The ratio u/u0 : 1/2
As the distance is doubled and the battery is connected, we know that Capacitance is given by: [tex]C= \frac{\epsilon_0 A}{d}[/tex]
As the distance between the plate is doubled, C will become: [tex]C= \frac{\epsilon_0 A}{2d} = \frac{C}{2}[/tex]
Now, as the battery is connected, Voltage will remain constant, therefore Charge Q will become: [tex]Q=\frac{CV}{2}[/tex]
The energy before doubling the distance between the plates was, U0 :
[tex]U_0 = \frac{1}{2}QV = \frac{1}{2}CV^2[/tex]
After doubling the distance, the Energy will become U:
[tex]U = \frac{1}{2}QV = \frac{1}{4}CV^2[/tex]
Therefore, the ratio will be:
[tex]\frac{U}{U_0} = \frac{\frac{1}{2}CV^2}{\frac{1}{4}CV^2} = \frac{1}{2}[/tex]
What is capacitor ?A capacitor is a bipolar electrical device that can store energy in the form of an electrical charge. It consists of two electrical conductors separated by a distance. The space between the conductors can be filled with a vacuum or an insulating material known as a dielectric. The ability of a capacitor to store charges is called capacitance. Capacitors store energy by keeping opposite charges away from each other. The simplest model of a capacitor is a parallel plate, which consists of two metal plates with a gap between them. However, different types of capacitors are manufactured in different shapes, styles, lengths, circumferences and materials.
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assume that you weight yourself on a bathroom scale. would the springs inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that was accelerating upward?
The springs inside a bathroom scale will be more compressed.
What is acceleration due to gravity?
In physics, gravitational acceleration is the acceleration of an object in free fall in a vacuum (hence no resistance). This is a steady increase in velocity caused solely by the gravitational pull. All objects accelerate at the same speed in a vacuum, regardless of their mass or composition . The measurement and analysis of these velocities is known as gravimetry.
At a fixed point on the surface, the magnitude of the Earth's gravity is the combined effect of gravity and the centrifugal force due to the rotation of the Earth. Free-fall acceleration at various points on the Earth's surface ranges from 9.764 to 9.834 m/s2 (32.03 to 32.26 ft /s2) depending on altitude, latitude and longitude . The old standard is precisely defined as 9.80665 m/s2 (32.1740 ft/s2). Locations that deviate significantly from this value are called gravity anomalies. Other effects such as lift and air resistance are not taken into account.
When the elevator accelerates and shows a higher weight reading. As the lift accelerates and descends, the springs in the bathroom scale are compressed less and the displayed weight value is reduced.
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a 68.1-kg boy is surfing and catches a wave which gives him an initial speed of 1.60 m/s. he then drops through a height of 1.56 m, and ends with a speed of 8.51 m/s. how much nonconservative work (in kj) was done on the boy?
The non-conservative work done on the boy is 1.337 kJ
Given that,
Mass of boy, m = 68.1 kg
Initial speed of boy, u = 1,60 m/s
The boy then drops through a height of 1.56 m
Final speed of boy, v = 8.51 m/s
Now, we have to find the non-conservative work was done on the boy.
The Work done by the non-conservative forces is equal to the sum of total change in kinetic energy and total change in potential energy.
[tex]W=\frac{1}{2}m (v^{2}-u^{2})+(0-mgh)[/tex]
[tex]W=\frac{1}{2}m (v^{2}-u^{2})-mgh[/tex]
[tex]W=\frac{1}{2}(68.1) ((8.51)^{2}-(1.60)^{2})-68.1*9.8*1.56[/tex]
W = 1337.62 Joules
or
W = 1.337 kJ
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two objects with equal masses are in motion. which object will have more kinetic energy? (1 point) responses the object with the greater speed the object with the greater speed the object with the greater density the object with the greater density the object with the greater acceleration the object with the greater acceleration the object with the greater volume the object with the greater volume
Answer:
I rephrased your question:
Two objects with equal masses are in motion. which object will have more kinetic energy?
A) the object with the greater speed
B) the object with the greater density
C) the object with the greater acceleration
D) the object with the greater acceleration
E) the object with the greater volume
F) the object with the greater volume
Explanation:
Kinetic Energy is equal to (1/2)mv^2, where m is the mass and v is the velocity.
