Your lab instructor has asked you to measure a spring constant using a dynamic method—letting it oscillate—rather than a static method of stretching it. You and your lab partner suspend the spring from a hook, hang different masses, m, on the lower end, and start them oscillating. One of you uses a meter stick to measure the amplitude, A, and the other uses a stopwatch to time 10 oscillations, t. Your data are as follows:Mass, m(g) Amplitude, A(cm) Time, T(s) 100 6.5 7.8150 5.5 9.8200 6.0 10.9250 3.5 12.4Use the best-fit line of an appropriate graph to determine the spring constant.
Answers
Answer:
k = 6,547 N / m
Explanation:
This laboratory experiment is a simple harmonic motion experiment, where the angular velocity of the oscillation is
w = √ (k / m)
angular velocity and rel period are related
w = 2π / T
substitution
T = 2π √(m / K)
in Experimental measurements give us the following data
m (g) A (cm) t (s) T (s)
100 6.5 7.8 0.78
150 5.5 9.8 0.98
200 6.0 10.9 1.09
250 3.5 12.4 1.24
we look for the period that is the time it takes to give a series of oscillations, the results are in the last column
T = t / 10
To find the spring constant we linearize the equation
T² = (4π²/K) m
therefore we see that if we make a graph of T² against the mass, we obtain a line, whose slope is
m ’= 4π² / k
where m’ is the slope
k = 4π² / m'
the equation of the line of the attached graph is
T² = 0.00603 m + 0.0183
therefore the slope
m ’= 0.00603 s²/g
we calculate
k = 4 π² / 0.00603
k = 6547 g / s²
we reduce the mass to the SI system
k = 6547 g / s² (1kg / 1000 g)
k = 6,547 kg / s² =
k = 6,547 N / m
let's reduce the uniqueness
[N / m] = [(kg m / s²) m] = [kg / s²]
The spring-mass system forms a linear graph between the time period and mass. And the value of spring-constant from the given data is 6.46 N/m.
Given data:
Mass suspended by spring is, [tex]m=100 \;\rm g =0.1 \;\rm kg[/tex].
Number of oscillations is, [tex]n =10\;\rm oscillations[/tex].
Time period of oscillation is, [tex]T=7.8 \;\rm s[/tex].
The expression for the angular frequency of spring-mass system is,
[tex]\omega =\drac \sqrt{\dfrac{k}{m} }[/tex] ......................................................(1)
Here, k is the spring constant.
Angular frequency is also expressed as,
[tex]\omega = 2 \pi f[/tex] .........................................................(2)
here, f is the linear frequency of spring-mass system.
And linear frequency is,
[tex]f=\dfrac{n}{T}\\f=\dfrac{10}{7.81}\\f=1.28 \;\rm cycles/sec[/tex]
Then substitute equation (2) in equation (1) as,
[tex]2 \pi f=\drac \sqrt{\dfrac{k}{m} }\\2 \pi \times 1.28=\drac \sqrt{\dfrac{k}{0.1} }\\(2 \pi \times 1.28)^{2}= \dfrac{k}{0.1}\\k = 6.46 \;\rm N/m[/tex]
Thus, the value of spring constant is 6.46 N/m. And the suitable graph for the spring-mass system is given below.
Learn more about spring-mass system here:
https://brainly.com/question/16077243?referrer=searchResults
Related Questions
first law of equilibrium
Answers
Answer:
For an object to be an equilibrium it must be experiencing no acceleration.
Explanation:
Hope it helps.
When you ride a bicycle, in what direction is the angular velocity of the wheels? When you ride a bicycle, in what direction is the angular velocity of the wheels? to your right forwards up to your left backwards g
Answers
When you ride a bicycle, the direction of the angular velocity of the wheels is; Option A; to your left
Complete question is;
When you ride a bicycle, in what direction is the angular velocity of the wheels? A) to your left B) to your right C) forwards D) backwards
While an object rotates, each particle will have a different velocity:
the 'Speed' component will vary with radius while the 'Direction' component will vary with angle.
Now, all of the velocity vectors are aligned in the same plane and as such we can be solve this by choosing a single vector normal to ALL of the possible velocity vectors of the rotating object in that plane.
The convention that will be used to answer this question is known as "Right-hand rule". The angular velocity vector points along the wheel's axle.
For instance, if you Imagine wrapping your right hand around the axle so that your fingers point in the direction of rotation, with your thumb sticking out. You will notice that your thumb points to the left.
Thus;
In conclusion, by right-hand rule, a wheel rotating on a forward - moving bicycle has an angular velocity vector pointing to the rider's left.
Read more at; https://brainly.com/question/25155073
A wire of length L is made up of two sections of two different materials connected in series. The first section of length L1 = 17.7 m is made of steel and the second section of length L2 = 28.5 m is made of iron. Both wires have the same radius of 5.30 ✕ 10−4 m. If the compound wire is subjected to a tension of 148 N, determine the time taken for a transverse pulse to move from one end of the wire to the other. The density of steel is 7.75 ✕ 103 kg/m3 and the density of iron is 7.86 ✕ 103 kg/m3.
