Answer:
t = 2 s
Explanation:
In order to find the time taken by the stone to fall from the top of the building to the ground we can use 2nd equation of motion. 2nd equation of motion is as follows:
s = Vit + (0.5)gt²
where,
t = time = ?
Vi = Initial Velocity = 20 m/s
s = height of building = 60 m
g = 9.8 m/s²
Therefore,
60 m = (20 m/s)t + (0.5)(9.8 m/s²)t²
4.9t² + 20t - 60 = 0
solving this quadratic equation we get:
t = -6.1 s (OR) t = 2 s
Since, the time cannot be negative in magnitude.
Therefore,
t = 2 s
A 1.40-kg block is on a frictionless, 30 ∘ inclined plane. The block is attached to a spring (k = 40.0 N/m ) that is fixed to a wall at the bottom of the incline. A light string attached to the block runs over a frictionless pulley to a 60.0-g suspended mass. The suspended mass is given an initial downward speed of 1.40 m/s . Part A How far does it drop before coming to rest? (Assume the spring is unlimited in how far it can stretch.)
Answer:
the mass drop by 6.5cm before coming to rest.
Explanation:
Given that:
the mass of the block M= 1.40 kg
angle of inclination θ = 30°
spring constant K = 40.0 N/m
mass of the suspended block m = 60.0 g = 0.06 kg
initial downward speed = 1.40 m/s
The objective is to determine how far does it drop before coming to rest?
Let assume it drops at y from a certain point in the vertical direction;
Then :
Workdone by gravity on the mass of the block is:
[tex]w_1g = 1.4*9.81*y*sin30[/tex] = - 6.867y
Workdone by gravity on the mass of the suspended block is:
[tex]w_2g = 0.06*9.81[/tex] = 0.5886
The workdone by the spring = -1/2ky²
= -0.5 × 40y²
= -20 y²
The net workdone is = -20 y² - 6.867y + 0.5886y
According to the work energy theorem
Net work done = Δ K.E
-20 y² - 6.867y + 0.5886 = 1/2 × 0.06 × 1.4²
-20 y² - 6.867y + 0.5886 = 0.5 × 0.1176
-20 y² - 6.867y + 0.5886 = 0.0588
-20 y² - 6.867y + 0.5886 - 0.0588
-20 y² - 6.867y + 0.5298 = 0
multiplying through by (-)
20 y² + 6.867y - 0.5298 = 0
Using the quadratic formula:
[tex]\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
where;
a = 20 ; b = 6.867 c= - 0.5298
[tex]\dfrac{-(6.867) \pm \sqrt{(6.867)^2-(4*20*-0.5298)}}{2*(20)}[/tex]
[tex]= \dfrac{-(6.867) + \sqrt{(6.867)^2-(4*20*-0.5298)}}{2*(20)} \ \ \ OR \ \ \ \dfrac{-(6.867) - \sqrt{(6.867)^2-(4*20*-0.5298)}}{2*(20)}[/tex]= 0.0649 OR −0.408
We go by the positive integer
y = 0.0649 m
y = 6.5 cm
Therefore; the mass drop by 6.5cm before coming to rest.
A 73 kg swimmer dives horizontally off a 462 kg raft initially at rest. If the diver's speed immediately after leaving the raft is 5.54 m/s, what is the corresponding raft speed
Answer:
Corresponding raft speed = -0.875 m/s (the minus sign indicates that the raft moves in the direction opposite to the diver)
Explanation:
Law of conservation of momentum gives that the momentum of the diver and the raft before the dive is equal to the momentum of the diver and the raft after the dive.
And since the raft and the diver are initially at rest, the momentum of the diver after the dive is equal and opposite to the momentum experienced by the raft after the dive.
(Final momentum of the diver) + (Final momentum of the raft) = 0
Final Momentum of the diver = (mass of the diver) × (diving velocity of the diver)
Mass of the diver = 73 kg
Diving velocity of the diver = 5.54 m/s
Momentum of the diver = 73 × 5.54 = 404.42 kgm/s
Momentum of the raft = (mass of the raft) × (velocity of the raft)
Mass of the raft = 462 kg
Velocity of the raft = v
Momentum of the raft = 462 × v = (462v) kgm/s
404.42 + 462v = 0
462v = -404.42
v = (-404.42/462) = -0.875 m/s (the minus sign indicates that the raft moves in the direction opposite to the diver)
Hope this Helps!!!
