A 4.0 kg block is moving at 5.0 m/s along a horizontal frictionless surface toward and ideal spring that is attached to a wall , After the block collides with the spring, the spring is compressed a maximum distance of 0.68m . what is the speed of the block when the spring is compressed to only one-half of the maximum distance?
A 4.0 kg block is moving at 5.0 m/s along a horizontal frictionless surface toward an ideal spring that is attached to a wall, the maximum speed of the block when the spring is compressed to one-half of the maximum distance is 4.33 m/s
From the conservation of energy; the kinetic energy of the mass is equal to the work done on the spring.
i.e.
[tex]\mathbf{\dfrac{1}{2} mv^2 = \dfrac{1}{2}kx^2_{max}}[/tex]
Given that:
the mass of the block = 4.0 kg the speed at which it is moving = 5.0 m/scompression of the spring = 0.68 m∴
From the equation above, multiplying both sides with 2, we have:
[tex]\mathbf{mv^2 =kx^2_{max}}[/tex]
Making (k) the subject of the formula;
[tex]\mathbf{k = \dfrac{mv^2}{x^2_{max}}}[/tex]
[tex]\mathbf{k = \dfrac{4 \times 5^2}{0.68^2}}[/tex]
k = 216.26 N/m
However, when compressed to one-half of the maximum distance; the speed is computed as follows:
x = 0.68/2 = 0.34 m
∴
[tex]\mathbf{\dfrac{1}{2}mv_o^2 - \dfrac{1}{2}mv^2 = \dfrac{1}{2}kx^2}[/tex]
[tex]\mathbf{m(v_o^2 -v^2) =kx^2}[/tex]
[tex]\mathbf{(v_o^2 -v^2) =\dfrac{kx^2}{m}}[/tex]
[tex]\mathbf{(5^2 -v^2) =\dfrac{216.26 \times 0.34^2}{4.0}}[/tex]
25 - v² = 6.25
25 -6.25 = v²
v² = 18.75
[tex]\mathbf{ v= \sqrt{18.75 }}[/tex]
v = 4.33 m/s
Therefore, we can conclude that the speed of the block when the spring is compressed to only one-half of the maximum distance is 4.33 m/s
Learn more about speed here:
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a train has an initial velocity of 30 m/s. If the train accelerates uniformly at a rate of 6.3 m/s ^ for 2.8 seconds what is the trains final velocity?
T
Answer:
the velocity is a second final to initial velocity of 39
Which of the
following
DECREASES
as you go UP a
mountain?
A. climate
B. altitude
C. amount of oxygen
D. buoyancy
Answer:
C. Amount of oxygen
Explanation:
Options A and D are invalid as they aren't affecting factors.
Option B is false as the altitude increases as you go up a mountain.
Option C is true as the air pressure (atmospheric pressure) is inversely proportional to the height/altitude of the mountain.
Which runner finished the 100 m race in the least amount of time?
Ming
Which runner stopped running for a few seconds during the race?
At what distance did Anastasia overtake Chloe in the race?
1: Ming
2: Chloe
3: 40m
The distance from the sun to Earth would be
Which phrase best completes the sentence?
any number of light years
more than one light year
exactly one light year
less than one light year
4
Answer:
less than one lightyear=d
Explanation:
I took the test.:D:D:D:D:D:D:D:D:D:D:D:D:D:D:D:D:D:D:D:D:D:D:D:D:D:D:D:D::):):):):):):):):):):):):):):):):):):):):):)
Each of the two grinding wheels has a diameter of 6 in., a thickness of 3/4 in., and a specific weight of 425 lb/ft3. When switched on, the machine accelerates from rest to its operating speed of 3450 rev/min in 5 sec. When switched off, it comes to rest in 35 sec. Determine the motor torque and frictional moment, assuming that each is constant. Neglect the effects of the inertia of the rotating motor armature.