Answers
Answer:
Explanation:
velocity of wave in a tense wire is given by the expression
[tex]v= \sqrt{\frac{T}{m} }[/tex]
v is velocity . T is tension and m is mass per unit length .
for steel wire
m = π r² ρ where r is radius and ρ is density
= 3.14 x (5.3 x 10⁻⁴)²x7.75 x 10³
= 683.57 x 10⁻⁵ kg/m
v = [tex]\sqrt{\frac{148}{683.57\times 10^{-5}} }[/tex]
= 1.47 x 10² m /s
= 147 m /s
for iron wire
m = π r² ρ where r is radius and ρ is density
= 3.14 x (5.3 x 10⁻⁴)²x7.86 x 10³
= 693.27 x 10⁻⁵ kg/m
[tex]v = \sqrt{\frac{148}{693.27\times 10^{-5}} }[/tex]
= 146 m /s
Time taken to move from one end to another
= 17.7 / 147 + 28.5 / 146
= .12 + .195
= .315 s .
Two hockey pucks, labeled A and B, are initially at rest on a smooth ice surface and are separated by a distance of 18.0 m . Simultaneously, each puck is given a quick push, and they begin to slide directly toward each other. Puck A moves with a speed of 3.90 m/s , and puck B moves with a speed of 4.30 m/s . What is the distance covered by puck A by the time the two pucks collide
Answers
Answer:
The distance covered by puck A before collision is [tex]z = 8.56 \ m[/tex]
Explanation:
From the question we are told that
The label on the two hockey pucks is A and B
The distance between the two hockey pucks is D 18.0 m
The speed of puck A is [tex]v_A = 3.90 \ m/s[/tex]
The speed of puck B is [tex]v_B = 4.30 \ m/s[/tex]
The distance covered by puck A is mathematically represented as
[tex]z = v_A * t[/tex]
=> [tex]t = \frac{z}{v_A}[/tex]
The distance covered by puck B is mathematically represented as
[tex]18 - z = v_B * t[/tex]
=> [tex]t = \frac{18 - z}{v_B}[/tex]
Since the time take before collision is the same
[tex]\frac{18 - z}{V_B} = \frac{z}{v_A}[/tex]
substituting values
[tex]\frac{18 -z }{4.3} = \frac{z}{3.90}[/tex]
=> [tex]70.2 - 3.90 z = 4.3 z[/tex]
=> [tex]z = 8.56 \ m[/tex]
A man pushes a 25kg box up an incline 2.0m by applying a steady force of 95N parallel to the incline. The box moves up the incline at a steady speed. The incline makes an angle 15 degrees to the horizontal
a) What is the force of friction between the incline and the box
b)If the box is released at the top of the incline, what will its speed be at the bottom
Answers
Answer:
a) Ff = 19.29 N
b) v = 3.00 m/s
Explanation:
a) To calculate the friction force you use the second Newton Law in the incline plane, with an acceleration equal to zero, because the motion of the box has a constant velocity:
[tex]F-F_f-Wsin(\theta)=0\\\\[/tex] (1)
F: force applied by the man = 95N
Ff: friction force
W: weight of the box = Mg = (25kg)(9.8m/s^2) = 245N
θ: degree of the inclined plane = 15°
You solve the equation (1) for Ff and you replace the values of all variables in the equation (1):
[tex]F_f=-Wsin(\theta)+F\\\\F_f=-(245N)sin18\°+95N=19.29N[/tex]
b) To fins the velocity of the box at the bottom you use the following formula:
[tex]W_N=\Delta K[/tex] (2)
That is, the net work over the box is equal to the change in the kinetic energy of the box.
The net work is:
[tex]W_N=Mgsin(18\°)d-Ffd[/tex]
d: distance traveled by the box = 2.0m
[tex]W_N=245sin18\°(2.0m)N-19.29(2.0m)N=112.83J[/tex]
You use this value of the net work to find the final velocity of the box, by using the equation (2):
[tex]112.8J=\frac{1}{2}m[v^2-v_o^2]\\\\v_o=0m/s\\\\v=\sqrt{\frac{2(112.8J)}{m}}=\sqrt{\frac{225.67J}{25kg}}=3.00\frac{m}{s}[/tex]
The speed of the box, at the bottom of the incline plane is 3.00 m/s
A Michelson interferometer operating at a 400 nm wavelength has a 3.95-cm-long glass cell in one arm. To begin, the air is pumped out of the cell and mirror M2 is adjusted to produce a bright spot at the center of the interference pattern. Then a valve is opened and air is slowly admitted into the cell. The index of refraction of air at 1.00 atmatm pressure is 1.00028.