In cricket how bowler and batsman use acceleration?
Points P and Q are separated by a distance of 0.10 m in a uniform electric field. The potential difference between points P and Q is 55 V. What is the magnitude of the electric field?
Answer:
E = 550 V/m = 550 N/C
Explanation:
The formula for calculating the potential difference between two points in an electric field is given as follows:
ΔV = E.Δr
where,
ΔV = Potential Difference between points P and Q = 55 V
Δr = Distance between P and Q = 0.1 m
E = Magnitude of Electric Field = ?
Therefore, using these values in the equation, we get:
55 V = E(0.1 m)
E = 55 V/0.1 m
E = 550 V/m = 550 N/C
Because, volt/meter is equivalent to Newton/Coulomb.
The exit nozzle in a jet engine receives air at 1200 K, 150 kPa with negligible kinetic energy. The exit pressure is 80 kPa, and the process is reversible and adiabatic. Use constant specific heat at 300 K to find the
Complete question:
The exit nozzle in a jet engine receives air at 1200 K, 150 kPa with negligible kinetic energy. The exit pressure is 80 kPa, and the process is reversible and adiabatic. Use constant specific heat at 300 K to find the exit velocity.
Answer:
The exit velocity is 629.41 m/s
Explanation:
Given;
initial temperature, T₁ = 1200K
initial pressure, P₁ = 150 kPa
final pressure, P₂ = 80 kPa
specific heat at 300 K, Cp = 1004 J/kgK
k = 1.4
Calculate final temperature;
[tex]T_2 = T_1(\frac{P_2}{P_1})^{\frac{k-1 }{k}[/tex]
k = 1.4
[tex]T_2 = T_1(\frac{P_2}{P_1})^{\frac{k-1 }{k}}\\\\T_2 = 1200(\frac{80}{150})^{\frac{1.4-1 }{1.4}}\\\\T_2 = 1002.714K[/tex]
Work done is given as;
[tex]W = \frac{1}{2} *m*(v_i^2 - v_e^2)[/tex]
inlet velocity is negligible;
[tex]v_e = \sqrt{\frac{2W}{m} } = \sqrt{2*C_p(T_1-T_2)} \\\\v_e = \sqrt{2*1004(1200-1002.714)}\\\\v_e = \sqrt{396150.288} \\\\v_e = 629.41 \ m/s[/tex]
Therefore, the exit velocity is 629.41 m/s
Which circuits are parallel circuits?
Answer:
The bottom two lines.
Explanation:
They need their own line of voltage quantity. A parallel circuit has the definition of 'two or more paths for current to flow through.' The voltage does stay the same in each line.
A traveling electromagnetic wave in a vacuum has an electric field amplitude of 62.5 V/m. Calculate the intensity S of this wave. Then, determine the amount of energy ???? that flows through area of 0.0231 m2 over an interval of 14.9 s, assuming that the area is perpendicular to the direction of wave propagation.
Answer:
a) 5.19 W/m²
b) 1.79 J
Explanation:
For the calculation of intensity, I. We have
I = E(rms)² / (cμ), where
c = speed of light
μ = permeability of free space
I = (62.5 / √2)² / [(2.99 x 10^8) (1.26 x 10^-6)]
I = 1954 / 376.74
I = 5.19 W/m²
Therefore, the intensity, I = 5.19 W/m²
t = 14.9 s
A = 0.0231 m²
Amount if energy flowing, U = IAt
U = (5.19) (0.0231) (14.9) J
U = 1.79 J
An electron moving in a direction perpendicular to a uniform magnetic field at a speed of 1.6 107 m/s undergoes an acceleration of 7.0 1016 m/s2 to the right (the positive x-direction) when its velocity is upward (the positive y-direction). Determine the magnitude and direction of the field.
Answer:
B = 0.024T positive z-direction
Explanation:
In this case you consider that the direction of the motion of the electron, and the direction of the magnetic field are perpendicular.
