Answers
If we rank these magnets from the strongest to the weakest magnetic field the correct order is 4, 3, 2, 1.
How does the magnetic field relate to the radius of a magnet?The magnetic field and radius are related in the context of a charged particle moving in a circular path under the influence of a magnetic field. When a charged particle moves in a circular path under the influence of a magnetic field, the force on the particle is directed toward the center of the circle. In this force, the radius can be expressed as r = mv / Bq.
This equation shows that the radius of the circular path is directly proportional to the velocity of the particle, and inversely proportional to the magnetic field strength and the charge of the particle.
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Related Questions
dx=7.14 m and dy=-7.55 m find the direction
Answers
Explanation:
arctan ( -7.55/7.14) = - 46.6 degrees ( or 313.4 degrees)
A model of a helicopter rotor has four blades, each 3.40 m long from the central shaft to the blade
trip. The model is rotated in a wind tunnel at 550 rev/min. (a) What is the linear speed of the blade
tip, in m/s? (b) What is the radial acceleration of the blade tip expressed as a multiple of the
acceleration of gravity, g?
Answers
The linear speed of the blade tip is approximately 114 m/s.
The radial acceleration of the blade tip is approximately 488 times the acceleration of gravity, g.
(a) To calculate the linear speed of the blade tip, we need to convert the rotational speed from revolutions per minute (RPM) to radians per second. One revolution is equivalent to 2π radians, so the angular velocity of the rotor is 550 rev/min x (2π/60) = 57.54 radians/second.
The linear speed of the blade tip is then the product of the angular velocity and the length of the blade, giving us 57.54 radians/second x 3.40 m = 195.6 m/s. The blade tip is only a small fraction of the total length of the blade, so we can assume that the linear speed of the blade tip is approximately equal to the linear speed of the rotor at a radius of 3.40 m. Therefore, the linear speed of the blade tip is approximately 114 m/s.
(b) The radial acceleration of the blade tip is given by the formula ar = rω², where r is the radius of the blade and ω is the angular velocity of the rotor in radians per second. Substituting in the values given, we get ar = (3.40 m) x (57.54 radians/second)² = 11,976 m/s². To express this in terms of g, we divide by the acceleration due to gravity, g = 9.81 m/s², giving us ar/g ≈ 488.
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. When a large truck
hits a small car, the
forces are equal.
• However, the small
.
car experiences a
much greater
change in velocity
much more rapidly
than the big truck.
Which vehicle ends up
with more damage?
Answers
Answer:
Car
Explanation:
Based on Newton 2nd law, energy are conserves. Meaning that if the Force is equal, the car with lower mass must be travelling in a much greater acceleration.
F = m.a
where,
a = Δv/Δt
When talking about energy, there are 2 factor: mass and velocity.
The change of Kinetic energy experience by the car is
ΔEk = 1/2.m.Δv²
Eventhough the car has smaller mass, notice that the velocity will be squared. In this case the velocity is the a more dominant factor. It means that energy absorbed by the car is much larger.
A boy of mass 60 kg and a girl of mass 40 kg are together and at rest on a frozen pond. What is the initial momentum of the girl?
A. 100 kgm/s
B. 40 kgm/s
C. 10 kgm/s
D. 0 kgm/s
Answers
Answer:
Explanation:
The answer is D. 0 ;
As We know when the net external force on an isolated system is absent then the total linear momentum of the system remains conserved.
=> By Conservation of linear Momentum of the system;
=> P1=P2 i.e initial momentum= final momentum;
=>if final momentum is '0' that is they are in rest position velocity is 0;
So momentum is 0 By p=mv;
Hence initial momentum will be zero;
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The initial momentum of the girl can be calculated using the formula:
p = mv
where p is the momentum, m is the mass, and v is the velocity.
Since the boy and the girl are at rest on the frozen pond, their initial velocity is zero. Therefore, the initial momentum of the girl is:
p = mv = (40 kg)(0 m/s) = 0 kgm/s
So, the answer is D. 0 kgm/s.
1. Two resistors R₁ (12 ohm) and R₁ (24 ohm) are
connected in series across a 6.0 V battery
of negligible internal resistance.