Required:
How many bright-dark-bright fringe shifts are observed as the cell fills with air?
Answers
Answer:
55.3
Explanation:
The computation of the number of bright-dark-bright fringe shifts observed is shown below:
[tex]\triangle m = \frac{2d}{\lambda} (n - 1)[/tex]
where
d = [tex]3.95 \times 10^{-2}m[/tex]
[tex]\lambda = 400 \times 10^{-9}m[/tex]
n = 1.00028
Now placing these values to the above formula
So, the number of bright-dark-bright fringe shifts observed is
[tex]= \frac{2 \times3.95 \times 10^{-2}m}{400 \times 10^{-9}m} (1.00028 - 1)[/tex]
= 55.3
We simply applied the above formula so that the number of bright dark bright fringe shifts could come
Two cars start moving from the same point. One travels south at 60 miyh and the other travels west at 25 miyh. At what rate is the distance between the cars increasing two hours later?
Answers
Answer:
65 m/h
Explanation:
Let the distance of the car moving south be y.
Let the distance of the car moving west be x.
Let the distance between the two cars be a.
These three distances can be represented as a right angled triangle. So we can say:
[tex]a^2 = x^2 + y ^2[/tex]
Let us differentiate with respect to time, since the distances are changing with respect to time:
[tex]2a\frac{da}{dt} = 2x\frac{dx}{dt} + 2y\frac{dy}{dt} \\\\=>a\frac{da}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}[/tex]__________(1)
da/dt = rate of change of distance between two cars
The speed of the car moving south (dy/dt) is 60 m/h and the speed of the car moving west (dx/dt) is 25 m/h.
Therefore:
dy/dt = 60 m/h and dx/dt = 25 m/h
After two hours, the distance of the two cars will be:
y = 2 * 60 = 120 miles
x = 2 * 25 = 50 miles
Therefore:
[tex]a^2 = 50^2 + 120^2\\\\a^2 = 2500 + 14400 = 16900\\\\a = \sqrt{16900}\\ \\a = 130 miles[/tex]
From (1):
130(da/dt) = 50(25) + 120(60)
130(da/dt) = 1250 + 7200 = 8450
da/dt = 8450/130 = 65 m/h
Therefore, after two hours, the distance between the two cars is changing at a rate of 65 m/h.
Find the equivalent resistance from the indicated terminal pair of the networks in the attached doc
Answers
Answer:
a) R = 2.5 Ω, b) R = 1 Ω, c) R = 2R / 3 Ω
Explanation:
The resistance configuration can be in series or in parallel, for each one the equivalent resistance can be calculated
series, the equivalent resistance is the sum of the resistances
parallel, the inverse of the equivalent resistance is the inverse of the sum of the resistances
let's apply these principles to each case
case a)
equivalent series resistance
R₁ = 1 +4 = 5 ohm
R₂ = 2 +3 = 5 ohn
these two are in parallel
1 / R = 1/5 +1/5
1 / R = 2/5
R = 2.5 Ω
case B
we solve the parallel
1 / R₁ = ½ + ½ = 1
R₁ = 1 Ω
we solve the resistors in series
R₂ = 1 + 1
R₂ = 2 Ω
finally we solve the last parallel
1 / R = ½ +1/2 = 1
R = 1 Ω
case C
we solve house resistance pair in series
R₁ = R + 2R = 3R
we go to the next mesh
R₂ = R + 2R = 3R
R₃ = R + 2R = 3R
last mesh
R₄ = R + R = 2R
now we solve the parallel of this equivalent resistance
1 / R = 1 / R₁ + 1 / R₂ + 1 / R₃ + 1 / R₄
1 / R = 1 / 3R + 1 / 3R + 1 / 3R + 1 / 2R
1 / R = 3 / 3R + 1 / 2R = 1 / R + 1 / 2R
1 / R = 3 / 2R
R = 2R / 3 Ω
Nowdothesameproblemwiththepivotatthe toes. A Ballet dancer puts all her weight on the toes of one foot. If her mass is 60 kg, what is the force that has to be exerted by her leg muscle to hold that pose? Assume the pivot is at the toes.
Answers
Answer:
The force is [tex]F = 2400 \ N[/tex]
Explanation:
The diagram for this question is shown on the first uploaded image
From the question we are told that
The mass of the dancer is [tex]m_d = 60 \ kg[/tex]
From the diagram the
The first distance is [tex]l_1 = 20 \ cm[/tex]
The second distance is [tex]l_2 = 5 \ cm[/tex]
At equilibrium the moment about the center of the dancers feet is mathematically represented as
[tex]F * l_2 - (mg* l_1)[/tex]
Where [tex]g= 10 \ m/s^2[/tex]
substituting values
[tex]F * 5 - (60* 9.8 * 20)[/tex]
=> [tex]F = \frac{60 * 10 * 30}{5}[/tex]
=> [tex]F = 2400 \ N[/tex]
A space ship traveling east flies directly over the head of an inertial observer who is at rest on the earth's surface. The speed of the space ship can be found from this relationship: . The navigator's on-board instruments indicate that the length of the space ship is 20 m. If the length of the ship is measured by the inertial earth-bound observer, what value will be obtained
Answers
Answer:
10 metres
Explanation:
So, we are given the following data or parameters or information which is going to assist us in solving this particular problem or Question efficiently.