-----
A) the object with the greater speed YES
B) the object with the greater density NO
C) the object with the greater density NO
D) the object with the greater acceleration MAYBE. Acceleration means energy is being added, so it depends on how much and the masses of each object.
E) the object with the greater volume NO
Answer:
Explanation: Two objects with equal masses are in motion. Which object will have more kinetic energy?
Responses
the object with the greater density
the object with the greater volume
the object with the greater acceleration
the object with the greater speed
Answer: The object with the greater speed
a cliff diver steps off a cliff and hits the water 2.2 seconds later. How high was the cliff?
The height of the cliff is 24.2 m.
Let:
'h' be the height of the cliff'u' be the initial velocity of diver; u = 0m/s'+'ve been the annotation for the Downward directiona = 10m/s^2 be the approximation of acceleration due to gravityUsing the Second Equation of Motion:
[tex]h = ut + 1/2 at^{2} \\h = 0 + 1/2 (10)(2.2)^{2} \\h = 0 + 5(2.2)^{2} \\h = 5(4.84)\\h = 24.2m[/tex]
The Second Equation of Motion establishes a relationship between displacement and time. It can be used to calculate the displacement and time, in different conditions.
The cliff was 24.2m high above the water surface, into which the cliff diver dived.
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a baseball player exerts a force of 100n on a ball for a distance of 0.5m as he throws it. if the ball has a mass of 0.15kg, what is its velocity as it leaves his hand?
a car is traveling at 100 mph down the highway. at some time the driver sees an obstruction in the road and slams on the brakes skidding to a halt reducing its kinetic energy to zero. what happened to the kinetic energy of the car?
The kinetic energy is changed to thermal energy by brake friction and turns to zero.
We need to know about kinetic energy to solve this problem. Kinetic energy is the energy from a moving object. It can be determined as
KE = 1/2 . m . v²
where KE is kinetic energy, m is mass and v is speed.
From the question above, we know that
v1 = 100 mph
KE2 = 0 joule
When the car moves at 100 mph, the car has kinetic energy. But on the way when the driver brakes the car, the kinetic energy is changed to thermal energy by brake friction. Hence, the kinetic energy is reduced every time and finally turns to zero.
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the barrel of a shotgun: group of answer choices is generally shorter than that of a rifle. is wider at the end to concentrate shot. is smooth without the grooves and lands found in rifles. is indistinguishable from that of a rifle.
Measures the diameter of a shotgun's barrel in terms of the quantity of lead balls needed to make the bore weigh one pound (12 gauge is the diameter of a lead ball weighing one-twelfth of a pound).
What differentiates a shotgun from a rifle?A shotgun has many projectile properties while a rifle only comes with one. Shotguns are helpful at close ranges when rifles are useful at a distance. Shotguns only have a front sight, whereas rifles have both front and rear sights.
Rifles are typically a little noisier than shotguns. Analyzing test results reveals that shotguns and rifles have decibel levels that are comparable. The typical decibel range
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If you wanted to visit a area with very little wind whear might you go
Answer:Ohio
Explanation:
In a resonance a turning fork of frequency 330hz produced the first loud sound when water level in a pipe was 17.8cm from the open-end ant the second at 57.3cm. calculate the wavelength of the sound, speed of sound in air, water level of the next resonant length ?
The wavelength, the speed of sound and the water level of the next resonant length (the fifth harmonics) are as follows;
The calculated wavelength of the sound from the tuning fork is 0.79 metersThe speed of the sound is 260.7 m/sThe water level of the fifth harmonics is 96.8 cmWhat is an harmonics of a sound wave?An harmonics are waves with a frequency that is an integer multiple of the fundamental frequency.