The magnitude of the magnetic force exerted on the electron is given by the following formula:
[tex]F=qvB[/tex] (1)
q: charge of the electron = 1.6*10^-19 C
v: speed of the electron = 1.6*10^7 m/s
B: magnitude of the magnetic field = ?
By the Newton second law you also have that the magnetic force is equal to:
[tex]F=qvB=ma[/tex] (2)
m: mass of the electron = 9.1*10^-31 kg
a: acceleration of the electron = 7.0*10^16 m/s^2
You solve for B from the equation (2):
[tex]B=\frac{ma}{qv}\\\\B=\frac{(9.1*10^{-31}kg)(7.0*10^{16}m/s^2)}{(1.6*10^{-19}C)(1.6*10^7m/s)}\\\\B=0.024T[/tex]
The direction of the magnetic field is found by using the right hand rule.
The electron moves upward (+^j). To obtain a magnetic forces points to the positive x-direction (+^i), the direction of the magnetic field has to be to the positive z-direction (^k). In fact, you have:
-^j X ^i = ^k
Where the minus sign of the ^j is because of the negative charge of the electron.
Then, the magnitude of the magnetic field is 0.024T and its direction is in the positive z-direction
Dolphins of the open ocean are classified as Type II Odontocetes (toothed whales). These animals use ultrasonic "clicks" with a frequency of about 55 kHz to navigate and find prey. You may want to review (Pages 465 - 467) . Part A Suppose a dolphin sends out a series of clicks that are reflected back from the bottom of the ocean 75 m below. How much time elapses before the dolphin hears the echoes of the clicks
Answer:
0.1 sec
Explanation:
frequency of the clicks produced = 55 kHz = 55000 Hz
depth of the bottom of ocean from the dolphin = 75 m
we know that the speed of sound in water is generally accepted to be ≅ 1480 m/s.
the total distance traveled by the sound from the dolphin, to the bottom of the ocean, and then back to the dolphin = 2 x 75 = 150 m
time elapsed will then be
time = distance traveled ÷ speed of sound
time = 150/1480 ≅0.1 sec
Explain how a refrigerator works to cool down warm objects that would otherwise be room temperature
Answer: evaporation
Explanation:
Refrigerators work by causing the refrigerant circulating inside them to change from a liquid into a gas. This process, called evaporation, cools the surrounding area and produces the desired effect.
Three particles are moving perpendicular to a uniform magnetic field and travel on circular paths (see the drawing). They have the same mass and speed. List the particles in order of their charge magnitude, largest to smallest.
Explanation:
Radius of a charged particle is given by
r=mv / Bq
= k/ q
where k = m v / B is a constant.
i.e. more is the magnitude of charge, less is the radius. (inversely proportional)
From the diagram r_3 > r_2 > r_1 (more the curvature, less is the radius)
( although drawing is not given i am assuming the above order, however, one can change the order as per the diagram. The concept used remains the same)
therefore, q_1 > q_2 > q_3 .
A force of 175 N is exerted on the pedal cylinder of an automatic hydraulic system. The pedal cylinder has a diameter of 0.475 cm. How much pressure is transmitted in the hydraulic system
Answer:
this is the required pressure transmitted in the hydraulic system.
g A mass of 2 kg is attached to a spring whose constant is 7 N/m. The mass is initially released from a point 4 m above the equilibrium position with a downward velocity of 10 m/s, and the subsequent motion takes place in a medium that imparts a damping force numerically equal to 10 times the instantaneous velocity. What is the differential equation for the mass-spring system.
Answer:
mass 20 times of an amazing and all its motion
Near the surface of Earth, an electric field points radially downward and has a magnitude of approximately 100 N/C. 1) What charge (magnitude and sign) would have to be placed on a penny that has a mass of 3.11 g to cause it to rise into the air with an upward acceleration of 0.190 m/s2
Answer:
Negative charge with a magnitude of 5.9*10^-6C
Explanation:
In order to calculate the required charge, for the penny is able to rise into the air with the given acceleration, you take into account the following formula for the electric force and also the Newton second law:
[tex]F_E=qE=ma[/tex] (1)
FE: electric force:
q: charge = ?