Draw a circuit diagram (to the right) and calculate:
The total resistance of the two resistors:
The total current flowing in the circuit:
The current flowing in R₁
The current flowing in R2
The total power consumed by R₁ and R₂
11
Answers
Here's the circuit diagram:
```
+---R₁---R₂---+
| |
- -
(6V) ( )
|
|
|
|
|
|
|
( )
-
```
Calculations:
1. The total resistance of the two resistors:
R_total = R₁ + R₂
= 12 ohm + 24 ohm
= 36 ohm
Answer: 36 ohm
2. The total current flowing in the circuit:
I = V / R_total
= 6.0 V / 36 ohm
= 0.167 A
Answer: 0.167 A
3. The current flowing in R₁:
I₁ = V / R₁
= 6.0 V / 12 ohm
= 0.5 A
Answer: 0.5 A
4. The current flowing in R₂:
I₂ = V / R₂
= 6.0 V / 24 ohm
= 0.25 A
Answer: 0.25 A
5. The total power consumed by R₁ and R₂:
P = I² * R_total
= (I₁ + I₂)² * R_total
= (0.5 A + 0.25 A)² * 36 ohm
= 0.1875 * 36 ohm
= 6.75 W
Answer: 6.75 W
A thin beam of light falls on mirror 1 as shown in the diagram below. four P.Q.Rands are placed in front of mirror 1 and mirror 2. Mirror 2 J|||||| RE Nanda wants to find out on which tikely box in the diagram in the beam to fall after reflecting off mirrov 1 and mirrov 2 List the steps that he should Follow in the correct order.
Answers
The steps assume that the mirrors and boxes are arranged in a simple, two-dimensional configuration.
The steps to be followedThe steps to be followed are;
Determine the angle of incidence of the beam of light on mirror 1. This can be done by drawing a line perpendicular to the mirror at the point where the beam of light hits the mirror and measuring the angle between this line and the incident beam of light.Use the law of reflection to determine the angle of reflection of the beam of light from mirror 1. This angle will be equal to the angle of incidence.Use the properties of parallel lines and angles to determine the angle of incidence of the beam of light on mirror 2. This can be done by noting that mirror 2 is parallel to mirror 1 and that the angle of incidence of the beam of light on mirror 2 will be equal to the angle of reflection of the beam of light from mirror 1.Use the law of reflection again to determine the angle of reflection of the beam of light from mirror 2. This angle will be equal to the angle of incidence of the beam of light on the likely box.Use the properties of parallel lines and angles again to determine the angle of incidence of the beam of light on each of the boxes in the diagram. The box that has an angle of incidence equal to the angle of reflection of the beam of light from mirror 2 is the likely box where the beam of light will fall.Learn more on reflection of mirror here https://brainly.in/question/54972410
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A clown figurine is located 21.0 cm in front of a thin lens that has a focal length of 17.0 cm. Where would the image appear, and would it be real or virtual?
15.2 cm, virtual
89.3 cm, real
111 cm, real
−65.2 cm, virtual
Answers
c) 111 cm, real.
Explanation:
We can use the thin lens equation to determine the location and nature of the image:
1/f = 1/do + 1/di
where f is the focal length of the lens, do is the distance from the object to the lens, and di is the distance from the image to the lens.
Substituting the given values, we get:
1/17 = 1/21 + 1/di
Simplifying and solving for di, we get:
di = 1 / (1/17 - 1/21)
di = 111 cm
Since the value of di is positive, the image is formed on the opposite side of the lens as the object, which means it is a real image.
Therefore, the image of the clown figurine would appear 111 cm behind the lens, and it would be a real image.
The correct option is (c) 111 cm, real.
The graph shows the decay of two different radioactive nuclei, Source A and Source B.
How long does it take Source B to complete two half-lives?
a. 10 s
b. 5 s
c. 40 s
d. 20 s
Answers
It takes source B 40 s to complete two half lives.
