Answers
Given:
Scale number of a penny = 3.5
Scale number of a fingernail = 2.5
Let's determine the mineral from the options which could be scratched by a penny but not a fingernail.
A mineral with a scale number can scratch any material with equal or lower scale number.
Since a penny has a scale number of 3.5, it can scratch any material with a scale number of 3.5 or lower.
Also, since a fingernail could not scratch the material here, this means the scale number if the material must be greater than 2.5.
Thus, the mineral that could be scratched by a penny but not a fingernail must have a scale number equal to or less than 3.5 but greater than 2.5.
Hence, from the MOHS Hardness Scale, the mineral with a scale number between 3.5 and 2.5 is the Calcite with a scale number of 3.
Therefore, the mineral which could be scratched by a penny but not a fingernail is Calcite.
• ANSWER:
C) Calcite.
Related Questions
If frictional forces and air resistance were acting upon the falling ball in #1 would the kinetic energy of theball just prior to striking the ground be more, less, or equal to the value predicted in #1?
Answers
Given that the ball is falling in two different situations.
Kinetic energy is the energy that an object possesses due to its motion and it is proportional to the square of the velocity of the object.
The frictional force and the air resistance are the forces that will be opposing the motion of the ball. That is these forces act in the opposite direction of the motion of the ball thus reducing the net acceleration acting on the ball.
As the acceleration decreases the final velocity of the ball decreases.
Thus the kinetic energy of the ball just prior to striking the ground will be less than before.
In deep water, a tsunami moves very fast and has a long wavelength and a small amplitude (see A in picture). As it enters shallower water, it slows down, and the wavelength decreases. This causes the wave to become much taller (see B in picture).As waves slow down, they start to bunch together, so they have a shorter wavelength than before. This can also be explained by the wave equation v = f x λ (speed = frequency x wavelength), which shows that, when a wave’s speed decreases, it must have a shorter wavelength than before – slowing down won’t change the wave’s frequency.Having a shorter wavelength means that the waves get higher. You could think of the shortened wave as being ‘squashed’ sideways – the water in the wave has to get higher because there’s not as much room for it within the shorter wavelength. It’s a bit like squeezing a toothpaste tube – all the toothpaste is forced upwards.
Answers
Given:
The wavelength of the wave decreases as it gets closer to the shore.
The speed of the wave decreases as it gets closer to the shore.
The waves get taller as it gets closer to the shore.
To find:
How does a change in velocity cause a change in amplitude?
Explanation:
The amplitude of a wave is described as the distance of the highest point of vibration or the oscillation of the wave from its mean position.
Given that as the velocity of the speed decreases the waves get taller. That is as the velocity decreases the distance of the highest point of vibration of the wave from its equilibrium or mean position increases.
Final answer:
Thus as the velocity of the wave decreases, its amplitude increases.
lc. A student makes a claim that states the first hill of a roller coaster is always the tallest(Point A) provided there is no mechanical assistance at any point after Point A on the track.Do you accept or reject her claim? Explain your answer. (2 points)
Answers
We accept the claim. This comes from the fact that if there is no mechanical assistance after point A (that is the tallest) then we make sure that the potential energy converts in kinetic energy and that way we make sure that the rollercoaester reaches all the other hills. If the tallest point is not the first one and there's no mechanical assitances then the rollercoester won't reach the hills that are taller than the first one (the kinetic energy won't be enough to reach it).
Which statement is not true of the reactions on the Sun?A.They are fusion reactions.B.They occur between helium atoms.C.Fast-moving nuclei collide.D.Hydrogen atoms are reacted.
Answers
Answer and explanation:
A correct option is an option (B). Option b is not true of the reaction on the sun because the reactions do not happen in between helium atoms.
All other options (A), (C), and (D) are incorrect because, in sun, the nuclear fusion reaction takes place between hydrogen atoms. Due to the sun's gravitational force and high temperature, the nuclei of helium move vary fast.