E: electric field = 100N/C
m: mass of the penny = 3.11g = 3.11*10^-3kg
a: acceleration of the charge = 0.190m/s^2
The positive charges experiences a force in the same direction of the electric field, and the negative charge, a force in a opposite direction.
The electric field points downward, then, the charge is negative (it is acceleration upwards).
Next, you solve the equation (1) for a, and replace the values of the other parameters:
[tex]q=\frac{ma}{E}=\frac{(3.11*10^{-3}kg)(0.190m/s^2)}{100N/C}=5.9*10^{-6}C[/tex]
The magnitude of the charge is 5.9*10^-6C and its sign is negative
when their center-to-center separation is 50 cm. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an electrostatic force of 0.2525 N. What were the initial charges on the spheres
Answer:
q1 = 7.6uC , -2.3 uC
q2 = 7.6uC , -2.3 uC
( q1 , q2 ) = ( 7.6 uC , -2.3 uC ) OR ( -2.3 uC , 7.6 uC )
Explanation:
Solution:-
- We have two stationary identical conducting spheres with initial charges ( q1 and q2 ). Such that the force of attraction between them was F = 0.6286 N.
- To model the electrostatic force ( F ) between two stationary charged objects we can apply the Coulomb's Law, which states:
[tex]F = k\frac{|q_1|.|q_2|}{r^2}[/tex]
Where,
k: The coulomb's constant = 8.99*10^9
- Coulomb's law assume the objects as point charges with separation or ( r ) from center to center.
- We can apply the assumption and approximate the spheres as point charges under the basis that charge is uniformly distributed over and inside the sphere.
- Therefore, the force of attraction between the spheres would be:
[tex]\frac{F}{k}*r^2 =| q_1|.|q_2| \\\\\frac{0.6286}{8.99*10^9}*(0.5)^2 = | q_1|.|q_2| \\\\ | q_1|.|q_2| = 1.74805 * 10^-^1^1[/tex] ... Eq 1
- Once, we connect the two spheres with a conducting wire the charges redistribute themselves until the charges on both sphere are equal ( q' ). This is the point when the re-distribution is complete ( current stops in the wire).
- We will apply the principle of conservation of charges. As charge is neither destroyed nor created. Therefore,
[tex]q' + q' = q_1 + q_2\\\\q' = \frac{q_1 + q_2}{2}[/tex]
- Once the conducting wire is connected. The spheres at the same distance of ( r = 0.5m) repel one another. We will again apply the Coulombs Law as follows for the force of repulsion (F = 0.2525 N ) as follows:
[tex]\frac{F}{k}*r^2 = (\frac{q_1 + q_2}{2})^2\\\\\sqrt{\frac{0.2525}{8.99*10^9}*0.5^2} = \frac{q_1 + q_2}{2}\\\\2.64985*10^-^6 = \frac{q_1 + q_2}{2}\\\\q_1 + q_2 = 5.29969*10^-^6[/tex] .. Eq2
- We have two equations with two unknowns. We can solve them simultaneously to solve for initial charges ( q1 and q2 ) as follows:
[tex]-\frac{1.74805*10^-^1^1}{q_2} + q_2 = 5.29969*10^-^6 \\\\q^2_2 - (5.29969*10^-^6)q_2 - 1.74805*10^-^1^1 = 0\\\\q_2 = 0.0000075998, -0.000002300123[/tex]
[tex]q_1 = -\frac{1.74805*10^-^1^1}{-0.0000075998} = -2.3001uC\\\\q_1 = \frac{1.74805*10^-^1^1}{0.000002300123} = 7.59982uC\\[/tex]
The energy band gap of GaAs is 1.4ev. calculate the optimum wavelength of the light for photovoltaic generation in a GaAs solar cell
Answer:
The wavelength is [tex]\lambda = 886 \ nm[/tex]
Explanation:
From the question we are told that
The energy band gap is [tex]E = 1.4 eV[/tex]
Generally the energy of a single photon of light emitted for an electron jump in a GaAS solar cell is mathematically represented as
[tex]E = \frac{hc}{\lambda }[/tex]
Where h is the Planck's constant with values
[tex]h = 4.1357 * 10^{-15} eV[/tex]
and c is the speed of light with values [tex]c = 3*10^{8} \ m/s[/tex]
So
[tex]\lambda = \frac{hc}{E}[/tex]
substituting values
[tex]\lambda = \frac{4.1357 *10^{-15} * 3.0 *10^{8}}{1.4}[/tex]
[tex]\lambda = 886 \ nm[/tex]
The gravity tractor, is a proposed spacecraft that will fly close to an asteroid whose trajectory threatens to impact the Earth. Due to the gravitational attraction between the two objects and a prolonged period of time over which it acts (several years), the asteroid's trajectory is changed slightly, thus hopefully diverting it from impacting the Earth. If the gravity tractor's weight on Earth is 20,000 lbs and it flies with a center of gravity 160ft from the surface of the asteroid, and the asteroid is homogenous pure iron with 1290 ft diameter spherical shape, detirmine the force of mutual attraction. Idealize the gravity tractor to be a particle.