The given frequency of the sound wave, f = 330 hz
The first water level that gives the first loud sound, l₁ = 17.8 cm
The water level from the open end at the second loud sound, l₂ = 57.3 cm
First part;
The first harmonics that gives the fundamental frequency for the pipe is expressed as follows;
[tex]\dfrac{\lambda}{4} = l_1+e[/tex]
Where;
e = The distance to the antinode of the wave above the top of the pipe
The third harmonics is given by the formula
[tex]\dfrac{3\cdot \lambda}{4} = l_2+e[/tex]
[tex]\dfrac{3\cdot \lambda}{4}- \dfrac{\lambda}{4} = \dfrac{\lambda}{2} = (l_2+e) - (l_1+e) = l_2 - l_1[/tex]
[tex]\dfrac{\lambda}{2} = l_2 - l_1[/tex]
λ = 2 × (l₂ - l₁)
λ = 2 × (57.3 - 17.8) = 79
The wavelength of the wave, λ = 79 centimeters = 0.79 meters
Second part;
Speed of sound, v = f × λ
Therefore; v = 330 Hz × 0.79 m = 260.7 m/s
The speed of sound in air, v = 260.7 m/sThird part;
[tex]\dfrac{\lambda}{4} = l_1+e[/tex]
[tex]\dfrac{3\cdot \lambda}{4} = l_2+e[/tex]
Which gives; 3·(l₁ + e) = l₂ + e
3·l₁ + 3·e = l₂ + e
3·e - e = l₂ - 3·l₁
2·e = l₂ - 3·l₁
Therefore, 2·e = 57.3 - 3 × 17.8 = 2.9
e = 3.9 ÷ 2 = 1.95The water level for the next resonant length, which is the fifth harmonics, is given by the formula;
[tex]\dfrac{5\cdot \lambda}{4} = l_3+e[/tex]
Which gives;
[tex]l_3 = \dfrac{5\cdot \lambda}{4} - e[/tex]
Therefore;
[tex]l_3 = \dfrac{5\times 79 }{4} - 1.95 = 96.8[/tex]
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10 N of force is applied to a spring and its length increases by 4 cm. If the spring is obeying Hooke's law, what will its extension be if 30 N of force is applied?
I think Twelve is the answer
Two ice skaters stand facing each other at rest on a frozen pond. They push off against one another and the 49 kg skater acquires a speed of 2. 10 m/s. If the other skater acquires a speed of 3. 81 m/s, what is her mass in kilograms?
Her mass is approximately equal to 27 kilograms.
How do you prove that?First of all, you need to understand that momentum is a conserved quantity and the solution to this problem involves elastic collision.
Momentum can be defined as p = mv where p is momentum, m is mass, and v is velocity. Just like energy, momentum is a physical quantity that is conserved in an isolated system. Momentum is conserved as a result of Newton's third law, which states that [tex]F_A=-F_B[/tex].
You are given that the ice skaters bounce off each other, meaning the collision is elastic. Remember that in an elastic collision, m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ where
m₁ is the mass of the first body, m₂ is the mass of the second body,u₁ is the initial velocity of m₁,u₂ is the initial velocity of m₂,v₁ is the final velocity of m₁, andv₂ is the final velocity of m₂.Suppose that m₁ = 49 kg, m₂ = x, u₁ and u₂ = 0 m/s, v₁ = 2.1 m/s, and v₂ = 3.81 m/s. Then the mass of the other ice skater is as follows:
49 · 0 + x · 0 = 49 · 2.1 + x · 3.81
0 = 102.9 + 3.81x
3.81x + 102.9 = 0
3.81x = -102.9
x ≈ -27
Since a mass value can't be negative, the absolute value of x is 27. Therefore, it's her actual mass in kilograms.
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points :)
don't mind this just getting to 20 words :)
Answer:
20 20 20 20 25 points 20 20 20 25 points
Explanation:
You want to lift a heavy box with a mass L = 64.0 kg using the two-ideal pulley system as shown. With what minimum force do you have to pull down on the rope in order to lift the box at a constant velocity? One pulley is attached to the ceiling and one to the box.