What is the half life?The half-life of a chemical is the amount of time it takes for half of the atoms in a sample to decay. This concept is widely used to describe how quickly a substance decays radioactively in nuclear physics and radiochemistry. Each radioactive substance has a unique half-life due to the properties of each atomic nucleus.
Looking at the graph, we can see that the half life of the source B is 20s .
Hence the time taken to complete two half lives = 2(20 s) = 40 s.
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What is a hydrogen displacement?
Answers
A chemical process known as hydrogen displacement occurs when hydrogen gas is replaced or displaced by another element or molecule.
It results from a number of reactions, most of which involve a reactive metal or substance. A metal reacting with an acid can displace hydrogen atoms of the acid, resulting in the formation of a salt and the release of hydrogen gas as an example.
Another example is the interaction of a metal with water molecules, which displaces hydrogen atoms and results in the formation of metal hydroxide and hydrogen gas. Chemistry studies hydrogen displacement reactions in great detail because they are important for understanding the reactivity of various compounds. They shed light on the behavior of elements, how well they can replace hydrogen, and how new compounds are formed.
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what happens according to newton if you let an untide ballon go?
Answers
Two small Styrofoam balls that are separated (between their centers) by 4 cm experience a force of attraction of 15 N. If the balls are separated by 8 cm, the force between them would be ___ N.
Answers
Answer:
f = 15/4 = 3.75
Explanation:
A rifle with a weight of 30 N fires a 5.0-g bullet with a speed of 300 m/s. (a) Find
the recoil speed of the rifle. (b) If a 700-N man holds the rifle firmly against his
shoulder, find the recoil speed of man and rifle.
Answers
_______________________________
Notes:
1grain = 64.8mg
1newton = 100g
= 300 m/s (speed)
= 30 × 100
= 3,000g (rifle mass)
= 5-g × 64.8
= 324mg (bullet mass)
= 700 × 100
= 70,000g (human mass)
= 70,000g + 3,000g
= 70,300g (human + rifle mass)
A) Newton's 2nd Law of MotionM1 V1 = - m2 v2Vr = - mb ÷ mrVb = - (324 ÷ 3,000) 300= 32.4 m/sB) Newton's 2nd Law of MotionM1 V1 = - m2 v2Vr = - mb ÷ mr Vb = - (324 ÷ 70,300) 300= 1.39 m/s_______________________________
HELP!!! You have two substances, both of which have the same boiling point (or attraction between their molecules).
The first substance is made from molecules that are small (just a few atoms bonded together), and the second substance is made from mol that are larger (many atoms bonded together).
How can it be possible for two such different molecules to yield substances with the same boiling point? Describe the kinds of intermolecu attractions that must be involved and any other properties of the molecules that could cause this result.
Answers
Despite having different molecular sizes, two substances can have the same boiling point due to the presence of intermolecular attractions that compensate for the difference in molecular weight.
What is the explanation for the above response?Despite having different molecular sizes, two substances can have the same boiling point due to the presence of intermolecular attractions that compensate for the difference in molecular weight.
These intermolecular attractions, such as London dispersion forces, dipole-dipole interactions, or hydrogen bonding, play a crucial role in determining a substance's boiling point. For example, the larger molecules may have more surface area for London dispersion forces to act upon, while smaller molecules may have more polar groups for dipole-dipole interactions or hydrogen bonding.
As a result, these different types of intermolecular forces can offset each other, leading to substances with different molecular sizes having the same boiling point.
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1 Consider a ring, sphere and Solidey clinder all with the same mass. They are all held at the top of the inclined Plane which is at 20° to the horizontal. the top of the inclined Plane is 1m high. The shapes are released simultaneously and allowed to roll down the inclined plane. Assume the abjects roll with out slipping and that they are all made from the same material. Assume the coefficient of static friction bin the objects and the plane is 0.3.
A) which shapes have the greater moment of inertia ?
B) workout what order they would get to the bottom of the Slope!
C ) determine the linear acceleration(a)
D) calculate the tangential (linear) Veloci ty of each shapes
E) How long will it take each shape to reach the bottom of the Slope ?
I give you 100 coin please help me
-
Answers
B) The solid cylinder will reach the bottom of the slope first, followed by the sphere, and then the ring.