Conclusion:
The correct option is option (B).
a block sliding on the ground where uk= 0.193 experiences a 14.7N friction force. what is the mass of the block in kg
Answers
Answer:
F = ma
14.7N = m(0.193)
m = 76.3 kg
A 1 kg mass has a kinetic energy of 1 Joule when its speed isA. 0.45 m/sB. 1.4 m/sC. 1 m/sD. 4.4 m/s
Answers
Kinetic energy = 1/2 x mass x velocity^2
Where:
Kinetic energy = 1 J
mass = 1 kg
Isolate v (speed)
KE = 1/2 m v^2
√(2KE/m) = v
v = √(2KE/m)
Replacing with the values given:
v = √(2*1/1)
v= √2 = 1.4 m/s
Answer: 1.4 m/s (B)
If your favorite radio station is on the FM Dial at100 MHz (Mega Hertz) Calculate the wave length for this Radio station. Hint use the equation c = Lf, Where L is the wavelength and c is given at the top of the exam.
Answers
In order to calculate the wavelength, let's use the given formula, using c = 3 * 10^8 m/s (speed of light in vacuum) and f = 100*10^6 Hz:
[tex]\begin{gathered} 3\cdot10^8=L\cdot100\cdot10^6\\ \\ L=\frac{3\cdot10^8}{100\cdot10^6}=\frac{3\cdot10^8}{1\cdot10^8}=3\text{ m} \end{gathered}[/tex]Therefore the wavelength is 3 meters.
How do i solve this problem? Hint: The cannonball is being launched vertically upwards, therefore, there is no initial horizontal speed. The given initial speed will also be the initial vertical speed.
Answers
The initial velocity of the ball is given as 36.0 m/s.
The horizontal component of velocity of ball is given as,
[tex]v_x=v\cos \theta[/tex]The ball is projected vertically, therefore, the angle made by ball is 90 degree.
Plug in the known values,
[tex]\begin{gathered} v_x=(36.0m/s)cos90^{\circ} \\ =(36.0\text{ m/s)(0)} \\ =0\text{ m/s} \end{gathered}[/tex]Therefore, the initial horizontal velocity of ball is 0 m/s.
The vertical component of velocity of ball is given as,
[tex]v_y=v\sin \theta[/tex]Plug in the known values,
[tex]\begin{gathered} v_y=(36.0m/s)\sin 90^{\circ} \\ =(36.0\text{ m/s)(1)} \\ =36.0\text{ m/s} \end{gathered}[/tex]Therefore, the initial vertical velocity of the ball is 36.0 m/s.
If a bullet with mass 2.7 grams is fired from a gun with a speed of 202
m/s into a block of wood. If the kinetic energy is transformed to heat,
what is the increase in temperature of the bullet in degrees C,
assuming the specific heat of the bullet is 234 J/kg/C.
Answers
The increase in temperature of the bullet in degrees C is 87.17
Define Specific Heat Capacity?
When a material's temperature rises by 1 K (or 1 °C), or when its mass increases by 1 kg, the specific heat capacity is defined as the amount of heat (J) absorbed per unit mass (kg).
This measurement is expressed as J/(kg K) or J/(kg °C).
The heat that is transferred to the bullet as a result of the conversion of kinetic energy to heat is what causes the bullet's temperature to rise.
Q = cm T,
where Q is the energy transferred, c is the substance's specific heat, m is its mass, and T is the temperature change, describes this relationship.
Given,
mass = 2.7 x 10^-3 kg
speed = 202 m/s
C = 234 J/kg/C.
The kinetic energy of the travelling bullet is,
1/2 m(v^2) = 1/2 x 2.7 x 10^-3 x 202 x 202
= 55.08 J
Energy that raises the temperature = 55.08 J
This is equal to mCΔT
Equalising the 2 energies,
55.08 = mCΔT
ΔT = 55.08 / mC
= 55.08 / 2.7 x 10^-3 x 234
= 87.17
Hence, the increase in temperature of the bullet in degrees C is 87.17
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The maximum possible efficiency of a reversible heat engine is 79.46% when the cold temperature is 224.0°C. What is the hot temperature in degrees Celsius?