=> The speed of the space ship can be found from this relationship: ✓(1 - [v^2/c^2] ) = 1/2.
=> The length of the space ship = 20 m.
=> Assumption = '' If the length of the ship is measured by the inertial earth-bound observer".
Thus, from the speed of the space ship can be found from this relationship we can determine the value;
✓(1 - [v^2/c^2] ) = 1/2.
V = 20 × 1/2 = 10 metres.
Note that we use the contraction formula to solve for V.
A rocket blasts off vertically from rest on the launch pad with an upward acceleration of 2.90 m/s2 . At 20.0s after blastoff, the engines suddenly fail, which means that the force they produce instantly stops.
(A) How high above the launch pad will the rocket eventually go?
(B) Find the rocket's velocity at its highest point.
(C) Find the magnitude of the rocket's acceleration at its highest point.
(D) Find the direction of the rocket's acceleration at its highest point.
(E) How long after it was launched will the rocket fall back to the launch pad?
(F) How fast will it be moving when it does so?
Answers
Answer:
A) 580m
B) 0 m/s
C) 9.8m/s^2
D) downward
E) 10.87s
F) 106.62 m/s
Explanation:
A) The distance traveled by the rocket is calculated by using the following expression:
[tex]y=\frac{1}{2}at^2[/tex]
a: acceleration of the rocket = 2.90 m/s^2
t: time of the flight = 20.0 s
[tex]y=\frac{1}{2}(2.90\frac{m}{s^2})(20.0s)^2=580m[/tex]
B) In the highest point the rocket has a velocity with magnitude zero v = 0m/s because there the rocket stops.
C) The engines of the rocket suddenly fails in the highest point. There, the acceleration of the rocket is due to the gravitational force, that is 9.8 m/s^2
D) The acceleration points downward
E) The time the rocket takes to return to the ground is given by:
[tex]t=\sqrt{\frac{2y}{g}}=\sqrt{\frac{2(580m)}{9.8m/s^2}}=10.87s[/tex]
10.87 seconds
F) The velocity just before the rocket arrives to the ground is:
[tex]v=\sqrt{2gy}=\sqrt{2(9.8m/s ^2)(580m)}=106.62\frac{m}{s}[/tex]
4) (7 pts.) A water molecule is centered at the origin of a coordinate system with its dipole moment vector aligned with the x axis. The magnitude of a water molecule dipole is 6.16 × 10−30 C·m. What is the magnitude of the electric field at x = 3.00 × 10−9 m?
Answers
Answer:
[tex]E=3.69*10^{-11}\frac{V}{m}[/tex]
Explanation:
To solve this problem you use the following formula, for the calculation of the electric field along the axis of the dipole.
[tex]E=\frac{p}{2\pi \epsilon_ox^3}[/tex] (1)
p: dipole moment = 6.16*10^-30 Cm
x: distance to the center of mass of the dipole = 3.00*10^-9m
eo: dielectric permittivity of vacuum = 8.85*10^-12 C^2/Nm^2
You replace the values of the variables in the equation (1):
[tex]E=\frac{6.16*10^{-30}Cm}{2\pi(8.85*10^{-12}C^2/Nm^2)(3.00*10^{-9}m)^3}\\\\E=3.69*10^{-11}\frac{V}{m}[/tex]
I need someone that knows physics. I have a test in 10 hrs and Im not good at it. Can anyone help me?
Answers
What grade of physics?
Answer:
I can help! What level of physics is it and what are your main topics?
The equation for distance is d= st. if a car has a speed of 20 m/s how long will it take to go 155m
Answers
Answer:
It will take 7.75 seconds for the car to go 155m
Explanation:
From the question, we can understand that the distance covered by the moving car is got by a product of its speed and the time it travels.
i.e distance = speed X time.
However, in this case, we have the distance travelled and the speed of the car, and we are looking for the time of travel
TO solve this, we will simply make the travel time the subject of the formula in the equation above.
i.e time = distance / speed
time = 155/20= 7.75 seconds.
Hence, it will take 7.75 seconds for the car to go 155m
What is the frequency if 140 waves pass in 2 minutes?
Answers
Answer:
1.16 Hz
Explanation:
frequency, basically, is the number of wave on 1 second
so, in math we write like this
f = n/t
n = number of waves
t = time to do that (in sec)
f = 140/120 = 7/6 Hz
f = 1.16 Hz
Leah is moving in a spaceship at a constant velocity away from a group of stars. Which one of the following statements indicates a method by which she can determine her absolute velocity through space?