Answer:
[tex]0.842\ \text{lb ft}[/tex]
[tex]0.1052\ \text{lb ft}[/tex]
Explanation:
d = Diameter of wheel = 6 in
r = Radius = 3 in = [tex]\dfrac{3}{12}=0.25\ \text{ft}[/tex]
t = Thickness = [tex]\dfrac{3}{4}=0.75\ \text{in}=\dfrac{0.75}{12}\ \text{ft}[/tex]
w = Specific weight = [tex]425\ \text{lb/ft}^3[/tex]
[tex]t_2[/tex] = Time taken to slow down = 35 s
[tex]t_1[/tex] = Time taken to reach operating speed = 5 s
[tex]\omega[/tex] = Angular velocity = [tex]3450\times \dfrac{2\pi}{60}\ \text{rad/s}[/tex]
Weight is given by
[tex]W=2\pi r^2tw\\\Rightarrow W=2\pi\times 0.25^2\times \dfrac{0.75}{12}\times 425\\\Rightarrow W=10.43\ \text{lbs}[/tex]
Mass is given by
[tex]m=\dfrac{W}{g}\\\Rightarrow m=\dfrac{10.43}{32}\\\Rightarrow m=0.326\ \text{lb}[/tex]
Moment of inertia is given by
[tex]I=\dfrac{mr^2}{2}\\\Rightarrow I=\dfrac{0.326\times 0.25^2}{2}\\\Rightarrow I=0.01019\ \text{lb ft}^2[/tex]
Angular acceleration while slowing down is given by
[tex]\alpha_f=\dfrac{\omega}{t_2}\\\Rightarrow \alpha_f=\dfrac{3450\times \dfrac{2\pi}{60}}{35}\\\Rightarrow \alpha_f=10.32\ \text{rad/s}^2[/tex]
Frictional moment is given
[tex]\tau_f=I\alpha_f\\\Rightarrow \tau_f=0.01019\times 10.32\\\Rightarrow \tau_f=0.1052\ \text{lb ft}[/tex]
Frictional moment is [tex]0.1052\ \text{lb ft}[/tex]
Angular acceleration while speeding up is given by
[tex]\alpha=\dfrac{\omega}{t_1}\\\Rightarrow \alpha=\dfrac{3450\times \dfrac{2\pi}{60}}{5}\\\Rightarrow \alpha=72.26\ \text{rad/s}^2[/tex]
Motor torque is given by
[tex]\tau_m=\tau_f+I\alpha\\\Rightarrow \tau_m=0.1052+0.01019\times 72.26\\\Rightarrow \tau_m=0.842\ \text{lb ft}[/tex]
Motor torque is [tex]0.842\ \text{lb ft}[/tex].
The elastic energy stored in your tendons can contribute up to 35 % of your energy needs when running. Sports scientists have studied the change in length of the knee extensor tendon in sprinters and nonathletes. They find (on average) that the sprinters' tendons stretch 41 mm , while nonathletes' stretch only 33 mm .
Hello. Your question is incomplete. However, I managed to find it completely on the internet and I realized that you forgot to mention that the question asks you for the maximum energy difference between velovistas and non-athletes, considering that the spring constant for the tendon of the two groups is equal to 33n/mm.
To make this calculation you will need to use Hooke's law, using the formula: ¹/2*K*x², where "K" will be the value of the spring constant for the tendon and "X" will be the value of the sprinter and non-athlete terms.
So for the sprinter we will have the calculation:
¹/2*33*41² -------> 0,5*33*1681 = 27736. 5 Nmm
(To facilitate the calculation, first solve the division of ¹/2 and then multiply 41 by 41, lastly, just multiply all the results.)
For the non-athlete we will have the calculation:
¹/2*33*33² -------> 0,5*33*1089 = 17968. 5 Nmm
(To facilitate the calculation, first solve the division of ¹/2 and then multiply 41 by 41, lastly, just multiply all the results.)
Now, to reach the final result, you only need to subtract the two values presented by the sprinter and the non-athlete.
27736.5 - 17968.5 = 9768 Nmm
Look at the diagram showing the different wavelengths in sunlight.
