force is:
[tex]F=\rho gV[/tex]here, ρ is the density, g is the acceleration due to gravity and V is the volume.
To find the buoyant force exerted by helium on the balloon, substitute the values for helium in the above equation.
[tex]\begin{gathered} F=0.177\text{ }\frac{kg}{m^3}\times9.8\text{ }\frac{m}{s^2}\times0.00889\text{ m}^3 \\ F=0.01542\text{ }\frac{kg\cdot m}{s^2} \\ F=0.01542\text{ N} \end{gathered}[/tex]The buoyant force exerted on the baloon is 0.01542 Newtons.
c)
The buoyant force exerted by the balloon is 0.01542 N and it acts in an upward direction. Whereas, the other force acting on the balloon is the force due to gravity, the weight of the balloon. The weight of the balloon is 0.01542 N and is always acts in the downwards direction.
Since the magnitude of buoyant force exerted on a balloon is equal to the weight of the balloon. Both these forces are acting in opposite directions. Thus the net effect will be zero.
[tex]\begin{gathered} F_{net}=F-W \\ F_{net}=0.01542\text{ N -0.01542 N} \\ F_{net}=0\text{ N} \end{gathered}[/tex]Thus, the net force acting on the balloon is 0 Newtons.
d)
For a helium balloon, 1 liter of helium can lift 1 gram of mass.
The mass of the child is 24.9 kg = 24900 grams.
Thus, to lift a child of mass 24900 grams, 24900 liters of helium is required.
Now, one balloon contains 8.89 liters of helium, thus for 24900 liters of helium volume, the number of ballons required will be,
[tex]\frac{1\text{ balloon}}{n\text{ balloons}}=\frac{8.89\text{ liters}}{24900\text{ liters}}[/tex]Rearranging above equation to find n, we get
[tex]\begin{gathered} n\text{ balloons = }\frac{24900}{8.89} \\ n\text{ balloons = 2800.89} \end{gathered}[/tex]Thus, approximately 2801 helium balloons are required to lift a child of mass 24.9 kg.
Final answer:
a) The weight of helium is 0.001542 Newtons.
b) The weight of helium is 0.001542 Newtons.
c) The net force acting on the balloon is 0 Newtons.
d) Approximately 2801 helium balloons are required to lift a child of mass 24.9 kg.
Divya and Melissa go to a restaurant. They decide to try something they have not eaten before and order chicken sandwiches with sriracha sauce. Both Divya and Melissa find it difficult to eat the sandwiches as they feel the sandwiches are too spicy. Which of the following processes help them identify the spicy taste?
The processes that help Divya and Melissa identify the spicy taste of the chicken sandwiches with sriracha sauce is sensation.
Sensation is the process in which one feels something after being in physical contact with something. As Divya and Melissa eats the chicken sandwiches with sriracha sauce, their senses tells that the food is spicy.
Acculturation is the process in which one adopts and adjusts to a new cultural environment. Homogenization is the process in which two non-soluble liquids are mixed uniformly. Adaptation is the process of changing one's trait to a new environment.
Therefore, the processes that helps them identify the spicy taste is sensation.
To know more about sensation
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A shopper in a supermarket pushes a loaded cart with a horizontal force of 14 N. The cart
has a mass of 32 kg.
The acceleration of gravity is 9.8 m/s
2
.
Disregarding friction, how far will the cart
move in 4 s, starting from rest?
Answer in units of m.
Answer:
ΔS = 3.5 m
Explanation:
First, apply the 2º Newton's Law to find the resulting acceleration.
∑F = m × a
F = m × a
14 = 32 × a
a = 14 /32 = 7/16
a = 0.4375 m/s²
Then, we must apply the equation of accelerated movement:
ΔS = V₀*t + (1/2)*a*t²
Starting from the rest and using the value of acceleration:
ΔS = 0*4 + (1/2)*(0.4375)*(4)²
ΔS = (1/2)*(0.4375)*(16)
ΔS = 3.5 m
At the beginning of a new school term, a
student moves a box of books by attaching a
rope to the box and pulling with a force of
F = 84.4 N at an angle of 64°, as shown in the
figure.
The acceleration of gravity is 9.8 m/s².
The box of books has a mass of 14 kg and
the coefficient of kinetic friction between the
bottom of the box and the floor is 0.3.
64°
14 kg
p=0.3
What is the acceleration of the box?
Answer in units of m/s².
Answer:
1.22 m/s² (3 s.f.)
Explanation:
Draw a diagram modelling the given situation (see attachment).
F = Friction.Given values:
Pulling force = 84.4 NMass (m) = 14 kgAcceleration due to gravity (g) = 9.8 m/s²Coefficient of friction (μ) = 0.3As the pulling force is at an angle to the plane (ground), resolve the force into components parallel and perpendicular to the plane.
Resolving vertically (↑) to find the Normal Reaction, R:
[tex]\begin{aligned}\implies R+82.2 \sin 64^{\circ}&=14g\\R&=14g-82.2 \sin 64^{\circ}\end{aligned}[/tex]
The frictional force takes its maximum value when an object starts to move (or is on the point of moving):
[tex]\boxed{F_{\text{max}}= \mu R}[/tex]
where R is the Normal Reaction and μ is the coefficient of friction.
Using F = μR to find the Frictional Force, F:
[tex]\begin{aligned}\implies F &= 0.3\left(14g-82.2 \sin 64^{\circ}\right)\\ & =0.3\left(14(9.8)-82.2 \sin 64^{\circ}\right)\\& =0.3\left(137.2-82.2 \sin 64^{\circ}\right)\\ & = 41.16-24.66\sin 64^{\circ}\end{aligned}[/tex]
Newton's second law states that the overall resultant force acting on a body is equal to the mass of the body multiplied by the body’s acceleration:
[tex]\boxed{F_{\text{net}}=ma}[/tex]
Resolving horizontally (→) using Newton's second law of motion to find acceleration:
[tex]\begin{aligned}\textsf{Using} \quad F_{\text{net}}&=ma\\\\\implies 82.2 \cos64^{\circ}-(41.16-24.66\sin 64^{\circ})&=14a\\17.0383694...&=14a\\a&=\dfrac{17.0383694...}{14}\\a&=1.21702638...\\a&=1.22\;\sf m/s^2\;(3\;s.f.)\end{aligned}[/tex]
Therefore, the acceleration of the box is 1.22 m/s² (3 s.f.).