Answer:
[tex]M = \left[\begin{array}{ccc}cos \ 60&0\\0&-sin \ 60\end{array}\right][/tex]
Explanation:
To find the matrix, let's decompose the vectors, the rotated angle is (-60C) for the prime system
x ’= x cos (-60)
y ’= y sin (-60)
we use
cos 60 = cos (-60)
sin 60 = - sin (-60)
we substitute
x ’= x cos 60
y ’= - y sin 60
the transformation system is
[tex]\left[\begin{array}{ccc}x'\\y'\end{array}\right] = \left[\begin{array}{ccc}cos 60&0\\0&-sin60\end{array}\right] \ \left[\begin{array}{ccc}x\\y\end{array}\right][/tex]x '
the transformation matrix is
[tex]M = \left[\begin{array}{ccc}cos \ 60&0\\0&-sin \ 60\end{array}\right][/tex]
the suns energy comes from which nuclear reaction?
A child is playing on a swing. As long as he does not swing too high the time it takes him to complete one full oscillation will be independent of
Answer:
We know that for a pendulum of length L, the period (time for a complete swing) is defined as:
T = 2*pi*√(L/g)
where:
pi = 3.14
L = length of the pendulum
g = gravitational acceleration = 9.8 m/s^2
Now, we can think on the swing as a pendulum, where the child is the mass of the pendulum.
Then the period is independent of:
The mass of the child
The initial angle
Where the restriction of not swing to high is because this model works for small angles, and when the swing is to high the problem becomes more complex.
A boy im50kg at rest on a skateboard is pushed by another boy who exerts a force of 200 N on him. If the first boy's
final velocity is 8 m/s, what was the contact time?
seconds
Answer:
Time, t = 2 seconds
Explanation:
Given the following data;
Mass, m = 50 kg
Initial velocity, u = 0 m/s (since it's starting from rest).
Final velocity, v = 8 m/s
Force, F = 200 N
To find the time, we would use the following formula;
[tex] F = \frac {m(v - u)}{t} [/tex]
Making time, t the subject of formula, we have;
[tex] t = \frac {m(v - u)}{F} [/tex]
Substituting into the formula, we have;
[tex] t = \frac {50(8 - 0)}{200} [/tex]
[tex] t = \frac {50*(8)}{200} [/tex]
[tex] t = \frac {400}{200} [/tex]
Time, t = 2 seconds
Glass lenses are practically opaque to an emission source with the wavelength shorter than 400nm. (True or False)
Answer:
the statement is TRUE
Explanation:
Most lenses are made of glass that has a strong absorption below 400 nm,
Only special evaporation lenses are made of quartz and fused silica which has a high absorption below 200 nm.
therefore the statement is TRUE
A box has a mass of 4kg and surface area 4m². Calculate the
pressure exerted by the box on the floor.
Answer:
10 pa
Explanation:
4kg* 10 (or 9.8m/s2) = 40
40N /4m2 =10
your initial speed is zero. if you increased your speed by 4 m/s after only 2 seconds and continue to accelerate at the same rate, what will your speed be after 10 seconds?
Answer:
20 m/ s
Explanation:
change in velocity = 4m/ s
[tex]acceleration = \frac{rate \: of \: change \: of \: velocity}{time} [/tex]
[tex]acc = \frac{4}{2} \\ = 2[/tex]
initial velocity = 0m/ s
let velocity after 10s be v[tex]2 = \frac{v - 0}{10} [/tex]
cross multiplying
[tex]20 = v[/tex]
so the velocity after 10s will be 20m/s
A cylindrical container closed of both end has a radius of 7cm and height of 6cm A.)find the total surface area of the container B.) find the volume of the container
what do you think will happen to the people in the airplane if their location is unknown?
Question:
What do you think will happen to the people in the airplane if their location is unknown?
My opinion:
I mean what are the circumstances? Is it just a rogue pilot that takes a random plane with all the passengers Hostage or is It bad whether an they lose connection to the airport? I Mean either way, If I was on a plane being held hostage, or the plane crashing, I Would be a in a panic type state of mind. I Would be worried about what will happen when the plane crashes, I would worry about my friends or family that is aboard the plane with me, I Would be scared for my life because I Don't know if i would make it out alive.
Also:
How would they know their location is unknown wouldn't the Pilot be the only one to know exactly where there with their navigating system, But then again there was this time I headed to Florida an They had mini tv's on the seats of each chair, where you could: Watch movies, listen to music, an Also see exactly where you are in the world. It was really amazing actually.