A diagram showing the human eye and visible light. Visible light is broken down by color with wavelength in nanometers. Red is 700, orange is 600, yellow is 580, green is 550, blue is 475, indigo is 450, violet is 400.
Which has a wavelength of 350 nanometers?
red light
violet light
infrared light
ultraviolet light
Answer:
ultraviolet light
plz mark me as brainliest.
Answer:
Ultra violet
Explanation:
Night terrors and nightmares are
really the same event.
True
False
Two identical loudspeakers are driven in phase by the same amplifier. The speakers are positioned a distance of 3.2 m apart. A person stands 5.0 m away from one speaker and 6.2 m away from the other. Calculate the second lowest frequency that results in destructive interference at the point where the person is standing. Assume the speed of sound to be 330 m/ s. A) 183 Hz B) 275 Hz C) 413 Hz D) 137 Hz E) 550 Hz
Answer:
C) 413 Hz
Explanation:
For destructive interference, the path difference ΔL = (n + 1/2)λ where ΔL = L₂ - L₁ where L₁ = person's distance from one speaker (the closer one) = 5.0m and L₂ = person's distance from other speaker (the farther one) = 6.2 m and λ = wavelength = v/f where v = speed of sound = 330 m/s and f = frequency
So, ΔL = (n + 1/2)λ
L₂ - L₁ = (n + 1/2)v/f
f = (n + 1/2)v/(L₂ - L₁)
At the second lowest frequency that results in destructive interference at the point where the person is standing, n = 1.
So,
f = (1 + 1/2)v/(L₂ - L₁)
f = 3v/2(L₂ - L₁)
Substituting the values of the variables into the equation, we have
f = 3v/2(L₂ - L₁)
f = 3(330 m/s)/2(6.2 m - 5.0 m)
f = 3(330 m/s)/2(1.2 m)
f = 990 m/s ÷ 2.4 m)
f = 412.5 Hz
f ≅ 413 Hz
Please answer this for 15 points please don’t put in a link.
Answer:
c. Double Replacement
Explanation:
As in Double Replacement reaction exchanges the cations (or the anions) of two ionic compounds.
Here, in BaCl2 , Ba has replaced with NO3 to form Ba(NO3)2
and in 2AgNo3 , Ag has replaced with Cl to form 2AgCl.
Telescopes are used for producing images, spectroscopy, and time monitoring of celestial objects.
True
False
May you please help?
Choice-A is the main reason that people use the thing in the picture.
The liquid emerges into a vertical jet as it drains from the container, with the velocity profile in the jet remaining uniform. The outlet of the container is located 2.0 m above ground, and the radius of the emerging liquid jet changes with vertical distance from the bottom of the container as it accelerates under the action of gravity. Neglecting viscous losses and surface tension effects in the liquid jet, what is the velocity of the water jet as it strikes the ground when the container begins to drain
Answer:
6.26 m/s
Explanation:
Since we are neglecting viscous losses and surface tension effects in the liquid jet, by conservation of energy, the potential energy loss of the jet = kinetic energy gain of the jet
So, mgh = 1/2mv² where m = mass of water in jet, g = acceleration due to gravity = 9.8 m/s², h = height of outlet = 2.0 mand v = velocity of liquid jet
So, mgh = 1/2mv²
gh = 1/2v²
v² = 2gh
v = √(2gh)
v = √(2 × 9.8 m/s² × 2.0 m)
v = √(39.2 m²/s²)
v = 6.26 m/s
Please solve for 15 points. Please don’t input a link.
Answer:
a). Single replacement.
Explanation:
Because one element replaces another element in a compound
What is an example of a combined approach in psychology?
Answer:
The third approach to cross-cultural studies of personality is the combined approach, which serves as a bridge between Western and indigenous psychology as a way of understanding both universal and cultural variations in personality
Explanation:
Answer:
The third approach to cross-cultural studies of personality is the combined approach, which serves as a bridge between Western and indigenous psychology as a way of understanding both universal and cultural variations in personality
Which is observed globally: "Earth Day" or "Arbor Day"?