A) She can measure her increases in mass.
B) She can measure the contraction of her ship.
C) She can measure the vibration frequency of a quartz crystal.
D) She can measure the changes in total energy of her ship.
E) She can perform no measurement to determine this quantity.
Answers
Answer:
E) She can perform no measurement to determine this quantity.
Explanation:
A spacecraft is a machine used to fly in outer space.
According to Isaac Newton's third law of motion, every action produces an equal and opposite reaction. When fuel is shoot out of one end of the rocket, the rocket moves forward for which no air is required.
As Leah is moving in a spaceship at a constant velocity away from a group of stars, she cannot measure to determine this quantity.
A 20 g "bouncy ball" is dropped from a height of 1.8 m. It rebounds from the ground with 80% of the speed it had just before it hit the ground. Assume that during the bounce the ground causes a constant force on the ball for 75 ms. What is the force applied to the ball by the ground in N?
The following are not correct: 0.513 N, 0.317 N, 0.121 N. Please show your work so I can understand!
Answers
Answer:
F = 0.314 N
Explanation:
In order to calculate the applied force to the ball by the ground, you first calculate the speed of the ball just before it hits the ground. You use the following formula:
[tex]v^2=v_o^2+2gy[/tex] (1)
y: height from the ball starts its motion = 1.8 m
vo: initial velocity = 0 m/s
g: gravitational acceleration = 9.8 m/s^2
v: final velocity of the ball = ?
You replace the values of the parameters in the equation (1):
[tex]v=\sqrt{2gy}=\sqrt{2(9.8m/s^2)(1.8m)}=5.93\frac{m}{s}[/tex]
Next, you take into account that the force exerted by the ground on the ball is given by the change, on time, of the linear momentum of the ball, that is:
[tex]F=\frac{\Delta p}{\Delta t}=m\frac{\Delta v}{\Delta t}=m\frac{v_2-v_1}{\Delta t}[/tex] (2)
m: mass of the ball = 20g = 20*10^-3 kg
v1: velocity of the ball just before it hits the ground = 5.93m/s
v2: velocity of the ball after it impacts the ground (80% of v1):
0.8(5.93m/s) = 4.75 m/s
Δt: time interval o which the ground applies the force on the ball = 75*10^-3 s
You replace the values of the parameters in the equation (2):
[tex]F=(20*10^{-3}kg)\frac{4.75m/s-5.93m/s}{75*10^{-3}s}=-0.314N[/tex]
The minus sign means that the force is applied against the initial direction of the motion of the ball.
The applied force by the ground on the bouncy ball is 0.314 N
A spherical balloon has a radius of 7.40 m and is filled with helium. Part A How large a cargo can it lift, assuming that the skin and structure of the balloon have a mass of 990 kg ? Neglect the buoyant force on the cargo volume itself. Assume gases are at 0∘C and 1 atm pressure (rhoair = 1.29 kg/m3, rhohelium = 0.179 kg/m3).
Answers
Answer:
The mass of the cargo is [tex]M = 188.43 \ kg[/tex]
Explanation:
From the question we are told that
The radius of the spherical balloon is [tex]r = 7.40 \ m[/tex]
The mass of the balloon is [tex]m = 990\ kg[/tex]
The volume of the spherical balloon is mathematically represented as
[tex]V = \frac{4}{3} * \pi r^3[/tex]
substituting values
[tex]V = \frac{4}{3} * 3.142 *(7.40)^3[/tex]
[tex]V = 1697.6 \ m^3[/tex]
The total mass the balloon can lift is mathematically represented as
[tex]m = V (\rho_h - \rho_a)[/tex]
where [tex]\rho_h[/tex] is the density of helium with a value of
[tex]\rho_h = 0.179 \ kg /m^3[/tex]
and [tex]\rho_a[/tex] is the density of air with a value of
[tex]\rho_ a = 1.29 \ kg / m^3[/tex]
substituting values
[tex]m = 1697.6 ( 1.29 - 0.179)[/tex]
[tex]m = 1886.0 \ kg[/tex]
Now the mass of the cargo is mathematically evaluated as
[tex]M = 1886.0 - 1697.6[/tex]
[tex]M = 188.43 \ kg[/tex]
A jeep starts from rest with a constant acceleration of 4m/s2.At the same time a car travels with a constant speed of 36km/h overtake and passes the jeep how far beyond the starting point will the jeep overtakes the car?
Answers
Answer:
25m
Explanation:
Let's assume the Jeep attains a velocity of 36km/h ; a constant speed same with that of the car.
While the Jeep is accelerating to that speed, the car with that speed passes it.
Now we can calculate the time taken for the Jeep to attain the velocity of 36km/h on her constant acceleration.
This time is t = v/a; from Newton's Law of Motion:
a = V-U / t ; a-acceleration
V is final velocity = 36km/h
U is initial velocity 0 since the body starts from rest.
