Answer:
The force exerted by the rubber band will increase. This is because the restoring force (force which acts to bring a body back to its equilibrium state) always acts in opposite direction to the force which acts to pull the body from its equilibrium position. And as the distance increases the force increases as well.
Explanation:
Fill in the blanks using the appropriate letters from the bottom.
A mass m is attached to an ideal spring with a spring constant k.
It has a period of [tex]T_{A}[/tex]=1.00 seconds measured in Boston, where g=9.80 [tex]m/s^{2}[/tex].
A simple pendulum of mass m and L has the exact same period [tex]T_{B}[/tex] =1.00s right there.
What will happen to the period of (A) the spring-mass system and (B) the pendulum,
A. when they are both moved to the moon; [tex]T_{A}[/tex]___, [tex]T_{B}[/tex]___
B. when they are both moved to the north pole where g = 9.83 m/s2; [tex]T_{A}[/tex]___
,[tex]T_{B}[/tex] ___
C. or when they are both moved to the equator where g = 9.78 m/s2? [tex]T_{A}[/tex]___
, [tex]T_{B}[/tex] ___
Select from below:
A. Stay the same.
B. Reduce by a factor of 6.
C. Increase by a factor of 6.
D. Reduce by a factor of 2.45.
E. Increase by a factor of 2.45.
F. Reduce by roughly 0.1%
G. Increase by roughly 0.1%
The force required to extend or compress a spring, divided by the lengthening or shortening of the spring, is known as the spring constant.
If a vertical is coupled to a mass M, when?A vertical spring with mass M that is attached steadily lowers to its equilibrium position. This causes the spring x to lengthen. Suppose the same thing was still tied to the same vertical spring, but it was allowed to fall suddenly instead.
How can you determine a spring's top speed?The maximum velocity is equal to the amplitude times the angular frequency, or v max=A v max = A, since the sine function oscillates between -1 and +1. The mass is travelling toward x=+A when the maximum velocity occurs at the equilibrium location (x=0).
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Insert tab A into slot B" is something you might read in the assembly instructions for pre-fabricated bookshelves. Suppose that tab A varies in size according to a Normal distribution with a mean of 30 mm. And a standard deviation of 0. 5 mm. , and the size of slot B is also Normally distributed, with a mean of 32 mm. And a standard deviation of 0. 8 mm. The two parts are randomly and independently selected for packaging. What is the probability that tab A won’t fit into slot B?
0.017 is the probability that tab A won’t fit into slot B
What is probability?Probability is related to possibility. Random event generation is the subject of this branch of mathematics. Values range from 0 to 1. Probabilities are built into mathematics to predict the likelihood of certain events.
P(tab A won't fit into slot B) = P (A>B)
= P( A-B > 0)
Given that, A ≈ N(30,0.5) B ≈ N(32, 0.8)
Here,
E (A-B) = 30-32 = -2
V(A-B) = V(A) + V(B) = (0.5)² + (0,8)²
= 0.89
SD (A-B) = [tex]\sqrt{0.89}[/tex]
So, (A-B) ≈ N (-2, 0.9433)
P( A-B > 0) = 1 - P(A-B ≤ 0)
= 1 - P [(A - B +2 / 0.9433) ≤ (+2 / 0.9433)]
= 1 - P (Z₁ ≤ 2.12)
= 1 - 0.98300
= 0.017
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A 5-ohm resistor is connected to a 1.5 V battery. The 5-ohm resistor is replaced with a smaller resistor. In order to keep the current through the resistor the same, what should be done to the voltage of the battery
(A) Increase it
(B) Decrease it
(C) Keep it the same
Explain why
Answer:
Below
Explanation:
V = IR
V/R = I
Now you can see that if you decrease R, you will need to decrease V to have the same value of I
if 5ev of energy is supplied to an electron with a binding energy of 2.3ev, with what kinetic energy will the electron be launched?
if 5ev of energy is supplied to an electron with a binding energy of 2.3ev, with what kinetic energy is [tex]\Rightarrow \mathrm{KE}=5-2.3=\mathbf{2 . 7} \mathrm{eV}[/tex]
What is kinetic energy?
The energy an object has as a result of motion is known as kinetic energy in physics. It is described as the effort required to move a mass-determined body from rest to the indicated velocity. The body holds onto the kinetic energy it acquired during its acceleration until its speed changes.
Photoelectric effect: The photoelectric effect is a phenomenon where electrons are ejected from a metal surface when the light of sufficient frequency is incident on it. These ejected electrons are called photoelectrons.