Example Problem
The potential energy of an object is given by U(x) = 8x2 - x4, where U is in joules and x is in
(a) Determine the force acting on this object.
(b) At what positions is this object in equilibrium?
(c) Which of these equilibrium positions are stable and which are unstable?
metres.
111 Unit 2 Concepts and Definitions Prof Mark Lester
Exam Part B Example
A neutron of mass m moving with velocity v collides head-on and elastically with a stationary nucleus of mass M.
(a) Show that the velocity of the nucleus after the collision, U, is given by
U= 2m v (m+M)
(b) Hence show that the neutron loses a fraction f of its energy where
f= 4mM (m+M)
10marks 5 marks
(c) A fast neutron enters a target of carbon nuclei which may be assumed to have masses 12 times that of the neutron. How many head-on collisions will it take
before the neutron loses 95% of its energy?
4 marks
(d) Suggest one reason why in a real reactor a neutron is likely to make more
collisions with the moderator nuclei before losing this much energy
2
1 mark
Answer:
Part A
a) F = -16x + 4, b) x = 0.25 m, c) STABLE
Explanation:
Part A
a) Potential energy and force are related
F = [tex]- \frac{dU}{dx}[/tex]- dU / dx
F = - (8 2x -4)
F = -16x + 4
b) The object is in equilibrium when the forces are zero
0 = -16x + 4
x = 4/16
x = 0.25 m
c) An equilibrium position is called stable if with a small change in position, the forces make it return to the initial position, in case the forces make it move away it is called unstable.
In this case there is only one equilibrium point
by changing the position a bit
x ’= x + Δx
we substitute
F ’= - 16 x’ + 4
F ’= - 16 (x + Δx) + 4
F ’= (-16x +4) - 16 Δx
at equilibrium position F = 0
F ’= 0 - 16 Δx
we can see that the body returns to the equilibrium position, therefore it is STABLE
PART B
This is an exercise in body collisions, let's define the system formed by the two bodies in such a way that the forces during the collisions are internal and the moment is conserved
initial instant. Before the shock
p₀ = m v
final instant. After the crash
p_f = (m + M) v_f
We have two possibilities: an elastic collision in which the bodies separate, each one maintaining its plus, and an INELASTIC collision where the neutron is absorbed by the nucleus and the final mass is M '= m + M, in this case they indicate that the collision is elastic
p₀ = pf
mv = mv ’+ M v_f
in the case of the elastic collision, the kinetic energy is conserved
K₀ = K_f
½ m v² = ½ m v’² + ½ M v_f²
we write the system of equations
mv = mv ’+ M v_f (1)
m (v² -v'²) = M v_f ²
m (v - v ’) = M v_f
m (v-v ’) (v + v’) = M v_f
v + v ’= v_f
we substitute in equation 1 and solve
v ’=[tex]\frac{m -M }{m+M } \ vo[/tex]
v_f = [tex]\frac{2m}{m+M} \ v_o[/tex]
the mechanical energy of the neutron is
initial
Em₀ = K = ½ m v²
final moment
Em_f = K + U = ½ m v_f ² + U
U is the energy lost in the collision
total energy is conserved
Em₀ = Em_f
½ m v² = ½ m v_f ² + U
U = ½ m (v² -v_f ²)
U = ½ m [v² - ( [tex]\frac{m-M}{m+M}[/tex] v)² ]
U = ½ m v² [1- ( [tex]\frac{m-M}{m+M}[/tex] )² ]
U = ½ m v2 [ [tex]\frac{2M}{m+M}[/tex]]
U = [tex]\frac{2 mM}{m +M } \ v^2[/tex]
Let's do the same calculations for the nucleus
initial Em₀ = 0
final Em_f = K + U = ½ M v_f ² + U
Em₀ = Em_f
0 = K + U
U = -K
U = - ½ M v_f ²
U = - ½ M [ [tex]\frac{2m}{m+M} \ v[/tex] ]²
U = [tex]\frac{2 m M }{m+M} \ v^2[/tex]
We can see that we obtain the same result, that is, the potential energy lost by the neutron is equal to the potential energy gained by the nucleus.