Answers
We have
A heat engine is 79.46%
TC= 224.0°C
TH=?
we have the next formula
[tex]\eta(\text{\%)}=1-\frac{T_C}{T_H}\times100[/tex]we substitute the values
[tex].7946=1-\frac{224}{T_H}\times100[/tex]then we isolate TH
[tex]\begin{gathered} .07946-1=-\frac{T_C}{T_H}\times1 \\ -0.2054=-\frac{T_C}{T_H}\times1 \\ \frac{T_C}{T_H}\times1=-0.2054 \\ \frac{T_C}{T_H}=\frac{0.2054}{1} \\ \frac{T_H}{T_C}=\frac{1}{0.2054} \\ T_H=4.8685\cdot224 \\ T_H=1090.55\text{ \degree{}C} \end{gathered}[/tex]the hot temperature is 1090.55 degrees Celsius.
Question 1: Assume that the pendulum of a grandfather clock acts as one of Planck'sresonators. If it carries away an energy of 8.1 x 10-15 eV in a one-quantumchange, what is the frequency of the pendulum? (Note that an energy this smallwould not be measurable. For this reason, we do not notice quantum effects in thelarge-scale world.)
Answers
Given:
Energy = 8.1 x 10⁻¹⁵ eV.
Let's find the frequency of the pendulum.
To find the frequency, apply the formula for the energy of a light quantum:
[tex]E=hf[/tex]Where:
E is the energy
h is Planck's constant = 6.63 x 10⁻³⁴ m² kg/s
f is the frequency.
Where:
1 eV = 1.6 x 10⁻¹⁹ J.
Rewrite the formula for f and solve:
[tex]f=\frac{E}{h}[/tex]Thus, we have:
[tex]f=\frac{8.1\times10^{-15}*(1.6\times10^{-19})}{6.63\times10^{-34}}[/tex]Solving further:
[tex]\begin{gathered} f=\frac{8.1\times10^{-15}*(1.6\times10^{-19})}{6.63\times10^{^{-34}}} \\ \\ \\ f=1.95\text{ Hz.} \end{gathered}[/tex]Therefore, the frequency of the pendulum is 1.95 Hz.
ANSWER:
1.95 Hz
A cyclist is freewheeling (not exerting additional force) down a 7 degree angle hill. The cyclists weight is 75N. What acceleration is the cyclist experiencing? I have to do the following:1. Draw a free body diagram2. Identify Givens and Unknowns3. Identify the Equations4. Set up the equation using the givens and unknowns5. Solve
Answers
The free body diagram in shown below:
From the diagram and the problem we have that:
• The weight and angle of the inclined plane are given.
,• The normal force and the components of the weight are unknown (this implies that the acceleration is unknown too); we also notice that the mass is not given the it is also an unknown.
We know that Newton's second law states that:
[tex]\vec{F}=m\vec{a}[/tex]where F is the resultant force and a is the acceleration. Since this is a vector equation we can decomposed it in two scalar equations (in this case we only need two scalar equations since the forces are coplanar), then we have:
[tex]\begin{gathered} Wx=ma_x \\ N-W_y=ma_y \end{gathered}[/tex]Since we don't expect the cyclist to move in the y direction (otherwise he will surely fall) the equations above would reduce to:
[tex]\begin{gathered} W_x=ma \\ N-W_y=0 \end{gathered}[/tex]From the first equation we can solve the acceleration, to do this we use the triangle to get the x-component of the weight:
[tex]\begin{gathered} W_x=ma \\ W\sin \theta=ma \\ a=\frac{W\sin \theta}{m} \end{gathered}[/tex]Since the weight is given but not the mass we use the fact that the weight is:
[tex]W=mg[/tex]to get the mass, then we have:
[tex]\begin{gathered} m=\frac{W}{g} \\ m=\frac{75}{9.8} \\ m=7.65 \end{gathered}[/tex]hence the mass of the cylcist is 7.65 kg.