C) The linear acceleration of the objects can be calculated using the following formula:
a = g * sin(θ) / (1 + I / mr^2)
where g is the acceleration due to gravity, θ is the angle of the incline, I is the moment of inertia, m is the mass, and r is the radius of the object.
Plugging in the numbers, we get:
a_ring = 9.8 m/s^2 * sin(20°) / (1 + 0.5 / 1^2) = 1.09 m/s^2
a_sphere = 9.8 m/s^2 * sin(20°) / (1 + 2 / 1^2) = 0.84 m/s^2
a_cylinder = 9.8 m/s^2 * sin(20°) / (1 + 0.5 / 0.5^2) = 1.47 m/s^2
Therefore, the linear accelerations are a_ring = 1.09 m/s^2, a_sphere = 0.84 m/s^2, and a_cylinder = 1.47 m/s^2.
D) The tangential velocity of each object can be calculated using the following formula:
v = a * r
where a is the linear acceleration, and r is the radius of the object.
Plugging in the numbers, we get:
v_ring = 1.09 m/s^2 * 0.5 m = 0.55 m/s
v_sphere = 0.84 m/s^2 * 1 m = 0.84 m/s
v_cylinder = 1.47 m/s^2 * 0.5 m = 0.74 m/s
Therefore, the tangential velocities are v_ring = 0.55 m/s, v_sphere = 0.84 m/s, and v_cylinder = 0.74 m/s.
E) The time it takes for each object to reach the bottom of the slope can be calculated using the following formula:
t = sqrt(2 * d / a)
where d is the distance traveled, and a is the linear acceleration.
Plugging in the numbers
A) The solid cylinder has the greatest moment of inertia.
B) The order in which the objects would reach the bottom of the slope is: sphere, cylinder, and ring.
C) The linear acceleration of each object is the same and is equal to 0.98 m/s^2.
D) The tangential velocity of the sphere, cylinder, and ring are 2.78 m/s, 3.53 m/s, and 4.24 m/s, respectively.
E) The time it takes for each object to reach the bottom of the slope can be calculated using the following formula:
time = square root(2h / g)
where h is the height of the slope (1m) and g is the acceleration due to gravity (9.8 m/s^2).
Plugging in the numbers, we get:
time for sphere = 0.45 s
time for cylinder = 0.51 s
time for ring = 0.57 s
Therefore, the sphere would reach the bottom first, followed by the cylinder, and then the ring.
5. An elephant has weight of 48000N and exerts pressure of 60000 Pa on the ground. What is the area of the elephant's feet in contact with the ground?
a. 1.25 m^2
b. 0.8 m^2
c. 2.0 m^2
d. 8.0 m^2
Answers
Answer:
A 1.25 m²
Explanation:
There are two major types of data storage: Hard copy (paper) and digital storage. Both have strengths and weaknesses. Which do you think is better and why?
Your response should be 3-5 sentences long
Answers
Answer:
Both hard copy and digital storage have their own advantages and disadvantages, and which one is better largely depends on the specific use case and personal preferences. Hard copies can be more reliable in case of power outages or system failures, and can be easily transported without requiring any special equipment. Digital storage, on the other hand, can be more convenient for accessing, sharing, and searching large amounts of data, and can be easily backed up and protected from physical damage. Ultimately, the choice between the two depends on the needs and priorities of the user.
Explanation:
I think that digital storage would be the better option of the two. The waste produced by paper-related industries does great harm to our ecosystem, using digital storage would help keep a reduction in pollution.
Also, having a hard copy paper, you might misplace and lose it. If you use digital storage you have easy access and retrieval. It can hold much more information, take up less space, and be created in a shorter amount of time than analog methods.
What is the S-P difference (sec)?
What is the amplitude (mm)?
What is the distance (km)?
What is the magnitude (M)?
Answers
(a) The S-P difference of the wave is determined as is 40 sec.
(b) The amplitude of the wave is determined as is 10 mm
(c) The distance of the wave is determined as is 380 km
(d) The magnitude of the wave is determined as is 4.5
What is amplitude of a wave?The amplitude of a wave is the maximum displacement or distance that a wave moves from its rest position to its crest (the highest point) or trough (the lowest point). In other words, it is the measure of the strength or intensity of a wave.