Answer:
[tex]F_g=461lb_f[/tex]
Explanation:
First calculate the mass of the asteroid. To do so, you need to find the volume and know the density of iron.
If r = d/2 = 645ft, then:
[tex]V = \frac{4}{3} \pi r^3[/tex]
[tex]V = \frac{4}{3} \pi r^3\\V = 1.124\times10^{9}ft^3\delta_{iron}=m/V=491lb/ft^3m=V\times\delta=5.519\times10^{11}lb[/tex]
In order to find force, use Newton's universal law of gravitation:
[tex]F_g=G\frac{m_1m_2}{d^2}[/tex]
Where,
G= the gravitational constant:
[tex]G= 1.068846 \times10^{-9} ft^3 lb^{-1} s^{-2}[/tex]
[tex]F_g=461lb_f[/tex]
A horizontal 790-N merry-go-round of radius 1.60 m is started from rest by a constant horizontal force of 45 N applied tangentially to the merry-go-round. Find the kinetic energy of the merry-go-round after 4.0 s. (Assume it is a solid cylinder. Also assume the force is applied at the outside edge.)
Answer:
404.3 J
Explanation:
Given that
Weight of the merry go round = 790 N
Radius if the merry go round = 1.6 m
Horizontal force applied = 45 N
Time taken = 4 s
To find the mass of the merry go round, we divide the weight by acceleration due to gravity. Thus,
m = F/g
m = 790 / 9.8
m = 80.6 kg
We know that the moment of inertia is given as
I = ½mr², on substitution, we have
I = ½ * 80.6 * 1.6²
I = 103.17 kgm²
Torque = Force applied * radius, so
τ = 45 * 1.6
τ = 72 Nm
To get the angular acceleration, we have,
α = τ / I
α = 72 / 103.17
α = 0.70 rad/s²
Then, the angular velocity is
ω = α * t
ω = 0.7 * 4
ω = 2.8 rad/s
Finally, to get the Kinetic Energy, we have
K.E = ½ * Iω², on substituting, we get
K.E = ½ * 103.17 * 2.8²
K.E = 404.3 J
Therefore, the kinetic energy is 404.3 J
A mass of 0.450 kg rotates at constant speed with a period of 1.45 s at a radius R of 0.140 m in the apparatus used in this laboratory. What is the rotation period for a mass of 0.550 kg at the same radius
Answer:
1.603 s
Explanation:
Given that
Initial mass, = 0.45 kg
Initial period, = 1.45 s
Initial radius, = 0.14 m
Final mass, = 0.55 kg
Final period, = ?
Final radios, = 0.14 m
Since we are finding the rotation period of two masses of same radius, we can assume that the outward force is the same in both cases. This means that
m₁r₁ω₁² = m₂r₂ω2²
Where, ω = 2π/T, on substituting, we have
0.45 * 0.14 * (2π / 1.45)² = 0.550 * 0.14 * (2π / T₂)²
0.45 / 1.45² = 0.550 / T₂²
T₂² = 0.550 * 1.45² / 0.45
T₂² = 2.56972
T₂ = √2.56972
T₂ = 1.603 sec
The rotation period for a mass of 0.550 kg at the same radius is 1.603 s
Calculation of the radius:Since
Initial mass = 0.45 kg
Initial period = 1.45 s
Initial radius = 0.14 m
Final mass = 0.55 kg
Final radios = 0.14 m
Now the following formulas should be used.