Now that we have all the values we need we plug them in the expression for the acceleration:
[tex]\begin{gathered} a=\frac{75\sin 7}{7.65} \\ a=1.19 \end{gathered}[/tex]Therefore the acceleration of the cyclist is 1.19 meters per second per second.
Good morning I really need some help on this question!
Answers
Sound travels faster in water than air
Here, C is the correct option.
What common unit is used to measure sound intensity? Answer here
Answers
Decibel (dB)
Explanation:Sound intensity is the power carried by sound waves per unit area in a perpendicular direction to that area.
The unit of sound intensity is the decibel
Two positive charges of 10 C are separated by 12 meters. What is the force between the charges?
Answers
In order to calculate the force between the charges, we can use the formula below:
[tex]F=K\cdot\frac{q_1\cdot q_2}{d^2}[/tex]Where F is the force (in Newtons), K is the Coulomb constant (K = 9 * 10^9), q1 and q2 are the charges (in Coulombs) and d is the distance between them (in meters).
So, for q1 = q2 = 10 C and d = 12 m, we have:
[tex]\begin{gathered} F=9\cdot10^9\cdot\frac{10\cdot10}{12^2} \\ F=\frac{900\cdot10^9}{144} \\ F=6.25\cdot10^9\text{ N} \end{gathered}[/tex]Therefore the force between the charges is 6.25 * 10^9 N.
A tractor travels at a constant speed of 6m/s. Find the power supplied by the engine if it can supply a maximum force of 467 kN.
Answers
speed = v = 6m/s
Force = 467 kn = 467000N
Power = Work/ time
Work = Force x distance
Speed = distance / time
Isolating Distance:
Distance = Speed * time
P =[ Force * (speed * time ) ] / time
P = Force * speed
Replacing:
P = 467000 N * 6 m/s = 2,802,000 W
I have finished most of this question just need help on making sure it’s correct and the last 2
Answers
Given
m: mass
m = 50 kg
KE: kinetic energ
PEg: gravitational potential energy
v: speed
Procedure
Point A
KE = 0
PEg = mgh
PEg = 50 kg * 10 m/s^2 * 100 m
PEg = 50000 J
v = 0 m/s
Point B
h = 60 m
PEg = mgh
PEg = 50 kg * 10 m/s^2 * 60 m
PEg = 30000 J
KE = 20000 J
[tex]\begin{gathered} v=\sqrt[]{\frac{2\cdot KE}{m}} \\ v=\sqrt[]{\frac{2\cdot20000\text{ J}}{50\text{ kg}}} \\ v=\sqrt[]{800\text{ }} \\ v=28.28\text{ m/s} \end{gathered}[/tex]Point C
h = 30 m
PEg = mgh
PEg = 50 kg * 10 m/s^2 * 30 m
PEg = 15000 J
KE = 35000 J
[tex]\begin{gathered} v=\sqrt[]{\frac{2\cdot KE}{m}} \\ v=\sqrt[]{\frac{2\cdot35000\text{ J}}{50\operatorname{kg}}} \\ v=37.41\text{ m/s} \end{gathered}[/tex]Point D
h = 60 m
PEg = mgh
PEg = 50 kg * 10 m/s^2 * 60 m
PEg = 30000 J
KE = 20000 J
[tex]\begin{gathered} v=\sqrt[]{\frac{2\cdot KE}{m}} \\ v=\sqrt[]{\frac{2\cdot20000\text{ J}}{50\text{ kg}}} \\ v=\sqrt[]{800\text{ }} \\ v=28.28\text{ m/s} \end{gathered}[/tex]
Point E
h = 0
PEg = 50 kg * 10 m/s^2 * 0
PEg = 0 J
KE = 50000 J
[tex]\begin{gathered} v=\sqrt[]{\frac{2\cdot KE}{m}} \\ v=\sqrt[]{\frac{2\cdot50000\text{ J}}{50\text{ kg}}} \\ v=44.72\text{ m/s} \end{gathered}[/tex]An airplane covers a straight-line distance of 8.13 km in 33.5 s, during which time it has a constant forward acceleration of 4.6 m/s2.1. what is the speed at the first begining of 33.5 s.2.what is the speed at the end of the 33.5 s.