Question 1:
From the graph, the S-P difference, that is between S and P = 40 s - 0 s
= 40 s
Question 2:
The distance (km) corresponding to 40 sec is 380 km.
Question 3:
The amplitude of the wave is the maximum displacement of the wave and it is equal to 10 mm.
Question 4:
The corresponding magnitude of the wave is 4.5.
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b) A rocket initially moving at v0=3.5 km/s in space fires its engines. The initial mass of rocket is m0=200,000 kg and the final mass of the rocket is m=20,000 kg. If the exhaust velocity is ve=5.2 km/s, calculate the final speed in km/s.
Answers
The final speed of the rocket is -11.8 km/s.
What is the final speed of the rocket?The final speed of the rocket is calculated by applying the principle of conservation of linear momentum.
m0v0 = mv + (m0 - m)ve
where;
m0 is initial massv0 is the initial speedve is exhaust velocityThe final speed of the rocket is calculated as;
200,000 kg x 3.5 km/s = 20,000 kg x v + (200,000 kg - 20,000 kg) x 5.2 km/s
700,000 = 20,000v + 936,000
v = -236,000/20,000
v = -11.8 km/s
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Which of the following statements regarding VDGS
Systems are true? (Select ALL that are true.)
You can guess what type of aircraft is being parked.
If the system stops the aircraft, you can just manually continue to park it.
You do not need to investigate the reason for the stop.
Anyone can give the "Stop" signal if a threat to the safety of the aircraft is
observed.
You must power on and check the system before arrival.
A qualified agent must man the Emergency stop.
Answers
The true statements regarding VDGS Systems are you must power on and check the system before arrival and a qualified agent must man the Emergency stop.
What is VDGS?VDGS stands for Visual Docking Guidance System. It is a technology used in airports to assist pilots in parking their aircraft at the gate by providing visual cues and guidance through the use of lights and/or displays.
The following statements regarding VDGS Systems are true:
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In a parallel circuit, the current amplitude is the same through the inductor branch, the capacitor branch, and the resisitor branch. For this circuit, L =
20.0 mH and C = 10.0 mF.
a. What is the source angular frequency?
b. What is the resistance of the resistor?
Answers
part a.
The source angular frequency is 2.23 rad/s.
part b.
The resistance of the resistor is 4.46 Ω.
How do we calculate?The source angular frequency is given as:
ω = 1/√(LC)
where = is the inductance,
C = capacitance,
ω= angular frequency.
Substituting the values, we have:
ω = 1/√(20.0 mH x 10.0 mF) = 1/√(0.2) = 1/0.447 = 2.23 rad/s
part b.
We use the impedance in a parallel RLC circuit:
Z = R/(1 - ω^2LC)
impedance of the inductor branch is given as:
Z = jωL
impedance of the capacitor branch :
Z = -j/(ωC)
impedance of the resistor branch :
Z = R
We set all the impedances together at:
jωL = -j/(ωC) = R
We now solve for
R = ωL/ωC
R = = (2.23 rad/s)(20.0 mH)/(10.0 mF)(2.23 rad/s)
R = 4.46 Ω
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A proton, moving with a velocity of viî, collides elastically with another proton that is initially at rest. If the speed of the initially moving proton is 1.90 times the speed of the initially at rest proton, find the following.
(a) the speed of each proton after the collision in terms of vi
(b) the direction of the velocity vectors after the collision
Answers
Answer:
We can approach this problem using the conservation of momentum and the conservation of kinetic energy.
Conservation of momentum:
The momentum before the collision is given by:
p1 = m1v1 = m1viî
where m1 is the mass of each proton (which we assume to be the same) and v1 is the velocity of the initially moving proton.
The momentum after the collision is given by:
p2 = m1v1' + m1v2'
where v1' and v2' are the velocities of the two protons after the collision.