The given problem can be solved using the following free-body diagram:
The diagram is the free-body diagram for the pulley that is holding the weight. Where:
[tex]\begin{gathered} T=\text{ tension} \\ m=\text{ mass} \\ g=\text{ acceleration of gravity} \end{gathered}[/tex]Now we add the forces in the vertical direction:
[tex]\Sigma F_v=T+T-mg[/tex]Adding like terms:
[tex]\Sigma F_v=2T-mg[/tex]Now, since the velocity is constant this means that the acceleration is zero and therefore the sum of forces is zero:
[tex]2T-mg=0[/tex]Now we solve for "T" by adding "mg" from both sides:
[tex]2T=mg[/tex]Now we divide both sides by 2:
[tex]T=\frac{mg}{2}[/tex]Now we substitute the values and we get:
[tex]T=\frac{(64\operatorname{kg})(9.8\frac{m}{s^2})}{2}[/tex]Solving the operations:
[tex]T=313.6N[/tex]Now we use the free body diagram for the second pulley:
Now we add the forces in the vertical direction:
[tex]\Sigma F_v=T-F[/tex]The forces add up to zero because the velocity is constant and the acceleration is zero:
[tex]T-F=0[/tex]Solving for the force:
[tex]T=F[/tex]Therefore, the pulling force is equal to the tension we determined previously and therefore is:
[tex]F=313.6N[/tex]
scientists are testing a transparent material whose index of refraction for visible light varies with wavelength as , where is in nm. if a 295-nm-thick coating is placed on glass for what visible wavelengths will the reflected light have maximum constructive interference?
The wavelength of the reflected light will have a range from 360 nanometers to 700 nanometers.
Constructive Interference may be defined as the process which occurs when the maxima of any two waves add up and the amplitude of the resulting wave will be equal to the sum of the two individual waves. According to the question thickness of coating, d = 295 nm and wavelength varies as n = [(30nm) ^1/2]/λ^1/2.
Also, the wavelength will be expressed as
λ = 2nd/M where M = 1,2,3......
λ = 2d[(30nm)^1/2]/Mλ^1/2
λ^3/2 = (d60nm^1/2)/M
λ = ∛d² 3600 nm/M
Now, if M = 1 then,
λ = ∛295² 3600nm/1 = 679.18 nm
Now, if M = 2 then,
λ = ∛295² 3600nm/2 = 679.18 nm
Now, if M = 3 then,
λ = ∛295² 3600nm/3 = 326.51 nm
So, the range is approximately 360 nm to 700 nm.
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Complete Question:
Scientists are testing a transparent material whose index of refraction for visible light varies with wavelength as n = 30.0 nm1/2 /l1/2, where l is in nm. If a 295-nm-thick coating is placed on glass 1n = 1.502 for what visible wavelengths will the reflected light have maximum constructive interference?
a powerful motorcycle can produce an acceleration of while traveling at 90.0 km/h. at that speed, the forces resisting motion, including friction and air resistance, total 400.0 n. (air resistance is analogous to air friction. it always opposes the motion of an object.) what is the magnitude of the force that motorcycle exerts backward on the ground to produce its acceleration if the mass of the motorcycle with rider is 245 kg? 34. a car with a mass o
1257.5 N is the magnitude of the force that motorcycle exerts backward on the ground to produce its acceleration.
What is a magnitude in physics?The definition of magnitude is simply "distance or quantity." It displays an object's size, direction, or speed, whether relative or absolute. It's used to indicate that something has a certain size or scope.
Briefing:A = 3.50 m/s² is the motorcycle's acceleration.
f = 400.0 N, the force of resistance to motion
M = 245 kg for the motorcycle's mass
F is the amount of force a motorcycle exerts when moving rearward.
The amount of force a motorcycle exerts when moving rearward is described as
F = f + ma
Inserting the values
F = 400.0 + (245) (3.50)
F = 1257.5 N
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The complete question is -
A powerful motorcycle can produce an acceleration of 3.50 m/s² while traveling at 90.0 km/h. At that speed, the forces resisting motion, including friction and air resistance, total 400.0 N. (Air resistance is analogous to air friction. It always opposes the motion of an object.) What is the magnitude of the force that motorcycle exerts backward on the ground to produce its acceleration if the mass of the motorcycle with rider is 245 kg?
This equation shows how the number of biscuits Olivia can bake is related to the amount of flour she has.
c = 15f
The variable f represents the number of scoops of flour Olivia has, and the variable c represents the number of biscuits she can bake. With 1 scoop of flour, how many biscuits can Olivia bake?
With 1 scoop of flour, Olivia can bake 15 biscuits if the the equation that shows the relation between number of biscuits and amount of flour is c = 15f.
c = 15 f
c = Number of biscuits
f = Number of scoops of flour
f = 1
c = 15 * 1
c = 15
This equation shows that number of biscuits that can be made is 15 times the number of scoops of flour. So if the number of scoops of flour is 1, the number of biscuits that can be made is 15.