Answer:
Earth Day is observed globally
Explanation:
a lens with f = 50.0 cm is held 55.0 cm from an object. what is the image distance? (unit = cm)
Answer: 550 cm
Explanation:
Original equation: 1/f= 1/do + 1/di.
F=50.0 cm, and do=55.0.
Since we don't have di, we'll have to subtract do to the other side, making the equation: 1/f - 1/do= 1/di.
Doing the math, 1/f - 1/do is 0.0018181818
Then to get di by itself, you multiply both sides by di. Then you divide by 0.0018181818 to get di by itself. You then get: di= 1/0.0018181818
At that point, you just divide 1 by 0.0018181818, which will give you 550 cm
There could be simpler way, but that is just what I did to get the answer. Answer was right on Acellus
Suppose a diode consists of a cylindrical cathode with a radius of 6.200×10−2 cm , mounted coaxially within a cylindrical anode with a radius of 0.5580 cm . The potential difference between the anode and cathode is 400 V . An electron leaves the surface of the cathode with zero initial speed (vinitial=0). Find its speed vfinal when it strikes the anode.
Answer:
The final speed will be "[tex]1.185\times 10^7 \ m/sec[/tex]".
Explanation:
The given values are:
Potential difference,
Δv = 400 v
Radius,
r = 0.5580 cm
As we know,
⇒ [tex]W=e \Delta v[/tex]
and,
⇒ [tex]\frac{1}{2}mv^2=e \Delta v[/tex]
then,
⇒ [tex]v=\sqrt{\frac{2e \Delta v}{m} }[/tex]
On substituting the values, we get
⇒ [tex]=\sqrt{\frac{2\times 1.6\times 10^{-19}\times 400}{9.11\times 10^{-31}} }[/tex]
⇒ [tex]=\sqrt{\frac{1.6\times 10^{-19}\times 800}{9.11\times 10^{-31}}}[/tex]
⇒ [tex]=1.185\times 10^7 \ m/sec[/tex]
You put a diode in a microelectronic circuit to protect the system in case an untrained person installs the battery backward. In the correct forward-bias situation, the current is 255 mA with a potential difference of 116 mV across the diode at room temperature (300 K). If the battery were reversed, so that the potential difference across the diode is still 116 mV but with the opposite sign, what would be the magnitude of the current in the diode
Answer:
The current in the new circuit is 0
Explanation:
A diode is an electronic component that allows the electric current to go only in one direction. If in the first case the current was 255 mA, and the battery was changed ( change in polarity ) no current will flow through the circuit. That change is similar or equivalent to change the diode to the no pass position
a disk of a radius 50 cm rotates at a constant rate of 100 rpm. what distance in meters will a point on the outside rim travel during 30 seconds of rotation?
Answer:
Wait lang po sandali po wait lang
Two protons (each with q = 1.60 x 10-19)
in a nucleus are located 1.00 x 10-15 m
apart. How much electric force do they
exert on each other?
[?] N.
Answer:
230.4 N
Explanation:
From the question given above, the following data were obtained:
Charge (q) of each protons = 1.6×10¯¹⁹ C
Distance apart (r) = 1×10¯¹⁵ m
Force (F) =?
NOTE: Electric constant (K) = 9×10⁹ Nm²/C²
The force exerted can be obtained as follow:
F = Kq₁q₂ / r²
F = 9×10⁹ × (1.6×10¯¹⁹)² / (1×10¯¹⁵)²
F = 9×10⁹ × 2.56×10¯³⁸ / 1×10¯³⁰
F = 2.304×10¯²⁸ / 1×10¯³⁰
F = 230.4 N
Therefore, the force exerted is 230.4 N
Answer:
230.4
Explanation:
acellus
A spiral staircase winds up to the top of a tower in an old castle. To measure the height of the tower, a rope is attached to the top of the tower and hung down the center of the staircase. However, nothing is available with which to measure the length of the rope. Therefore, at the bottom of the rope a small object is attached so as to form a simple pendulum that just clears the floor. The period of the pendulum is measured to be 6.82 s. What is the
Answer:
The answer is "[tex]11.55780\ m[/tex]"
Explanation:
Using formula:
[tex]= 2 \pi f= \frac{2\pi}{T} =\sqrt{\frac{g}{L}}[/tex]
L = length of pendulum.