- When a photon falls on the metal surface, the photon's energy is transferred to the electron.
- Some part of the energy gets utilized in removing the electron from the metal surface, and the remaining goes into giving kinetic energy for the ejected electron.
- Work function [tex](\phi)[/tex]: It is the minimum amount of energy required to cause photo-emission of electrons from a metal surface when light is incident on it.
- Einstein's Photoelectric Equation gives the relationship between work function[tex](\phi)[/tex], the kinetic energy of the emitted electron, and the energy of the photon [tex](E)[/tex]
[tex]$$E=\phi+K E$$[/tex]
Given that:
Energy of incident light, [tex]E=5 \mathrm{eV}[/tex]
Work function,[tex]$\phi=2.3 \mathrm{eV}$[/tex]
Using Einstein's Photoelectric Equation,
[tex]$$\begin{aligned}& \mathrm{E}=\phi+\mathrm{KE} \\& 5=2.3+\mathrm{KE} \\& \Rightarrow \mathrm{KE}=5-2.3=\mathbf{2 . 7} \mathrm{eV}\end{aligned}$$[/tex]
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During practice, a student kicks a 0.40 kg soccer ball with a velocity of 8.5 m/s to the right into a 0.15 kg stationary bucket
lying on its side. The bucket travels with the ball after the collision. What is the velocity of the bucket and ball?
Answer:
Below
Explanation:
Using conservation of momentum
m1v1 = m2v2
.4 (8.5) = (.40 + .15) v^2
6.18 m/s
Astrology, that unlikely and vague pseudoscience, makes much of the position of the planets at the moment of one's birth. The only known force a planet exerts on Earth is gravitational.
(a) Calculate the magnitude of the gravitational force exerted on a 4.20 kg baby by a 100 kg father 0.200 m away at birth (he is assisting, so he is close to the child).
(b) Calculate the magnitude of the force on the baby due to Jupiter if it is at its closest distance to Earth, some 6.29×10^11 m away. How does the force of Jupiter on the baby compare to the force of the father on the baby?
Other objects in the room and the hospital building also exert similar gravitational forces. (Of course, there could be an unknown force acting, but scientists first need to be convinced that there is even an effect, much less that an unknown force causes it.)
The magnitude of the gravitational force is 7×10⁻⁷ N
Baby weighs (m₁) 4.20 kg.
Father weighs (m₂) 100 Kg.
The gravitational force (F) between the body and the earth has a magnitude of 6.67×10⁻
The separation between them is: 0.200 m
The gravitational constant is
F=Gm₁×m₂÷ R²
F= 6.67×10⁻¹¹×4.20×100÷ (0.200)²
F= 7×10⁻⁷ N
Gravitational force: The gravitational force between any two mass-containing objects causes them to be drawn together. The gravitational force is said to as attractive because it continually seeks to unite masses rather than to drive them away. In truth, you and everything else in the universe are being pulled in different directions. It is referred to as Newton's Universal Law of Gravitation.
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a. If there is to be no relative motion between the train and the edge of the platform, how fast must
the train move compared to the rim speed of the rotating platform?
b. Why is the stairway located at the center of the platform?
2. The design below shows a train that makes round trips from Station A to Station B in a
continuous loop.
a. How is the size of the round platform and train speed related to the amount of time that
passengers have for boarding?
b. Why would this rotating platform be impractical for high-speed trains?
CONCEPTUAL PHYSICS
Train must move with equal speed as of platform in opposite direction i order to maintain zero relative velocity.
What is velocity?Velocity is the speed in which something move in a paticular Direction.
From the question it is given that
relative velocity between platform and train = 0
since relative velocity of train with respect to platform is given by
where, is the velocity of train and is the velocity of platform
⇒ vt = vp
since platform is always at stationary i.e.,
thus train velocity = 0
Therefore, train does not move
If, Platform is moving then train must move with equal speed as of platform in opposite direction.
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Find A mass of 10 kg is moving in a circular path of radius 2 m with a uniform speed of 50 ms the centripetal acceleration and the corresponding centripetal force
Answer:
Centripetal acceleration: [tex]1250\; {\rm m\cdot s^{-2}}[/tex].
Resultant force on the object should be [tex]12500\; {\rm N}[/tex].
(Assuming that the speed of the object is [tex]50\; {\rm m\cdot s^{-1}}[/tex].)