Therefore, with 1 scoop of flour, Olivia can bake 15 biscuits
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after driving a portion of the route, the taptap is fully loaded with a total of 23 people including the driver, with an average mass of 65 kg per person. in addition, there are three 15- kg goats, five 3- kg chickens, and a total of 25 kg 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?
The compression of the spring at the given weight is 61 cm.
Given,
The spring constant is k =2.4 × 10⁴ N/m
mass of each of the 23 persons, = 65 kg
mass of each of the 3 goats, = 15 kg
mass of each of the 5 chickens, = 3 kg
mass of the bananas, = 25 kg
The total mass of all the passengers contained in the laptop is calculated as;
total mass of the persons = 23 x 65 = 1495 kg
total mass of the goats = 3 x 15 = 45 kg
total mass of the chickens = 5 x 3 = 15 kg
the total mass of the bananas = 25 kg
The total mass = (1495 + 45 + 15 + 25)kg
1The total mass = 580 kg
The calculation for the lengthy of spring:-
F = kx
x = F/k = mg/k
x = (1495*9.8)/2.4*10^4
x = 0.610 m
x = 61 cm
Hence, the compression of the spring at the given weight is 61 cm.
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similar to the case in the experiment you use two rubber bands, side to side first, to hold a weight of 3 reference objects. then, as in the experiment, the bands are pulled apart in their free ends until they form an angle of 30 degrees with respect to the horizontal. what are the deformations observed in these bands? ...
Three units deformations observed in these bands.
What forces do a rubber band encounter?Elastic force is the force that permits some materials to regain their former shape after being stretched or crushed. Thus, a stretched rubber band is subject to an elastic force.
The rubber band experiment uses a straightforward rubber band to show entropic force and a refrigeration cycle. The rubber band experiment involves stretching and then releasing a rubber band while measuring its temperature.
Always acting in the opposite direction of motion is friction. This indicates that if friction is there, it cancels out some of the force driving the motion (if the object is being accelerated). This results in a decreased acceleration and a smaller net force.
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a 5.25-g bullet is fired into a 360-g block of wood suspended as a ballistic pendulum. the combined mass swings up to a height of 8.75 cm. what was the magnitude of the momentum of the combined mass immediately after the collision?
magnitude of the momentum of the combined mass immediately after the collision p = 0. 478 (kg. m/sec)
Mass of bullet : m = 5. 25 (g) = 0. 00525 (kg)
Mass of block : M = 360 (g) = 0. 360 (kg)
Height : h = 8. 75 (m) = 0. 0875 (m)
Here we need to find the momentum :
Now,
As we know that,
The conservation of energy :
Now,
Kinetic energy = Potential energy
= 1/2( m + M)v² = (m+M)gh (m,M is mass of bullet and block)
Now,
v = [tex]\sqrt{2gh}[/tex]
Now,
Momentum can be defined as :
Here,
p = (m+ M) [tex]\sqrt{2gh}[/tex]. . . eqn 1
Putting the values in eqn 1 :
We get,
p = 0.478 (kg. m/sec)
Hence, the momentum : p = 0. 478 (kg. m/sec)
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a 7.50-nc point charge is located 1.80 m from a 4.20-nc point charge. (a) find the magnitude of the electric force that one particle exerts on the other. (b) is the force attractive or repulsive?
The electric force is 8.370 x 10^9N.
We need to know about the electric force to solve this problem. The electric force produced by charges interacting each other, whose strength is given by the equation
F = k.Q1 . Q2/r²
where F is the electric force, Q1 and Q2 is the charge and r is the radius.
From the question above, we know that
k = 9 x 10⁹ Nm²/C²
Q1 =e = 7.50 x 10^-9 C
Q2 = e = 4.02 x 10^-9 C
r = 1.80 m
The electric force will attract each other when the charges are different and will repel each other when the charges are same.
F = k.Q1 . Q2/r²
F = 9 x 10⁹ . 7.50 x 10^-9 . 4.02 x 10^-9/(1.80)²
F = 8.37 x 10^9 N
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In 1993 itleana salvador at italy walked 30 km under 12 min suppose that during 115m at her walk she steadly increased her speed from 42m/s to 5m/s how long does it increase took
When acceleration is constant, we may connect displacement to time and velocity, two of the other three parameters that describe motion, using the following three equations: d = ( 1 2 ) ( 1 2 ) (v f + v I (t) (Equation 1) D = v I t + a t + 1 2 (Equation 2) V I 2 + 2 a d = v f 2 (Equation 3).