Hence t = 36000/3600 ÷ 4 = 2.5s
Note conversting from km/h to m/s we multiply by 1000/3600.
But the distance covered by the car while the Jeep just accelerates is
S = U × t = 10× 2.5 = 25m.
Note From Newton's law of Motion, distance for constant speed is defined as: U × t
Hence the Car would be 25m off the starting point just as the Jeep accelerates. It would overtake the Jeep when it just covers 25m from the Jeep starting point.
Car A is traveling at twice the speed of car B. They both hit the brakes at the same time and decrease their velocities at the same rate. If car B travels a distance D before stopping, how far does car A travel before stopping?
A) 4D
B) 2D
C) D
D) D/2
E) D/4
Answers
Answer:
A) 4D
Explanation:
The distance traveled by the cars before coming to rest can be determined by 3rd equation of motion:
2as = Vf² - Vi²
s = (Vf² - Vi²)/2a
where,
s = distance traveled
Vf = Final Speed = 0 m/s
Vi = Initial Speed
a = deceleration rate
First, we consider Car B and we assign a subscript 2 for it:
Vf₂ = 0 m/s (As, car finally stops)
s₂ = D
a₂ = - a (due to deceleration)
D = (0² - Vi₂²) /(-2a)
D = Vi₂²/2a -------- equation (1)
Now, we consider Car A and we assign a subscript 1 for it:
Vf₁ = 0 m/s (As, car finally stops)
s₁ = ?
a₁ = - a (due to deceleration)
Vi₁ = 2 Vi₂ (Since, car A was initially traveling at twice speed of car B)
s₁ = (0² - Vi₁²) /(-2a)
s₁ = (2Vi₂)²/2a
s₁ = 4 (Vi₂²/2a)
using equation (1), we get:
s₁ = 4D
Therefore, the correct option is:
A) 4D
A roller coaster car may be approximated by a block of mass m. Thecar, which starts from rest, is released at a height h above the ground and slides along a frictionless track. The car encounters a loop of radius R. Assume that the initial height h is great enough so that the car never losses contact with the track.
Required:
a. Find an expression for the kinetic energy of the car at the top of the loop. Express the kinetic energy in terms of m, g, h, and R.
b. Find the minimum initial height h at which the car can be released that still allows the car to stay in contact with the track at the top of the loop.
Answers
Answer:
Explanation:
At height h , potential energy of coaster car having mass m = mgh .
The car will lose potential energy and gain kinetic energy.
height lost by car when it is at the top of loop of radius R
= h - 2R
potential energy lost = mg ( h - 2R )
kinetic energy gained = mg ( h - 2R )
kinetic energy = 0 + mg ( h - 2R )
= mg ( h - 2R )
b )
For the car to remain in contact with the track , if v be the minimum velocity
centripetal force at top = mg
m v² / R = mg
v² = gR
kinetic energy = 1/2 mv²
= 1/2 m x gR
= mgR /
If h be the minimum height that can give this kinetic energy
mg ( h - 2R ) = mgR / 2
h - 2R = R / 2
h = 2.5 R .
You are at a stop light in your car, stuck behind a red light. Just before the light is supposed to change, a fire engine comes zooming up towards you traveling at a horrendous 85.0 km/h. If the siren has a rated frequency 665 Hz, what frequency of the sound do you hear
Answers
Answer:
The frequency of the sound you will hear is 713.85 Hz
Explanation:
Given;
speed of your car, [tex]v_s[/tex] = 85.0 km/h
frequency of the siren, f = 665 Hz
Speed of sound in air, v = 345 m/s
The frequency of the sound you hear, can be calculated as;
[tex]f' = f(\frac{v}{v-v_s})[/tex]
Convert the speed of the car to m/s
[tex]85 \ km/h =\frac{85 \ km}{h} (\frac{1000\ m}{1 \ km})(\frac{1 \ h}{3600 \ s} ) = 23.61 \ m/s[/tex]
[tex]f' = f(\frac{v}{v-v_s} )\\\\f' = 665(\frac{345}{345-23.61} )\\\\f' = 665 (1.07346)\\\\f' = 713.85 \ Hz[/tex]
Therefore, the frequency of the sound you will hear is 713.85 Hz
Near the top of the Citigroup Center building in New York City, there is an object with mass of 4.8 x 105 kg on springs that have adjustable force constants. Its function is to dampen wind-driven oscillations of the building by oscillating at the same frequency as the building is being driven-the driving force is transferred to the object, which oscillates instead of the entire building X 50%
Part (a) What effective force constant, in N/m, should the springs have to make them oscillate with a period of 1.2 s? k = 9.5 * 106 9500000 X Attempts Remain 50%
Part (b) What energy, in joules, is stored in the springs for a 1.6 m displacement from equilibrium?