Explanation:
For an object that travels along a circle path of radius [tex]r[/tex] at a speed of [tex]v[/tex], (centripetal) acceleration will be [tex]a = (v^{2} / r)[/tex].
In this example, speed is [tex]v = 50\; {\rm m\cdot s^{-1}}[/tex] while the radius of the circular path is [tex]r = 2\; {\rm m}[/tex]. The (centripetal) acceleration of this object will be:
[tex]\begin{aligned}a &= \frac{v^{2}}{r} \\ &= \frac{(50\; {\rm m\cdot s^{-1}})^{2}}{(2\; {\rm m})} \\ &= 1250\; {\rm m\cdot s^{-2}}\end{aligned}[/tex].
For an object of mass [tex]m[/tex], the resultant force to achieve acceleration [tex]a[/tex] is [tex]F(\text{net}) = m\, a[/tex]. In this example, [tex]m = 10\; {\rm kg}[/tex] while [tex]a = 1250\; {\rm m\cdot s^{-2}}[/tex]. The required resultant force will be:
[tex]\begin{aligned}F(\text{net}) &= m\, a \\ &= (10\; {\rm kg})\, (1250\; {\rm m\cdot s^{-2}}) \\ &= 12500\; {\rm kg \cdot m\cdot s^{-2}} \\ &= 12500\; {\rm N} \end{aligned}[/tex].
g what best describes the camera motion in the scenes directly prior to the old man's defiant hand gesture?
The action that best describes the camera motion in the scenes directly prior to the Old Man's Defiant hand gesture is: "Zooming in and out" (Option C)
What are the various types of Camera Motions and why are they important?Some interesting camera motions are:
Static shot - The camera is stationary and does not move during the shot. This can create a sense of stability and calm.Panning shot - The camera moves horizontally from left to right or vice versa, following the action or moving to reveal a new part of the scene.Tilt shot - The camera moves vertically up or down, following the action or revealing a new part of the scene.Tracking shot - The camera moves horizontally, vertically, or diagonally while following the action or a moving object.Note that the different camera motions described above are important because they allow filmmakers to convey mood and emotion, create visual interest, and guide the audience's attention within a scene.
For example, a static shot can create a sense of calm or stability, while a handheld shot can create a sense of intimacy or instability. A panning shot can follow the action and keep the audience engaged, while a zoom shot can draw attention to a specific part of the scene.
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Full Question:
What best describes the camera motion in the scenes directly prior to the old man's defiant hand gesture?
O Static and secured on a tripod
O Moving chaotically
O Zooming in and out
O Filming at 96 frames a second
190) a small car and an suv are at a stoplight. the car has a mass equal to half that of the suv, and the 190) suv's engine can produce a maximum force equal to twice that of the car. when the light turns green, both drivers floor it at the same time. which vehicle pulls ahead of the other vehicle after a few seconds?
Given the
Half the weight of an SUV
If the mass of the SUV is 2m, the mass of the car is m
An SUV can produce twice as much power as a car, or 2 F.
Experience acceleration in an SUV
;SUV=2F/2m
;SUV=F/m
car acceleration
; car = F/m
They both start with an initial velocity of zero, so after a few seconds they have the same velocity and share the same position.
speed-
Velocity is a vector representation of the displacement an object or particle experiences with respect to time. The standard unit for velocity magnitude (also called velocity) is meters per second (m/s). Alternatively, centimeters per second (cm/s) can be used to express velocity magnitude. The direction of the velocity vector can be expressed in different ways depending on the number of dimensions involved. speed
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to study problems concerned with the motion of matter under the influence of forces, i.e., dynamics, it is necessary to locate a point called
The center of mass must be found in order to analyze issues involving the flow of matter when subjected to forces, or dynamics.
Motion: A Simple DefinitionMotion is the alteration of a skin's position or orientation over time. The movements of people and animals is just one illustration of how everything in the cosmos is always moving. In addition, the fundamental building block of matter, the atom, is likewise constantly in motion.
Describe a motion example.Motion is the free flow of a body in relation to time. For instance, the fan, the carpet's dust blowing off of it, the water running from the faucet, a ball rolling about, a moving car, etc. Even just the universe is always changing.
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PLEASE HELP!
Jadee pulls a piece of luggage across the airport, notices that she is lagging behind her parents and wants to catch up for a short amount of time. She pulls with a horizontal force of 33.3 N. The force due to friction for the luggage is 12.3 N and the mass of the luggage is 50.0 kg.