m₁r₁ω₁² = m₂r₂ω2²
here ω = 2π/T
So,
0.45 * 0.14 * (2π / 1.45)² = 0.550 * 0.14 * (2π / T₂)²
0.45 / 1.45² = 0.550 / T₂²
T₂² = 0.550 * 1.45² / 0.45
T₂² = 2.56972
T₂ = √2.56972
T₂ = 1.603 sec
hence, The rotation period for a mass of 0.550 kg at the same radius is 1.603 s
learn more about mass here: https://brainly.com/question/15858212?referrer=searchResults
A place-kicker must kick a football from a point 36.0 m (about 40 yards) from the goal. Half the crowd hopes the ball will clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 21.6 m/s at an angle of 50.0° to the horizontal.
Required:
By how much does the ball clear or fall short (vertically) of clearing the crossbar?
Answer:
The difference is height is [tex]\Delta h =6.92 \ m[/tex]
Explanation:
From the question we are told that
The distance of ball from the goal is [tex]d = 36.0 \ m[/tex]
The height of the crossbar is [tex]h = 3.05 \ m[/tex]
The speed of the ball is [tex]v = 21.6 \ m/s[/tex]
The angle at which the ball was kicked is [tex]\theta = 50 ^o[/tex]
The height attained by the ball is mathematically represented as
[tex]H = v_v * t - \frac{1}{2} gt^2[/tex]
Where [tex]v_v[/tex] is the vertical component of velocity which is mathematically represented as
[tex]v_v = v * sin (\theta )[/tex]
substituting values
[tex]v_v = 21.6 * (sin (50 ))[/tex]
[tex]v_v = 16.55 \ m/s[/tex]
Now the time taken is evaluated as
[tex]t = \frac{d}{v * cos(\theta )}[/tex]
substituting value
[tex]t = \frac{36}{21.6 * cos(50 )}[/tex]
[tex]t = 2.593 \ s[/tex]
So
[tex]H = 16.55 * 2.593 - \frac{1}{2} * 9.8 * (2.593)^3[/tex]
[tex]H = 9.97 \ m[/tex]
The difference in height is mathematically evaluated as
[tex]\Delta h = H - h[/tex]
substituting value
[tex]\Delta h = 9.97 - 3.05[/tex]
[tex]\Delta h =6.92 \ m[/tex]
An object is dropped from a tower, 576576 ft above the ground. The object's height above ground t seconds after the fall is s(t)equals=576 minus 16 t squared576−16t2. Determine the velocity and acceleration of the object the moment it reaches the ground.
Answer: 192 ft/s
Explanation:
The initial height of the object is:
576ft above the ground.
The position equation is:
p(t) = -16*t^2 + 576
in the position equation, we only can see the therm of the initial height and the term of the acceleration (that is equal to the gravitational acceleration g = 32 ft/s^2 over 2)
So we have no initial velocity, this means that at the beginning we only have potential energy:
U = m*g*h
where m is the mass of the object, g = 32m/s^2 and h = 576 ft.
Now, as the object starts to fall down, the potential energy is transformed into kinetic energy, and when the object is about to hit the ground, all the potential energy has become kinetic energy.
The kinetic energy equation is:
K = (m/2)*v^2
where v is the velocity of the object, then the maximum kinetic energy (when the object reaches the ground) is equal to the initial potential energy:
m*g*h = (m/2)*v^2
now we can solve this for v.
v = √(2*g*h) = √(2*32ft/s^2*576ft) = 192 ft/s
In a double-slit interference experiment you are asked to use laser light of different wavelengths and determine the separation between adjacent maxima. You observe that this separation is greatest when you illuminate the double slit with In a double-slit interference experiment you are asked to use laser light of different wavelengths and determine the separation between adjacent maxima. You observe that this separation is greatest when you illuminate the double slit with:
1. yellow light.
2. red light.
3. blue light.
4. green light.