b) the fraction of energy lost
f = U / Em₀
f = 4 m M / m + M
c) let's calculate the fraction of energy lost in a collision
m = 1.67 10⁻²⁷ kg
M = 12 1.67 10⁻²⁷= 20 10⁻²⁷ kg
f = 4 1.6 20 / (1.6+ 20) 10⁻²⁷
f = 5.92 10⁻²⁷ J
the energy of a fast neutron is greater than 1 eV
Eo = 1 eV (1.67 10⁻¹⁹ J / 1eV) = 1.67 10⁻¹⁹ J
Let's use a direct portion rule if in a collision f loses in how many collisions it loses 0.95Eo
#_collisions = 0.95 Eo / f
#_collisions = 0.95 1.67 10⁻¹⁹ / 5.92 10⁻²⁷
#_collisions = 2.7 10⁷ collisions
An object weighs 2.2 pounds on Earth and has a mass of 1 kilogram. What are the weight and mass of the same object in space where there is no gravity acting on it?
Answer:
Heavier than 2.2 pounds
Explanation:
Two uses of static electricity and dangers of static electricity
Answer: The uses of static electricity include:
--> photocopying machines
--> precipitators
The dangers of static electricity include:
--> sparks that can lead to explosion
--> Damage to electronic equipment
Explanation:
STATIC electricity is defined as the imbalance that exists between a positive and a negative charge either within or outside an object. This is because all physical objects are made up of atoms which contains protons, electrons and neutrons. The protons are positively charged, the electrons are negatively charged, and the neutrons are neutral. This shows that physical objects are made up of charges.
Opposite charges attract each other (negative to positive). Like charges repel each other (positive to positive or negative to negative). Most of the time positive and negative charges are BALANCED in an object, which makes that object neutral.
Applications( uses) of static electricity include:
--> photocopying machines: Inkjet photocopiers and printers use static electricity to guide a minute jet of ink to the page’s precise position.
--> precipitators: the static electricity is applied in an electrostatic precipitator whereby they remove smoke from waste gases before they pass out of the chimneys in power stations that burn fossil fuels.
The disadvantages (dangers) of static electricity include:
--> Sparks that can lead to explosion: sparks generated from static electricity can cause fires or explosions due to the ignition of flammable or explosive mixtures.
--> Damage to electronic equipment: this is due to components from electrostatic discharge.
A drone traveling horizontally at 100 m/s over flat ground at an elevation of 3000 meters must drop an emergency package on a target on the ground. The trajectory of the package is given by x=100t , y=−4.9t2+3000 ,t≥0 where the origin is the point on the ground directly beneath the drone at the moment of release. How many horizontal meters before the target should the package be released in order to hit the target? Round to the nearest meter.
Answer:
The package should be dropped 244.7 meters before the target
Explanation:
We need to find how long the package will take to hit the ground then solve for position.
y=0
-4.9t^2=-3000
t= sqrt (3000/4.9)
t= 24.74 seconds.
x= 247.4 meters.
Fluorometers are designed so that the path of the excitation light is at a right angle to the path of the emitted light. What is the purpose of this design
Answer: prevent excitation light from reaching the detector
Explanation:
A fluorometer refers to the device that's used in the measurement of parameters that are of visible spectrum fluorescence. They also prevent excitation light from reaching the detector.
These parameters are used in the identification of the amount and presence of molecules in a medium.
URGENT
A student runs at 4.5 m/s [27° S of W] for 3.0 minutes and then he turns and runs at 3.5 m/s [35° S of E] for 4.1 minutes.
a. What was his average speed?
b. What was his displacement?
PLEASE SHOW ALL WORK
Answer:
(a) 3.93 m/s
(b) 861.66 m
Explanation:
A = 4.5 m/s [27° S of W] for 3.0 minutes
B = 3.5 m/s [35° S of E] for 4.1 minutes
Distance A = 4.5 x 3 x 60 = 810 m
Distance B = 3.5 x 4.1 x 60 = 861 m
(a) The average speed is defined as the ratio of the total distance to the total time.