Answers
Answer:
The force constant is [tex]k =1.316 *10^{7} \ N/m[/tex]
The energy stored in the spring is [tex]E = 1.68 *10^{7} \ J[/tex]
Explanation:
From the question we are told that
The mass of the object is [tex]M = 4.8*10^{5} \ kg[/tex]
The period is [tex]T = 1.2 \ s[/tex]
The period of the spring oscillation is mathematically represented as
[tex]T =2 \pi \sqrt{ \frac{M}{k}}[/tex]
where k is the force constant
So making k the subject
[tex]k = \frac{4 \pi ^2 M }{T^2}[/tex]
substituting values
[tex]k = \frac{4 (3.142) ^2 (4.8 *10^{5}) }{(1.2)^2}[/tex]
[tex]k =1.316 *10^{7} \ N/m[/tex]
The energy stored in the spring is mathematically represented as
[tex]E = \frac{1}{2} k x^2[/tex]
Where x is the spring displacement which is given as
[tex]x = 1.6 \ m[/tex]
substituting values
[tex]E = \frac{1}{2} (1.316 *10^{7}) (1.6)^2[/tex]
[tex]E = 1.68 *10^{7} \ J[/tex]
man stands on a platform that is rotating (without friction) with an angular speed of 1.2 rev/s; his arms are outstretched and he holds a brick in each hand.The rotational inertia of the system consisting of the man, bricks, and platform about the central vertical axis of the platform is 6.0 k g times m squared. If by moving the bricks the man decreases the rotational inertia of the system to 2.0 k g times m squared, what is the resulting angular speed of the platform in rad/s? Express to 3 sig figs.
Answers
Answer:
w₂ = 22.6 rad/s
Explanation:
This exercise the system is formed by platform, man and bricks; For this system, when the bricks are released, the forces are internal, so the kinetic moment is conserved.
Let's write the moment two moments
initial instant. Before releasing bricks
L₀ = I₁ w₁
final moment. After releasing the bricks
[tex]L_{f}[/tex] = I₂W₂
L₀ = L_{f}
I₁ w₁ = I₂ w₂
w₂ = I₁ / I₂ w₁
let's reduce the data to the SI system
w₁ = 1.2 rev / s (2π rad / 1rev) = 7.54 rad / s
let's calculate
w₂ = 6.0/2.0 7.54
w₂ = 22.6 rad/s
A layer of ethyl alcohol (n = 1.361) is on top of water (n = 1.333). To the nearest degree, at what angle relative to the normal to the interface of the two liquids is light totally reflected?
a. 78 degree
b. 88 degree
c. 68 degree
d. 49 degree
e. the critical angle isundefined
Answers
Answer:
a. 78 degree
Explanation:
According to Snell's Law, we have:
(ni)(Sin θi) = (nr)(Sin θr)
where,
ni = Refractive index of medium on which light is incident
ni = Refractive index of ethyl alcohol = 1.361
nr = Refractive index of medium from which light is refracted
nr = Refractive index of ethyl alcohol = 1.333
θi = Angle of Incidence
θr = Angle of refraction
So, the Angle of Incidence is know as the Critical Angle (θc), when the refracted angle becomes 90°. This is the case of total internal reflection. That is:
θi = θc
when, θr = 90°
Therefore, Snell's Law becomes:
(1.361)(Sin θc) = (1.333)(Sin 90°)
Sin θc = 1.333/1.361
θc = Sin⁻¹ (0.9794)
θc = 78.35° = 78° (Approximately)
Therefore, correct answer will be:
a. 78 degree
The angle relative to the normal interface of the two liquids at which the light is totally reflected is 78 degrees.
From the information given;
the refractive index of the ethyl alcohol [tex]\mathbf{n_1= 1.361}[/tex]the refractive index of the water [tex]\mathbf{n_2 = 1.333}[/tex] the angle of incidence is the critical angle [tex]\theta_i = \theta_c[/tex] the angle of refraction [tex]\theta _r = 90^0[/tex]According to Snell's Law of refraction;
[tex]\mathbf{n_1 sin \theta _c = n_2 sin \theta_r}[/tex]
[tex]\mathbf{1.361 \times sin \theta _c = 1.333 \times sin 90}[/tex]
[tex]\mathbf{ sin \theta _c =\dfrac{ 1.333 \times sin 90}{1.361}}[/tex]
[tex]\mathbf{ sin \theta _c =\dfrac{ 1.333 \times 1}{1.361}}[/tex]
[tex]\mathbf{ \theta _c = sin^{-1} (0.9794)}[/tex]
[tex]\mathbf{ \theta _c =78.35^0}[/tex]
[tex]\mathbf{ \theta _c \simeq78^0}[/tex]
Therefore, we can conclude that the angle relative to the normal interface of the two liquids at which the light is totally reflected is 78 degrees.