5. The separation is the same for all wavelengths.
Answer:
we see that the lights with the most extreme wavelength are blue and red
we see that the separation between the interference lines (y) increases linearly with the wavelength for which the phenomenon is best observed in the RED response 2
Explanation:
In Young's double-slit experiment, constructive interference is written by the equation
d sin θ = m λ
where you give the gap separation, lam the length of the donda used and m the order of interference
in many he uses trigonometry to express the synth in confusing the distances on a very distant screen
so θ = y / L
in this experiment the angles are generally very small, so
tan θ = sin θ / cos θ = sin θ
sint θ = y / L
let's replace
d y / L = mλ
y = (m L / d) λ
now let's examine the effect of changing the wavelength
1 yellow lam = 600 10⁻⁹ m
2) red lam = 750 10⁻⁹m
3) blue lam = 450 10⁻⁸ nm
4) green lam = 550 10⁻⁹ nm
we see that the lights with the most extreme wavelength are blue and red
we see that the separation between the interference lines (y) increases linearly with the wavelength for which the phenomenon is best observed in the RED response 2
An airplane is flying on a bearing of N 400 W at 500 mph. A strong jet-stream speed wind of 100 mph is blowing at S 500 W.
Required:
a. Find the vector representation of the plane and of the wind.
b. Find the resultant vector that represents the actual course of the plane.
c. Give the resulting speed and bearing of the plane.
Answer:
A. a (-321.393, 383.022) b (-76.40, -64.278)
B. (-397.991, 318.744)
C. a. resulting speed 509.9mph b. bearing of the plane = 51.6°
Explanation:
A disk of mass m and moment of inertia of I is spinning freely at 6.00 rad/s when a second identical disk, initially not spinning, is dropped onto it so that their axes coincide. In a short time, the two disks are corotating. What is the angular speed of the new system
Answer:
The angular speed of the new system is [tex]3\,\frac{rad}{s}[/tex].
Explanation:
Due to the absence of external forces between both disks, the Principle of Angular Momentum Conservation is observed. Since axes of rotation of each disk coincide with each other, the principle can be simplified into its scalar form. The magnitude of the Angular Momentum is equal to the product of the moment of inertial and angular speed. When both disks begin to rotate, moment of inertia is doubled and angular speed halved. That is:
[tex]I\cdot \omega_{o} = 2\cdot I \cdot \omega_{f}[/tex]
Where:
[tex]I[/tex] - Moment of inertia of a disk, measured in kilogram-square meter.
[tex]\omega_{o}[/tex] - Initial angular speed, measured in radians per second.
[tex]\omega_{f}[/tex] - Final angular speed, measured in radians per second.
This relationship is simplified and final angular speed can be determined in terms of initial angular speed:
[tex]\omega_{f} = \frac{1}{2}\cdot \omega_{o}[/tex]
Given that [tex]\omega_{o} = 6\,\frac{rad}{s}[/tex], the angular speed of the new system is:
[tex]\omega_{f} = \frac{1}{2}\cdot \left(6\,\frac{rad}{s} \right)[/tex]
[tex]\omega_{f} = 3\,\frac{rad}{s}[/tex]
The angular speed of the new system is [tex]3\,\frac{rad}{s}[/tex].
A bag is gently pushed off the top of a wall at A and swings in a vertical plane at the end of a rope of length l. Determine the angle θ for which the rope will break, knowing that it can withstand a maximum tension equal to twice the weight of the bag.
Answer:
Dear user,
Answer to your query is provided below
The angle for which the rope will break θ = 41.8°
Explanation:
Explanation of the same is attached in image
A bag is gently pushed off the top of a wall at A and swings in a vertical plane at the end of a rope of length l. The angle θ for which the rope will break, is 41.81°
What is tension?The tension is a kind of force which acts on linear objects when subjected to pull.
The maximum tension Tmax =2W
From the work energy principle,
T₂ = 1/2 mv²
Total energy before and after pushing off
0+mglsinθ = 1/2 mv²
v² = 2gflsinθ..............(1)
From the equilibrium of forces, we have
T= ma +mgsinθ = mv²/l +mgsinθ
2mg = mv²/l +mgsinθ
2g = v²/l +gsinθ
Substitute the value of v² ,we get the expression for θ
θ = sin⁻¹(2/3)
θ =41.81°
Hence, the angle θ for which the rope will break, is 41.81°
Learn more about tension.