[tex]= T =2 \pi \sqrt{\frac{L}{g}}[/tex]
Calculate the value for L:
[tex]L= g (\frac{T}{2 \pi})^2 \\\\[/tex]
[tex]= (9.80 \ \frac{m}{s^2}) (\frac{6.82 \ s}{2 \pi})^2\\\\= (9.80 \ \frac{m}{s^2}) (\frac{46.5124 \ s^2}{4 \times \pi^2})\\\\= (9.80 \ \frac{m}{s^2}) (\frac{46.5124\ s^2}{4 \times 9.8596 })\\\\= (9.80 \ \frac{m}{s^2}) (\frac{46.5124 \ s^2}{ 39.4384 })\\\\= \frac{455.82152}{39.4384} \ m\\\\=11.55780\ m[/tex]
The height of the tower = 11.55780 m
Pls help me mark Brainliest here the answer choices
4.0N
8.0N
12.0N
16.0N
20.0N
Answer:
20.0N
Becuase It's the largest
Answer:
20.0
Explanation:
It's the biggest number
Easy question I’ll give extra points. Help
Answer:
the answer is A
I wish you a good day!
Answer:
THe answer is graph 2 as it represents the puck going in a linear motion
Explanation:
a disk of a radius 50 cm rotates at a constant rate of 100 rpm. what distance in meters will a point on the outside rim travel during 30 seconds of rotation?
Answer:
239 rpm
Explanation: So the distance covered in one minute is 75,000 centimeters. The diameter of the wheel is 100 cm, so the radius is 50 cm, and the circumference is 100π cm. How many of these circumferences (or wheel revolutions) fit inside the 75,000 cm? In other words, if I were to peel this wheel's tread from the cart and lay it out flat, it would measure a distance of 100π cm. How many of these lengths fit into the entire distance covered in one minute? To find out how many of (this) fit into so many of (that), I must divide (that) by (this), so:
100πcm/rev
75,000cm/min
750 min rev≈238.7324146RPM
An 80.0-kg skydiver jumps out of a balloon at an altitude of 1,000 m and opens his parachute at an altitude of 200 m. A. Assuming the total friction (resistive) force on the skydiver is constant at 50.0 N with the parachute closed and constant at 3,600 N with the parachute open, find the speed of the skydiver when he lands on the ground. B. At what height should the parachute be opened so that the final speed of the skydiver when he hits the ground is 5.00 m/s
Answer:
[tex]24.9\ \text{m/s}[/tex]
[tex]206.7\ \text{m}[/tex]
Explanation:
m = Mass of skydiver = 80 kg
[tex]x_1[/tex] = Height for which the parachute is closed = 1000-200 = 800 m
[tex]x_2[/tex] = Height for which the parachute is open = 200 m
[tex]f_1[/tex] = Resistive force when parachute is closed = 50 N
[tex]f_2[/tex] = Resistive force when parachute is open = 3600 N
v = Velocity of skydiver on the ground
g = Acceleration due to gravity = [tex]9.81\ \text{m/s}^2[/tex]
h = Height from which the skydiver jumps = 1000 m
The energy balance of the system will be
[tex]mgh-f_1x_1-f_2x_2=\dfrac{1}{2}mv^2\\\Rightarrow 80\times 9.81\times 1000-50\times 800-3600\times 200=\dfrac{1}{2}\times 80\times v^2\\\Rightarrow v=\sqrt{\dfrac{2(80\times 9.81\times 1000-50\times 800-3600\times 200)}{80}}\\\Rightarrow v=24.9\ \text{m/s}[/tex]