Since the collision is elastic, the total momentum is conserved:
p1 = p2
m1viî = m1v1' + m1v2'
We can simplify this equation by dividing both sides by m1:
viî = v1' + v2'
Conservation of kinetic energy:
The kinetic energy before the collision is given by:
K1 = (1/2)m1 We need the value of the velocity v1, which is not given in the problem statement.
Some people think that we should try to live outside of the Earth (on the Moon, or even on Mars, for example). Write your ideas about this. Will this be possible some day soon? When will this happen? How are we going to live there? What will be different up there?
Answers
Living outside the Earth, on the Moon or Mars, is a future possibility with continued research.
Living outside of the earthThe idea of living outside of Earth has been a subject of interest for many years. While it may seem like a daunting task, it is definitely possible. Advancements in technology have made it easier to explore space and even establish human settlements on other planets.
Living on the Moon or Mars would require creating sustainable ecosystems that provide food, water, and oxygen for the settlers. It would also require building living quarters that can withstand the harsh environmental conditions on these planets.
However, we are still a long way from achieving this goal, and it will likely take several decades or even centuries before we can establish a permanent human presence on another planet.
Nonetheless, with continued research and development, we may one day be able to call another planet our home.
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state the energy transfer that takes place as the ball changes shape during the contact between the racquet and the ball
Answers
When the ball hits the racquet, it gets squished, and it gains elastic energy, since it is compressed.
1.5 Find the center of gravity of a 100 mm x 150 mm x 30 mm T-section. H 150 mm -100 mm- G D BI 30 mm E -30 mm Figure 1.5 1.
Answers
Answer:
Explanation:
que ricos puntitos
A blue train of mass 50 kg moves at 4 m/s toward a green train of 30 kg initially at rest. The trains collide. After the collision the green train moves with a speed of 3 m/s. What is the final momentum of the blue train?
A. 200 kgm/s
B. 20 kgm/s
C. 110 kgm/s
D. 90 kgm/s
Answers
Answer:
C. 110 kgm/s
Explanation:
Law of Conservation of Momentum states that total momentum before the collision must equal total momentum after the collision.
Momentum = p = mv
x = final velocity of the blue train
(50 kg)(4 m/s) + (30 kg)(0 m/s) = (50 kg)(x) + (30 kg)( 3 m/s)
200 kg·m/s + 0 = (50 kg)(x) + 90 kg·m/s
50 kg(x) = 110 kg·m/s
x = (110 kg·m/s)/(50 kg) = 2.2 m/s
p-final (blue train) = (50 kg)(2.2 m/s) = 110 kg·m/s
Answer:
According to the law of conservation of momentum, the total momentum of the system before and after the interaction must be equal.
The total initial momentum of the system is:
P_initial = 50 * 4 + 30* 0 = 200kgm/s
The total final momentum of the system
let the velocity of the blue train is=v
P_final = 30* 3 + 50* v = 200
after solving v=2.2m/sec
the momentum of blue train will be= 50* 2.2=110kgm/s
What is the S-P difference (sec)?
What is the amplitude (mm)?
What is the distance (km)?
What is the magnitude (M)?
Answers
(a) The S-P difference (sec) is 40 sec.
(b) The amplitude (mm) is 10 mm
(c) The distance (km) is 380 km
(d) The magnitude (M) is 4.5
What is the S-P wave difference (sec)?The S-P wave difference (sec) is a measure used in seismology to determine the distance between a seismic station and an earthquake source.
From the graph, the S-P difference, that is between S and P = 40 s - 0 s
= 40 s
The distance (km) corresponding to 40 sec is 380 km.
The amplitude of the wave is the maximum displacement of the wave and it is equal to 10 mm.
The corresponding magnitude of the wave is 4.5.
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Toy cars of different masses accelerate as they move down a ramp as shown in the figure. A motion sensor is used to measure the speed of each car. It is found that all of the cars have the same speed at the bottom of the ramp. This graph shows how the mass of the car affects the car’s kinetic energy at the bottom of the ramp. Based on the graph, describe the relationship between the mass and the kinetic energy of the car, and then predict, in joules the kinetic energy of a car with a mass of 80 grams.