Answers
Given data
*The given distance is s = 8.13 km = 8130 m
*The given time is t = 33.5 s
*The given acceleration is a = 4.6 m/s^2
(1)
The formula for the speed at the first beginning of 33.5 seconds is given as
[tex]s=ut+\frac{1}{2}at^2[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} 8130=u(33.5)+\frac{1}{2}(4.6)(33.5)^2 \\ u=165.6\text{ m/s} \end{gathered}[/tex]Hence, the speed at the first beginning of 33.5 s is u = 165.6 m/s
(2)
The formula for the speed at the end of the 33.5 s is given as
[tex]v=u+at[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} v=(165.6)+(4.6)(33.5)_{} \\ =319.7\text{ m/s} \end{gathered}[/tex]Hence, the speed at the end of the 33.5 s is v = 319.7 m/s
A spaceship and an asteroid are moving in the same direction away from Earth with speeds of 0.8 c and 0.45 c, respectively. What is the relative speed between the spaceship and the asteroid?
Answers
Answer:
0.35c
Explanation:
The relative speed between the spaceship and the asteroid can be calculated as the difference between their speeds, so it is equal to
Relative speed = 0.8c - 0.45c
relative speed = 0.35c
Therefore, the answer is
0.35c
Which of the following is NOT a requirement for a planet? A. must orbit a star, but is not a star or satellite of another planetB. must be roundC. must clear its orbit of debrisD. must have a moon
Answers
Answer:
D. must have a moon
Explanation:
Scientists say that a planet must orbit a star, must be round, and must be big enough so its gravity clears its orbit of other objects. Therefore, the statement that is not a requirement for a planet is
D. must have a moon
For example, Mercury and Venus are planets with no moons.
When an arrow is released from its bow, its energy is transformed from potential energy to kinetic energy. Determine if the statement is correct.
Answers
Let's determine if the statement ''When an arrow is released from its bow, its energy is transformed from potential energy to kinetic energy'' is correct.
Let's first define kinetic and potential energies.
Potential energy is the energy stored in an object due to its position which depends on the relative position of various parts of the system.
Kinetic energy is the energy possesed by an object in motion.
Therefore, before the arrow is released from the bow, it is at rest and the energy is stored.
Hence, it posssess potential energy.
When the arrow is now released from the bow, it is now in motion. Since it is now in motion, the potential energy is now transformed to kinetic energy.
Therefore, the statement ''When an arrow is released from its bow, its energy is transformed from potential energy to kinetic energy'' is correct.
Calculate the mass of an object with a weight of 467 N.
Answers
We will have that the mass of the object is:
[tex]\begin{gathered} m=\frac{467N}{9.8m/s^2}\Rightarrow m=\frac{2335}{49}kg \\ \\ \Rightarrow m\approx47.65kg \end{gathered}[/tex]So, the mass of the object is 2335/49 kg, that is approximately 47.65 kg.
In Denver, children bring their old jack o lanterns to the top of a tower and compete for accuracy in hitting a target on the ground. suppose that the tower is 9.0m high and that the bullseye is a horizontal distance of 3.5m from the launch point.if the pumpkin is thrown horizontally what is the launch speed needed to hit the ground? (b) If the jack o lantern is given an initial horizontal speed of 3.3m/s, what are the direction and magnitude of its velocity (c) 0.75s later and (d) just before it lands.