The velocity fo the skydiver when he lands will be [tex]24.9\ \text{m/s}[/tex]
x = Height where the person opens the parachute
v = 5 m/s
[tex]mgh-f_1x_1-f_2x_2=\dfrac{1}{2}mv^2\\\Rightarrow 80\times 9.81\times 1000-50\times (1000-x)-3600\times x=\dfrac{1}{2}\times 80\times 5^2\\\Rightarrow 80\times 9.81\times 1000-50000+50x-3600x=\dfrac{1}{2}\times 80\times 5^2\\\Rightarrow x=\dfrac{80\times 9.81\times 1000-50000-\dfrac{1}{2}\times 80\times 5^2}{3550}\\\Rightarrow x=206.7\ \text{m}[/tex]
The height at which the parachute is to be opened is [tex]206.7\ \text{m}[/tex]
A scientist measuring the resistivity of a new metal alloy left her ammeter in another lab, but she does have a magnetic field probe. So she creates a 4.5-m-long, 2.0-mm-diameter wire of the material, connects it to a 1.5 V battery, and measures a 3.0 mT magnetic field 1.0 mm from the surface of the wire. What is the material's resistivity
Answer:
[tex]3.49\times 10^{-8}\ \Omega\text{m}[/tex]
Explanation:
r = Radius = [tex]\dfrac{2}{2}=1\ \text{mm}[/tex]
B = Magnetic field = 3 mT
1 mm = Distance from the surface of the wire
V = Voltage
x = Distance from the probe = [tex]r+1=1+1=2\ \text{mm}[/tex]
R = Resistance
L = Length of wire = 4.5 m
Magnetic field is given by
[tex]B=\dfrac{\mu_0I}{2\pi x}\\\Rightarrow I=\dfrac{B2\pi x}{\mu_0}\\\Rightarrow I=\dfrac{3\times 10^{-3}\times 2\times \pi 2\times 10^{-3}}{4\pi 10^{-7}}\\\Rightarrow I=30\ \text{A}[/tex]
Voltage is given by
[tex]V=IR\\\Rightarrow R=\dfrac{V}{I}\\\Rightarrow R=\dfrac{1.5}{30}\\\Rightarrow R=0.05\ \Omega[/tex]
Resistivity is given by
[tex]\rho=\dfrac{RA}{L}\\\Rightarrow \rho=\dfrac{0.05\times \pi (1\times 10^{-3})^2}{4.5}\\\Rightarrow \rho=3.49\times 10^{-8}\ \Omega\text{m}[/tex]
The resistivity of the material is [tex]3.49\times 10^{-8}\ \Omega\text{m}[/tex].
HELP URGENT PLEASE!!!!!!!
Answer:
I think c I dont know sorry if I'm wrong
A solenoid of 2100 turns, area 10 cm2, and length 30 cm carries a current of 4.0 A. (a) Calculate the magnetic energy stored in the solenoid from 1/2 LI 2. J [2 points] 0 attempt(s) made (maximum allowed for credit
Answer:
E = 0.1472 J
Explanation:
Given that,
The number of turns in the solenoid, N = 2100
Area of the solenoid, A = 10 cm² = 0.001 m²
The length of the solenoid, l = 30 cm = 0.3 m
Current in the solenoid, I = 4 A
We need to find the magnetic energy stored in the solenoid. The expression for the stored energy is :
[tex]E=\dfrac{1}{2}LI^2[/tex]
Where
L is self inductance of the solenoid,
[tex]L=\dfrac{\mu_oN^2A}{l}\\\\L=\dfrac{4\pi \times 10^{-7}\times 2100^2\times 0.001}{0.3}\\\\L=0.0184\ H[/tex]
So,
[tex]E=\dfrac{1}{2}\times 0.0184\times 4^2\\\\E=0.1472\ J[/tex]
So, 0.1472 J of energy is stored in the solenoid.