Learn more about Snell Law of refraction here:
https://brainly.com/question/14029329?referrer=searchResults
Plaskett's binary system consists of two stars that revolve In a circular orbit about a center of mass midway between them. This statement implies that the masses of the two stars are equal . Assume the orbital speed of each star is |v | = 240 km/s and the orbital period of each is 12.5 days. Find the mass M of each star. (For comparison, the mass of our Sun is 1.99 times 1030 kg Your answer cannot be understood or graded.
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
The mass is [tex]M =1.43 *10^{32} \ kg[/tex]
Explanation:
From the question we are told that
The mass of the stars are [tex]m_1 = m_2 =M[/tex]
The orbital speed of each star is [tex]v_s = 240 \ km/s =240000 \ m/s[/tex]
The orbital period is [tex]T = 12.5 \ days = 12.5 * 2 4 * 60 *60 = 1080000\ s[/tex]
The centripetal force acting on these stars is mathematically represented as
[tex]F_c = \frac{Mv^2}{r}[/tex]
The gravitational force acting on these stars is mathematically represented as
[tex]F_g = \frac{GM^2 }{d^2}[/tex]
So [tex]F_c = F_g[/tex]
=> [tex]\frac{mv^2}{r} = \frac{Gm_1 * m_2 }{d^2}[/tex]
=> [tex]\frac{v^2}{r} = \frac{GM}{(2r)^2}[/tex]
=> [tex]\frac{v^2}{r} = \frac{GM}{4r^2}[/tex]
=> [tex]M = \frac{v^2*4r}{G}[/tex]
The distance traveled by each sun in one cycle is mathematically represented as
[tex]D = v * T[/tex]
[tex]D = 240000 * 1080000[/tex]
[tex]D = 2.592*10^{11} \ m[/tex]
Now this can also be represented as
[tex]D = 2 \pi r[/tex]
Therefore
[tex]2 \pi r= 2.592*10^{11} \ m[/tex]
=> [tex]r= \frac{2.592*10^{11}}{2 \pi }[/tex]
=> [tex]r= 4.124 *10^{10} \ m[/tex]
So
[tex]M = \frac{v^2*4r}{G}[/tex]
=> [tex]M = \frac{(240000)^2*4*(4.124*10^{10})}{6.67*10^{-11}}[/tex]
=> [tex]M =1.43 *10^{32} \ kg[/tex]
A merry-go-round is shaped like a uniform disk and has moment of inertia of 50,000 kg m 2 . It is rotating so that it has an angular momentum of 10,000 (kg m 2 radians/s) and its outer edge has a speed of 2 m/s. What is its radius, in m
Answers
Answer:
r = 20 m
Explanation:
The formula for the angular momentum of a rotating body is given as:
L = mvr
where,
L = Angular Momentum = 10000 kgm²/s
m = mass
v = speed = 2 m/s
r = radius of merry-go-round
Therefore,
10000 kg.m²/s = mr(2 m/s)
m r = (10000 kg.m²/s)/(2 m/s)
m r = 5000 kg.m ------------- equation 1
Now, the moment of inertia of a solid uniform disc about its axis through its center is given as:
I = (1/2) m r²
where,
I = moment of inertia = 50000 kg.m²
Therefore,
50000 kg.m² = (1/2)(m r)(r)
using equation 1, we get:
50000 kg.m² = (1/2)(5000 kg.m)(r)
(50000 kg.m²)/(2500 kg.m) = r
r = 20 m
A projectile is launched on the Earth with a certain initial velocity and moves without air resistance. Another projectile is launched with the same initial velocity on the Moon, where the acceleration due to gravity is one-sixth as large. How does the maximum altitude of the projectile on the Moon compare with that of the projectile on the Earth?
Answers
With smaller gravitational forces and therefor less vertical acceleration, the projectile launched on the moon ... with the same initial speed and direction ...
-- climbs faster,
-- spends more time climbing,
-- reaches a higher peak,
-- falls slower,
-- spends more time falling, and
-- covers more horizontal distance
than the projectile launched on the Earth.
This is not because of air resistance. It would be true even if there were no air resistance on the Earth. It's entirely a gravity thing.
what statement is true according to newton’s first law of motion?
a. in the absence of unbalanced force an object at rest will stay at rest and an object in motion will come to a stop.
b. in the absence of an unbalanced force, an object will start moving and an object in motion will come to a stop.
c. in the absence of an unbalanced force, an object at rest will stay at rest and an object in motion will stay in motion.
d. in the absence of an unbalanced force, an object will start moving and an object in motion will stay in motion.
Answers
Answer:
c. in the absence of an unbalanced force, an object at rest will stay at rest and an object in motion will stay in motion.
Explanation:
First law: things keep doing what they are doing, unless force is applied.
state Ohm`s law as applied in electricity
Answers
Answer:
Ohm's Law (E = IR) is as fundamentally important as Einstein's Relativity equation (E = mc²) is to physicists. When spelled out, it means voltage = current x resistance, or volts = amps x ohms, or V = A x Ω.