Total distance, d = 810 + 861 = 1671 m
total time, t = 3 + 4.1 = 7.1 minutes = 7.1 x 60 = 426 seconds
The average speed is
[tex]v=\frac{1671}{426}=3.93 m/s[/tex]
(b)
[tex]\overrightarrow{A} = 810(- cos 27 \widehat{i} - sin 27 \widehat{j})=- 721.7 \widehat{i} - 367.7 \widehat{j}\\\\\overrightarrow{B} = 861( cos 35 \widehat{i} - sin 35 \widehat{j})= 705.3 \widehat{i} - 493.8 \widehat{j}\\\\\overrightarrow{C} = (- 721.7 + 705.3) \widehat{i} - (367.7 + 493.8) \widehat{j} \\\\\overrightarrow{C}= - 16.4 \widehat{i} - 861.5 \widehat{j}[/tex]
The magnitude is
[tex]C =\sqrt{16.4^2+861.5^2} = 861.66 m[/tex]
a stone of mass 250kg and another stone of mass 400 kg are kept at a distance of 100m what amount of gravitational force develops between them?
Explanation:
Hey there!
Given;
Mass of one object (m1) = 250kg
Mass of another object (m2) = 400 kg
Distance (d) = 100 m
Gravitational constant (g) = 6.67*10^-11
Now;
[tex]f = \frac{g.m1.m2}{ {d}^{2} } [/tex]
Keep all values;
[tex]f = \frac{6.67 \times {10}^{ - 11} \times 250 \times 400}{ {(100)}^{2} } [/tex]
Simplify
[tex]f = \frac{6.67 \times {10}^{ - 11} {10}^{5} }{10000} [/tex]
[tex]f = \frac{6.67 \times {10}^{ - 6} }{10000} [/tex]
Therefore, gravitational force is 6.67*10^-10.
Hope it helps!
A stream leaving a mountain range deposits a large part of its load in a __
Answer:
(n) alluvial fan sandbar
Explanation:
what happens to gravitational force when distance is quarter from the original
please answer it faster help me
Answer:
The force of gravitational attraction between them also decreas
The idea that the universe began from a single point and expanded to its current size explains a large number of observations, including those in the table below.
Observations Explained
The universe consists mostly of low-mass elements.
Cosmic microwave background is nearly the same in all directions.
Light from other galaxies shows that these galaxies are moving away from Earth.
In addition, many predictions based on the idea have led to additional observations that support it. Which best describes this idea of the origin of the universe?
Answer:
theory
Explanation:
took the quiz
In the hydraulic system depicted, the cylinder on the left has a diameter of 2 inches and the cylinder on the right has a diameter of 6 inches. If 100 lbs of force was applied to the cylinder on the left, what force would be exerted on the cylinder on the right
Answer:
F2 = 900 lbs
Explanation:
From pascal principle;
F1/A1 = F2/A2
Force on cylinder at left; F1 = 100 lbs
Diameter of cylinder at left; d1 = 2 inches
Diameter of cylinder at right; d2 = 6 inches
Formula for area of top of cylinder = πr²
Thus;
Area of top of left cylinder; A = π × 2² = 4π
Area of top of right cylinder; A = π × 6² = 36π
Thus;
100/4π = F2/36π
F2 = (36π × 100)/4π
F2 = 900 lbs
Find the moment of inertia of a hoop (a thin-walled, hollow ring) with mass MMM and radius RRR about an axis perpendicular to the hoop's plane at an edge.
Answer:
I = sum m *r^2 where m represents the (small) individual masses and r is the distance of that mass from center of rotation
Note: sum m = M
For the hoop given all masses are at a distance RRR from the center of rotation
I = MMM * RRR^2
100 POINTS !!! PLEASE HELP !!!!
What is the independent variable?
What is the dependent variable?
I
Materials
1. 4 antacid tablets
2. 2 clear cups labeled Hot and Cold
3. Water
4. Timing device
Answer:
dependent: the outcome of the experience
independent variable: everything literaly.
Independent is where you change some variables and see the result
Dependent is literaly the result, or the outcome dependent on the exprience.
Explanation:
I got u.
The designer tested how the number of cells affected the number of steps that could
be taken before the lights stopped working.
Figure 2 shows the results.
Figure 2
1600
1400
1200
1000
Number of
steps in
800
thousands
600
400
200
0
1
5
2 3 4
Number of cells
1
3
Determine how many more steps could be taken when the number of cells was
increased from 3 to 5
[2 marks
Number of steps
=
thousand
Answer:
1000.
Explanation:
Thousand more steps could be taken when the number of cells was increased from 3 to 5 because in the data, the number of cells i.e. 5 was achieved on 1000 steps. According to the data, the number of cells i.e. 1 was achieved on 800 steps, the number of cells i.e. 5 was achieved on 1000 steps, the number of cells i.e. 2 was achieved on 600 steps, the number of cells i.e. 3 was achieved on 400 steps and the number of cells i.e. 4 was achieved on 200 steps. So we can say that 1000 steps are needed for the number of cells increased from 3 to 5.