Defining displacement If acceleration is constant, then?Displacement is directly proportional to the square of the length of the linear motion when acceleration is constant and beginning velocity is zero.
Solution:-
vi =+245km/h
aavg = -3.0m/s2
vf =vi -(0.200)vi
vi =(245km/h)(1h/3600s)(103m/1km)= +68.1m/s
vf =(1.000-0.200)vi =(0.800)(68.1m/s)=+54.5m/s
Δt=vf -vi /aavg
= 54.5m/s - 68.1m/s / -3.0m/s2
=-13.6m/s /-3.0 m/s2
= 4.5s
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an apple drops from a tree and hits the ground in 1.4 s how far does it fall?
It falls 9.8m far for the apple to drop from tree in 1.4sec.
Apple fall time t = 1.4 s
The free fall distance in time t is given by
d = 1/2at²
where a = g = 10 m/s² = free fall acceleration
calculation:
Using the above formula and the values given, the distance the apple will fall free in 1.4 seconds is
d = 1/2(10)(1.4)²
= 9.8 m
Therefore the distance um the apple will fall is 9.8 m.
Isaac Newton formulated gravitational theory in 1665 or 1666 after watching an apple fall. An apple falling from a tree is an example of Straight-line motion because gravity causes it to fall vertically in a straight line.
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Someone is standing on a trampoline. They have a mass of 65kg and each of their feet a 25cm x 10cm, what is the pressure exerted by both on the trampoline?
The pressure exerted by both on the trampoline is 25,480 N/m².
What is the pressure exerted?The pressure exerted by both on the trampoline is the force per unit area which is calculated as follows;
P = F/A
where;
F is the force applied by their weight A is the area of their feetP is the pressure exertedSubstitute the given parameters and solve for the pressure exerted.
P = (mg)/A
A = 0.25 m x 0.1 m
A = 0.025 m²
P = (65 x 9.8) / (0.025)
P = 25,480 N/m²
Thus, the pressure exerted at any given surface depends on the applied force and the area of the given surface.
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What is the main reason sea level is rising?
A: Ice Melting
B: Thermal Expansion
The main reason for the sea level rise is the melting of the ice, as the icebergs are melting due to the increase in the average temperature of the earth, therefore the correct answer is option A.
What is thermal energy?It can be defined as the form of the energy in which heat is transferred from one body to another body due to their molecular movements, thermal energy is also known as heat energy.
Thermal expansion is unrelated to the sea level rising.
Since icebergs are melting due to an increase in the earth's average temperature, melting ice is the primary cause of sea level rise, therefore the correct answer is option A.
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suppose we want to place a weather satellite into a circular orbit 300 kmkm above the earth's surface. what speed, period, and radial acceleration must it have? the earth's radius is 6380km
a. The speed of the satellite is 244 m/s
b. The period of the satellite is 1.72 × 10⁷ s
c. The radial acceleration of the satellite is 8913 rad/s
What is the speed of the satellite?The speed of the satellite is given by v = √(GM/R) where
G = universal gravitational constant = 6.67 × 10⁻¹¹ Nm²/kg², M = mass of earth = 5.972 × 10²⁴ kg and R = radius of orbit = r + r' where r = radius of earth = 6380 km and r' = radius of orbit = 300 kmSo, substituting the values of the variables into the equation, we have that
v = √(GM/R)
v = √(6.67 × 10⁻¹¹ Nm²/kg² × 5.972 × 10²⁴ kg /6380 km + 300 km)
v = √(6.67 × 10⁻¹¹ Nm²/kg² × 5.972 × 10²⁴ kg /6680 km)
v = √(39.83324 × 10¹³ Nm²/kg ÷ 6.680 × 10⁶ m)
v = √(5.963 × 10⁻³ × 10⁷ Nm²/kg)
v = √(5.963 × 10⁴ Nm/kg)
v = 2.44 × 10² m/s
V = 244 m/s
So, the speed of the satellite is 244 m/s
b. What is the period of the orbit?The period of the orbit is given by T = 2πR/v where
R = radius of orbit = 6680 km and v = speed of orbit = 244 m/sSo, substituting the values of the variables into the equation, we have
T = 2πR/v
T = 2π × 6680 km/244 m/s
T = 2π × 6680 × 10³ m/244 × 10⁵ m/s
T = 13660π × 10³ m/244 × 10⁵ m/s
T = 41971.68 × 10³ m/244 × 10⁵ m/s
T = 17201.5 × 10³ s
T = 1.72015 × 10⁷ s
T ≅ 1.72 × 10⁷ s
So, the period of the satellite is 1.72 × 10⁷ s
What is the radial acceleration of the satellite?The radial acceleration of the satellite is given by a = v²/R where
v = speed of satellite = 244 m/s and R = radius of orbit = 6680 kmSubstituting the values of the variables into the equation, we have
a = v²/R
a = (244 m/s)²/6680 km
a = 59536 m²/s²/6680 × 10³ m
a = 8.913 × 10³ rad/s
a = 8913 rad/s
So, the radial acceleration of the satellite is 8913 rad/s
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A piece of rock weighs 5 Newtons. A force F is applied to it and it produces an acceleration of a. Now, if there is a second piece of rock, what force needs to be applied to the second piece of rock to produce an acceleration of 8a?