Answers
a)
In order to calculate the required horizontal speed, first let's calculate the falling time, using the free-fall formula:
[tex]d=\frac{gt^2}{2}[/tex]For d = 9 and g = 9.8, we have:
[tex]\begin{gathered} 9=4.9t^2 \\ t^2=\frac{9}{4.9} \\ t=1.355\text{ s} \end{gathered}[/tex]Then, let's use this time in the following formula for horizontal distance, so we can calculate the horizontal speed:
[tex]\begin{gathered} \text{distance}=\text{speed}\cdot\text{time} \\ 3.5=\text{speed}\cdot1.355 \\ \text{speed}=\frac{3.5}{1.355}=2.58\text{ m/s} \end{gathered}[/tex]b)
Let's calculate the vertical velocity after 0.75 seconds, using the formula:
[tex]\begin{gathered} V=V_0+a\cdot t \\ V=0+9.8\cdot0.75 \\ V=7.35\text{ m/s} \end{gathered}[/tex]The magnitude can be calculated using the Pythagorean Theorem with the horizontal and vertical velocities:
[tex]\begin{gathered} V^2=7.35^2+3.3^2 \\ V^2=54.0225+10.89 \\ V^2=64.9125 \\ V=8.06\text{ m/s} \end{gathered}[/tex]And the direction is given by the arc tangent of the vertical velocity divided by the horizontal velocity (for this, let's use a negative value of vertical velocity, since it points downwards)
[tex]\theta=\tan ^{-1}(-\frac{7.35}{3.3})=\tan ^{-1}(-2.2272)=-65.82\degree[/tex](d)
To find the vertical velocity, let's use Torricelli's equation:
[tex]\begin{gathered} V^2=V^2_0+2\cdot a\cdot d \\ V^2=0^2+2\cdot9.8\cdot9 \\ V^2=176.4 \\ V=13.28\text{ m/s} \end{gathered}[/tex]Calculating the final speed magnitude and orientation, we have:
[tex]\begin{gathered} V^2=13.28^2+3.3^2 \\ V^2=187.2484 \\ V=13.68\text{ m/s} \\ \\ \theta=\tan ^{-1}(-\frac{13.68}{3.3})=\tan ^{-1}(-4.145)=-76.44\degree \end{gathered}[/tex]Kinematics question. Please note I’ve never done kinematics before so lots and lots of explanation very necessary.
Answers
Given figure is Time -velocity graph that indicate acceleration .
Now, according to problem
1) A graph line is parallel to time axis i.e. velocity is not changing with passes of time , so acceleration (a) = 0.
Here,
acceleration (a)= 0
time (t)= 20 sec
starting speed (u)= 40 m /s
final speed (v)= 40m /s
distance covered( s)= ?
Now using formula for linear motion ,we get
[tex]\begin{gathered} s=ut+\text{ }\frac{1}{2}at^2; \\ s=\text{ 40}\times20+\text{ 0}\begin{cases}a={0} \\ t={20}\end{cases} \\ s=800m; \end{gathered}[/tex]Answer is 800m
2) For graph line B---
Starting speed(u)= 25 m/s ( when time =0)
final speed (v) = 50 m/s (when time =20 s)
time (t)= 20 sec
acceleration (a)= ?
distance travelled (s)= ?
Now acceleration is given by
[tex]\begin{gathered} a=\frac{v-u}{t}; \\ a=\frac{50-25}{20}=\text{ }\frac{25}{20}=\text{ 1.25ms}^{-2} \end{gathered}[/tex]Again distance travelled in 20 s is given by
[tex]\begin{gathered} s=ut\text{ +}\frac{1}{2}at^2; \\ s=\text{ 25}\times20+\frac{1}{2}\times1.25\times20^2; \\ s=500+250=750\text{ m} \end{gathered}[/tex]Answer is a= 1.25m/s² and s= 750m
3) when t= 20 sec then distance travelled by A=800m and distance travelled by B= 750 m . Therefore A is ahead of B
4) distance travelled by car A in 40 sec is given by
[tex]\begin{gathered} s=ut\text{ +}\frac{1}{2}at^2 \\ s=\text{ 40}\times40+0\begin{cases}a={0} \\ u={40}\end{cases} \\ s=1600m \end{gathered}[/tex]Now distance travelled by B is given by
[tex]undefined[/tex]Here are three stress and strain graphs shown on approximately the same scale. Match each graph to one of either copper, glass or rubber. Give reason for your choices, perhaps making reference to the grey circular points
Answers
For the three graphs A,B and C in the graph C we see that the strain is larger for a small value of stress.