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Your roommate is working on his bicycle and has the bike upside down. He spins the 68.0 cm -diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second. A. What is the pebble's speed? B. What is the pebble's acceleration?
Answer:
a. 6.41 m/s
b. 120.85 m/s^2
Explanation:
The computation is shown below:
a. Pebble speed is
As we know that according to the tangential speed,
[tex]v = r \times \omega[/tex]
[tex]= \frac{0.68}{2} \times 18.84[/tex]
= 6.41 m/s
The 18.84 come from
[tex]= 2 \times 3.14 \times 3[/tex]
= 18.84
b. The pebble acceleration is
[tex]a = \frac{v^2}{r}[/tex]
[tex]= \frac{6.41^2}{0.34}[/tex]
= 120.85 m/s^2
We simply applied the above formulas so that the pebble speed and the pebble acceleration could come and the same is to be considered
A motorcycle cover a distance of 1.8 km in 5 minute. calculate its average velocity?
Answer:
6 m/s[tex]solution \\ distance \: travelled = 1.8 \: km \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 1.8 \times 1000m \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 1800 \: m \\ time \: taken = 5 \: minute \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 5 \times 60 \: seconds \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 300 \: seconds \\ average \: velocity = \frac{distance \: travelled}{time \: taken} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1800}{ 300} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 6 \: {ms}^{ - 1} [/tex]
hope this helps..
Its average speed is (1,800 m) / (300 sec) = 6 m/s .
There's not enough information in the question to calculate the velocity with. We would need to know the straight-line distance and direction from the place he started from to the place he ended at.
A high-jumper clears the bar and has a downward velocity of - 5.00 m/s just before landing on an air mattress and bouncing up at 1.0 m/s. The mass of the high-jumper is 60.0 kg. What is the magnitude and direction of the impulse that the air mattress exerts on her
-- As she lands on the air mattress, her momentum is (m v)
Momentum = (60 kg) (5 m/s down) = 300 kg-m/s down
-- As she leaves it after the bounce,
Momentum = (60 kg) (1 m/s up) = 60 kg-m/s up
-- The impulse (change in momentum) is
Change = (60 kg-m/s up) - (300 kg-m/s down)
Magnitude of the change = 360 km-m/s
The direction of the change is up /\ .
The direction of a body or object's movement is defined by its velocity.In its basic form, speed is a scalar quantity.In essence, velocity is a vector quantity.It is the speed at which distance changes.It is the displacement change rate.
Solve the problem ?
Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path.In other words, velocity is a vector, whereas speed is a scalar value. We discuss the conceptive impulse in this puzzle.A high jumper weighing 60.0 kg sprints on the matrix at minus 6 meters per second in the downhill direction before falling to the mattress.her admirer.Speed drops to 0 meters/second.We must determine the impulse's size and presumed direction, which is upward and positive.The change in momentum is then equal to the impulse.The impulse therefore equals m times.the end velocity less the starting velocity.60.0kg times 0 minus minus 6 meters per second is the impulse, therefore.The impulse is 360 kilogram meters per second, or 360 newtons, to put it another way.The second is upward, and the direction.To learn more about magnitude refer
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Using only the trainiris dataset, for each feature, perform a simple search to find the cutoff that produces the highest accuracy, predicting virginica if greater than the cutoff and versicolor otherwise. Use the seqfunction over the range of each feature by intervals of 0.1 for this search. Which feature produces the highest accuracy?
A. Sepal. Length
B. Sepal. Width
C. Petal. Length
D. Petal. Width
Answer: C. Petal. Length
Explanation: Petal are unit of Corolla which are usually brightly colored. This part of a plant or flower, helps attracts insects to the plant for pollination. And also provide protection to the reproductive parts of the plant or flower.
Examples of flowers with petals is the Sun Flower, which coincidentally is the flower plant with most petals.
Question 9(Multiple Choice Worth 4 points) (05.03 LC) What most likely happens when water vapor cools? It changes into gas. It changes into liquid. Its temperature increases. Its temperature remains constant.
Answer:
it changes into liquid
Answer:
It changes in to liquids
Explanation:
This is because the water vapor cools down and condenses it attaches it self to dust forming water droplets. Those water droplets are water.