Given,
weight of a piece of rock, W = mg = 5N
So, mass of a piece of rock is m = W ÷ g = 5N ÷ 9.8 m/[tex]s^{2}[/tex] = 0.51 kg.
When a force F is applied, it produces an acceleration 'a'. From Newton's second law of motion, F = ma = 0.51 a.
⇒a = F / 0.51.
Acceleration produced by 2nd piece of the rock is a' = 8a.
Assuming the mass of 2nd piece of rock to be same as the 1st piece, force to be applied on 2nd piece is F' = m'a'.
⇒ F' = m' × 8a = 8m'a
If the mass of both pieces of rock are equal, then m' = m = 0.51 kg.
⇒ F' = 0.51kg × 8a
⇒ F' = 0.51kg × 8 (F / 0.51)
⇒ F' = 8F.
Thus, a force equal to 8 times the force applied on 1st piece should be applied on the 2nd piece of the rock to produce an acceleration of 8a (if their masses are equal.
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A cart is set up as shown below, with three fans directed to the left and two of the fans running. The motion of the cart is represented by the v vs t graph shown. If the experiment were repeated with all three fans running, what might the resulting v vs t graph look like?
A. Graph A
B. Graph B
C. Graph C
D. Graph D
A child boards a bus for summer camp. His mom is waiting next to the bus. The bus begins
moving 3 m/s east with respect to the ground. The child is walking 0.5 m/s west towards the back
of the bus with respect to the bus. The mother begins running 1 m/s east with respect to the
ground, chasing after the bus and thoroughly humiliating her child. What is the child's velocity
a) relative to the ground?
b) relative to the mother?
Answer:
a) relative to the ground
Explanation:
Ida Haitarun is captain of the Varsity cross country team. During the after-school practice on Tuesday, he led the team on the following run from school to a nearby park. From the road, he ran at a 20 degree angle North of East for 8 miles. Determine how far east and how far north they are from where they started.
The displacement of the team is 2.74 miles due east and 7.52 miles due north from where they started.
What is the eastward displacement of the team?
The eastward displacement of Ida Haitarun and his team during the cross country race is calculated by forming a right triangle from the displacement of the team.
The angle of inclination of the displacement is calculated as follows;
θ = 90⁰ - 20⁰ = 70⁰ (above the horizontal)
The eastward displacement is the base of the triangle and it is calculated as follows;
cos θ = base / hypotenuse side
cos 70 = base / 8 miles
base = (8 miles) x (cos 70)
base = 2.74 miles
The northward displacement is calculated as follows;
sin θ = height / hypotenuse side
sin 70 = height / 8 miles
height = (8 miles) x (sin 70)
height = 7.52 miles
Thus, the team is 2.74 miles due east and 7.52 miles due north from where they started.
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Both speed and velocity measure how fast something is moving. However, since speed is not a _________ it does not require a(n) ___________ .
Responses
A scalar, directionscalar, direction
B quantity, unitquantity, unit
C magnitude, unitmagnitude, unit
D vector, direction