A dart is thrown horizontally with an initial speed of 19 m/s toward point P, the bull's-eye on a dart board. It hits at point Q on the rim, vertically below P, 0.19 s later. (a) What is the distance PQ
Answer:
Explanation:
The dart will go forward horizontally with velocity of 19 m/s. It will also fall downwards with initial velocity of zero and gravitational acceleration of 9.8 m/s².
Distance PQ covered by the dart can be calculated using the following formula.
s = ut + 1/2 at²
u is initial velocity , a is acceleration and t is time.
Putting the values
s = 0 + 1/2 x 9.8 x .19²
= .1769 m
= 17.69 cm.
A car is stationary. It accelerates at 0.8 ms^2
for 10 s and then at 0.4 ms^2
for a further 10 s. Use
the equations of motion to deduce the car’s final displacement. You will have to split the journey
into two parts, since the acceleration changes after 10 s.
Answer:
the car’s final displacement is 60 m
Explanation:
Given;
initail velocity of the car, u = 0
acceleration of the car, a = 0.8 m/s²
time of motion, t = 10 s
The first displacement of the car:
[tex]x_1 = ut + \frac{1}{2} at^2\\\\x_1 = 0 + \frac{1}{2} (0.8)(10)^2\\\\x_1 = 40 \ m[/tex]
The second displacement of the car;
acceleration, a = 0.4 m/s², time of motion, t = 10 s
[tex]x_2 = ut + \frac{1}{2} at^2\\\\x_2 = 0 + \frac{1}{2} (0.4)(10)^2\\\\x_2 = 20 \ m[/tex]
The final displacement of the car;
x = x₁ + x₂
x = 40 m + 20 m
x = 60 m
Therefore, the car’s final displacement is 60 m
The standard metric unit of volume is the _____.
cubic centimeter
liter
milliliter
cubic meter
Answer:
. The SI unit of volume is the cubic meter (m3), which is a derived unit.
Liter (L) is a special name for the cubic decimeter (dm3).
Stellar nucleosynthesis a. produces elements with an atomic number greater than 26 (iron). b. is a process that happens during the death of stars. c. is the process by which stars create the heavier elements. d. is a stream of atoms emitted from a star.
Answer:
C: the process by which stars create the heavier elements
Explanation:
Stellar nucleosynthesis is defined as the process of nuclear fusion by which heavier elements are formed within stars by from the combination of protons and neutrons gotten from the nuclei of lighter elements.
Looking at the options, the correct one is Option C
What is the acceleration of a motorcycle that starts from rest and reaches a velocity of 24 m/s in 8.5 seconds?
Answer:
2.82 m/s²
Explanation:
[tex]v = u + at \\ 24 = 0 + a(8.5) \\ a = 2.82 \: ms {}^{ - 2} [/tex]
The acceleration of a motorcycle is 2.82 m/s^2.
What is acceleration?Acceleration is the rate at which speed and direction of velocity vary over time. A point or object going straight ahead is accelerated when it accelerates or decelerates.
Even if the speed is constant, motion on a circle accelerates because the direction is always shifting. Both effects contribute to the acceleration for all other motions.
Given that:
Initial velocity of the motor cycle: u = 0 m/s.
Final velocity of the motorcycle = 24 meter/second.
Time taken to reach this velocity = 8.5 second.
Hence, acceleration of the motor cycle = change in velocity/time interval
= ( final velocity - initial velocity)/time interval
= ( 24 m/s - 0 m/s)/8.5 s
= 2.82 m/s^2.
Its acceleration is 2.82 m/s^2.
Learn more about acceleration here:
brainly.com/question/12550364
#SPJ2
coulomb what is the meaning in physics??
Answer:
Coulomb, unit of electric charge in the metre- kilogram- second- ampere system, the basis of SI system of physics unit. The coulomb is defined as the quantity of electricity transported in one second by a current of one ampere.
What will happen to the gravitational force when the distance between the centre of the two bodies is halved ?
Explanation:
when the distance between the 2 objects is halved, the gravitational force between the 2 objects is doubled. when the distance between the 2 objects is doubled then the gravitational force doubles.
When should a line graph be used?