This type of graph is for the polymers (rubber).
The graph A has smallest amount of strain for stress in comparison with B.
Upto the grey circle stress and strain are proportional .
Graph A is for Glass and B for Copper.
Calculate the answer to the correctnumber of significant digits.1.899+ 0.58
Answers
ANSWER
2.48
EXPLANATION
We have to add like we normally do with whole numbers and put the decimal point in the same place it is in each summand:
The significant digits start with the first digit different from zero, reading from left to right:
This number has 4 significant digits in total: 2, 4, 7 and 9
Note that the numbers added don't have the same number of decimal places. The first one has three decimal places while the second one has two decimal places. This means that we have to round the answer to the second decimal place - which is hte 3rd significant digit. SInce the 4th significant digit is more than 5, we have to add one to the third significant digit:
[tex]2.479\Rightarrow2.48[/tex]A jet plane has a maximum deceleration rate of -7.30 m/s/s. It touches down on a runway with a speed of 122 m/s. From the instant it touches the runway, what is the minimum time needed before it comes to rest??
Answers
The maximum time needed before the jet plane that has a maximum deceleration of -7.30 m/s² comes to rest is 16.71 seconds.
What is time?Time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future.
To calculate the maximum time needed for the jet to come to rest, we use the formula below.
Formula:
t = (v-u)/a........... Equation 1Where:
t = Maximum time needed for the jet to come to restv = Final speedu = Initial speeda = Maximum deceleration of the jetFrom the question,
Given:
v = 0 m/s (to rest)u = 122 m/sa = - 7.30 m/s²Substitute these values into equation 1
t = (0-122)/(-7.3)t = -122/7.3t = 16.71 secondsHence, the maximum time needed is 16.71 seconds.
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A. How many Coulombs are there in one fundamental/elementary charge?B. How many electrons are there in one coulomb of negative charge?
Answers
(A). The number of Coulombs in one fundamental charge of an electron is,
[tex]1e\text{ = 1.}6\times10^{-19}\text{ C}[/tex](B). The charge in terms of the number of electrons is,
[tex]q=ne[/tex]where q is the net charge, e is the fundamental charge and n is the number of electrons,
For the net charge of q = 1 Coulomb, the number of electrons is,
[tex]\begin{gathered} 1\text{ C=n}\times1.6\times10^{-19}\text{ C} \\ n=\frac{1}{1.6\times10^{-19}} \\ n=0.625\times10^{19} \\ n=6.25\times10^{18}\text{ } \end{gathered}[/tex]Thus, the number of electrons in the 1 Coulomb of charge is,
[tex]6.25\times10^{18}[/tex]
One coulomb (1 C) is equal to approximately 6.24 x 10 18 elementary charges. Thus, an elementary charge is approximately 1.60 x 10 -19 C.
The unit of electrical charge quantity in the International System of Units is the coulomb. Coulomb is the SI unit of electric charge which is equal to the amount of charge transported by a current of one ampere in one second. It can be also, a property of a matter due to which electrical and magnetic effects are produced. It is denoted by C. Mathematically, 1 Coulomb = 1 Ampere × 1 second.
To illustrate the magnitude of 1 Coulomb, an object would need an excess of 6.25 x 1018 electrons to have a total charge of -1 C. And of course, an object with a shortage of 6.25 x 1018 electrons would have a total charge of +1 C. The charge on a single electron is -1.6 x 10 -19 Coulomb.