Answers
The Kinetic energy of the car with a mass of 80 grams is 0.40 joules
How do i determine the kinetic energy?From the graph given, we can see that the as the mass increase, the kinetic energy also increase. Thus, we can say that the kinetic energy and mass of the car are in direct proportionality.
Now, we shall obtain the velocity of the car. Details below:
Kinetic energy (KE) = 0.1 JMass of (m) = 20 g = 20 / 1000 = 0.02 KgVelocity (v) = ?KE = ½mv²
0.1 = ½ × 0.02 × v²
0.1 = 0.01 × v²
Divide both side by 0.01
v² = 0.1 / 0.01
Take the square root of both side
v = √(0.1 / 0.01)
v = 3.16 m/s
Finally, we shall determine the kinetic energy of the car of mass 80 grams. Details below:
Mass (m) = 80 g = 80 / 1000 = 0.08 KgVelocity (v) = 3.16 m/sKinetic energy (KE) =?KE = ½mv²
KE = ½ × 0.08 × 3.16²
Kinetic energy = 0.40 joules
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You decide to go skiing but fall over. As you are attempting to get back up, you see a child start to head down the hill straight for you. If the coefficient of friction between the child and the snow is assumed to be 0, and the child appears to be 20 m above you when they start down the mountain, and the incline of the mountain is 31 degrees, how long do you have to get up and out of the way before you and the child collide?
Answers
The time taken to get up and out of the way before you and the child collide is 2.82 s.
What is the time taken to get up?The time taken to get up and out of the way before you and the child collide is calculated as follows;
s = v + ¹/₂at²
s = v + ¹/₂(g sin (31)t²
where;
v is the initial velocitys is the displacementt is the time of motionThe time taken to get up is calculated as;
20 = 0 + ¹/₂(9.8 sin (31)t²
20 = 2.524t²
t² = 20/2.524
t² = 7.925
t = 2.82 s
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A team of astronauts is on a mission to land on and explore a large asteroid. In addition to collecting samples and performing experiments, one of their tasks is to demonstrate the concept of the escape speed by throwing rocks straight up at various initial speeds. With what minimum initial speed esc will the rocks need to be thrown in order for them never to "fall" back to the asteroid? Assume that the asteroid is approximately spherical, with an average density =2.02×106 g/m3 and volume =1.71×1012 m3.Recall that the universal gravitational constant is =6.67×10−11 N·m2/kg2.
Answers
The escape velocity is given by the following equation:
(1)
Where:
is the Gravitational Constant and its value is
is the mass of the asteroid
is the radius of the asteroid
On the other hand, we know the density of the asteroid is and its volume is .
The density of a body is given by:
(2)
Finding :
(3)
(4) This is the mass of the spherical asteroid
In addition, we know the volume of a sphere is given by the following formula:
(5)
Finding :
(6)
(7)
(8) This is the radius of the asteroid
Now we have all the necessary elements to calculate the escape velocity from (1):
(9)
Finally:
This is the minimum initial speed the rocks need to be thrown in order for them never return back to the asteroid
A block is dropped from rest. It takes a time t, to fall the first third of the distance. How long does it take to fall the entire distance? a) √3t₁ b) 3t₁ c) 9t₁ d) None of the above to = 0 ti t₂ TITI Vo = 0 S₂ = X S₁ = x/3
Answers
The time it will take the block to fall the entire distance is (a) √3t₁.
How to determine time in motion?Use the equations of motion to solve this problem. The equation to use is:
S = (1/2)gt²
where S = distance, g = acceleration due to gravity, and t = time.
First find the time it takes to fall the first third of the distance. The distance fallen is S₁ = x/3, so:
x/3 = (1/2)gt₁²
Solving for t₁:
t₁ = √((2x)/(3g))
Now, find the time it takes to fall the entire distance. The total distance is S₂ = x, so:
x = (1/2)gt₂²
Solving for t₂:
t₂ = √((2x)/g)
Substituting x with 3S₁:
t₂ = √((6S₁)/g)
Substituting t₁:
t₂ = √((4x)/(3g)) = √(4/3)t₁
Therefore, the answer is (a) √3t₁.
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