Charge on an electron(e)= 1.6∗10^−19 C approximately.
By quantization property of charge(Smallest unit is e),
Charge (Q) = 1C where n-number of electrons.
Electron (e) = 1.6× 10^-19
A number of electrons (n) =?
Q= ne
1 C = n × 1.6×10^-19 C
n = 1/(1.6×10^-19)
Which gives, n= 6.25*10^18 electrons
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A ball of mass 1.86 kilograms is attached to a cord 1.29 meters long and swung in a vertical circle at a constant speed of 5.27 meters per second. What is the centripetal force acting on the ball? Include units in your answer. What is the tension in the cord when the ball is at the bottom of its path? Include units in your answer. What is the tension in the cord when the ball is at the top of its path? Include units in your answer. All answers must be in 3 significant digits.
Answers
Explanation
Step 1
Draw
so
a)centripetal force:
the centripetal force is given by.
[tex]\begin{gathered} F=ma \\ F=m\frac{v^2}{r} \\ \text{where } \\ F_{C\text{ }}\text{ is the centripetal force} \\ m\text{ is the mass } \\ v\text{ is the velocty } \\ r\text{ is the radius} \end{gathered}[/tex]now, replace
[tex]\begin{gathered} F=m\frac{v^2}{r} \\ F=1.86\text{ kg }\frac{(\text{ 5.27 }\frac{m}{s})^2}{1.29\text{ m}} \\ F=40.044\text{ Newtons} \end{gathered}[/tex]so, the centripetal force is 40.0446 Newtons
b) What is the tension in the cord when the ball is at the bottom of its path?
to find the tension in bottom, we need to add the weigth of the ball,so
[tex]\begin{gathered} \text{weigth}=\text{ mass}\cdot accelofgravity \\ w=mg \end{gathered}[/tex]hence, the tension would be
[tex]\begin{gathered} T_{bottom}=m\frac{v^2}{r}+mg \\ \end{gathered}[/tex]replace
[tex]\begin{gathered} T_{bottom}=m\frac{v^2}{r}+mg \\ T_{bottom}=40.044\text{ N+(1.86 kg}\cdot9.81\text{ }\frac{\text{m}}{s^2}) \\ T_{bottom}=40.044\text{ N+18.2466 N} \\ T_{bottom}=58.291\text{ N} \end{gathered}[/tex]c)What is the tension in the cord when the ball is at the top of its path?
to find the tension in the top we need to subtract the weigth, so
[tex]\begin{gathered} T_{\text{top}}=m\frac{v^2}{r}-mg \\ replace \\ T_{\text{top}}=40.044\text{ N-18.2466 N} \\ T_{\text{top}}=21.79\text{ Newtons} \end{gathered}[/tex]I hope this helps you
it would be greatly appreciated if you plug in the numbers according to the format of my worksheet.
Answers
a. List variables
[tex]\begin{gathered} m_{1i}=\text{ 0.015 kg} \\ v_{1i}=\text{ 0.225 m/s} \\ m_{2i}=\text{ 0.03 kg} \\ v_{2i}\text{ =-0.18 m/s} \\ m_{1f}=\text{ 0.015 kg} \\ v_{1f}=-0.315\text{ kg} \\ m_{2f}=\text{ 0.03 kg} \\ v_{2f}\text{ = ?} \end{gathered}[/tex]b. plug into the equation
[tex]\begin{gathered} m_{1i}v_{1i}+m_{2i}v_{2i}=m_{1f}v_{1f}+m_{2f}v_{2f} \\ 0.015\times0.225+0.03\text{ }\times(-0.18)=0.015\times(-0.315)+0.03(v_{2f}) \end{gathered}[/tex]c. solve for missing
[tex]\begin{gathered} v_{2f}=\frac{0.015\times0.225+0.03(-0.18)-0.015\times(-0.315)}{0.03} \\ =0.09\text{ m/s} \end{gathered}[/tex]