The acceleration of the luggage across the airport is 0.42 m/s².
What is the acceleration of the luggage?
The acceleration of the luggage across the airport is calculated by applying Newton's second law of motion as follows;
Mathematically, the Newton's second law of motion is given as;
F(net) = ma
where;
F(net) is the net force on the luggagem is the mass of the luggagea is the acceleration of the luggageF - Ff = ma
where;
F is the applied force on the luggageFf is the force of friction33.3 - 12.3 = 50a
21 = 50a
a = 21/50
a = 0.42 m/s²
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The complete question is below:
Jadee pulls a piece of luggage across the airport, notices that she is lagging behind her parents and wants to catch up for a short amount of time. She pulls with a horizontal force of 33.3 N. The force due to friction for the luggage is 12.3 N and the mass of the luggage is 50.0 kg. find the acceleration of the luggage.
A ray of light strikes a smooth surface and is reflected. The angle of incidence is 35°. What can be predicted about the angle of reflection?
Answer:
35 degrees
Explanation:
The law of reflection states that the angle of incidence = to the angle of reflection
Answer:
The answer is C:
Rays will follow the law of reflection, so the angle of reflection will be 35°.
Explanation:
what is the difference between speed and velocity? what is the difference between speed and velocity? velocity contains information about the direction of motion while speed does not. speed is an average quantity while velocity is not. the concept of speed applies only to objects that are neither speeding up nor slowing down, while velocity applies to every kind of motion. speed is measured in mph, while velocity is measured in m/s.
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.
In other terms, the distance that an object travels in a unit of time is referred to as its speed. It merely takes into account the magnitude of the object and ignores its orientation. Speed is referred to as a scalar quantity. When referring to velocity, however, it is said that velocity is the rate at which displacement changes. It is a vector quantity. Speed is a scalar measure of "how quickly an object is moving." The rate at which an object travels a distance can be thought of as its speed. A fast-moving object travels at a high speed and completes a significant distance relatively quickly. A slow-moving object with a low speed, on the other hand, travels a relatively little distance in the same length of time. Zero speed refers to an object that is not moving at all. When evaluating the velocity of an item, one must retain track of direction. It wouldn't be sufficient to merely state that something moves at 80 km/h. To fully define an object's velocity, direction information must be included. For instance, 80 km/h reflects the speed of a car travelling along a road, while 80 km/h east shows the speed of the car.
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how will the image change if you move the lens closer or further from the lightbulb? how will you have to move the paper to keep the lightbulb in focus?
The image will still get progressively smaller as we pull the object more and more away. The focal point will draw the image's location ever-closer.
What is the name for a focal point?The focal point or point of focus on the axis of the a lens or mirror where parallel light rays converge or appear to split after refraction or reflection.
How is a focal point created?Contrast can be used by an artist to establish focal points in the following methods: 1) Value—A focus point will naturally develop in the area where there is the greatest disparity between light and dark. 2) Form—If a composition of geometric squares added a circle, the circle would be composition's main point.
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Consider two stars that we’ll call A and B. Both are the same distance from Earth. Star A is much smaller than star B, but it also has a much higher temperature. Which one do you think would appear brighter? Why?
Both stars A and B will have the same brightness to the earth because luminosity is dependent on the temperature and size where A is hotter but smaller and B is bigger but colder.
What makes a star brighter?There are several factors that determine the luminosity of a star namely, the size, temperature, distance and magnitude. The two main factors that determine luminosity of a star when the distance is the same are temperature and size.
When the temperature of a Star is higher than the other with equal distance from the earth the star is brighter than that with lower temperature. Also, when the size of a star is bigger, it possesses a higher surface area to absorb light and energy. This makes A and B as bright as the other.
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what is the angular momentum of a hydrogen atom in (a) a state and (b) a state? give your answers as a multiple of
According to the given statement [tex]\sqrt{2h}[/tex] and [tex]2\sqrt{3h}[/tex] and is the angular momentum of a hydrogen atom.
What does the word "momentum" mean?Momentum may be viewed as a body's "power" while it is moving, or the amount of force it can exert on another body. For instance, a slow-moving bowling ball might have the same acceleration as a baseball being thrown fast.
Briefing:
The angular momentum of a hydrogen atom can be defined as:
[tex]L=\sqrt{l(l+1)}h,[/tex]
where l represents the orbital quantum number which defines the subshells s, p, d, f.
The 4p subshell has an orbital quantum number of 1 . This means that the angular momentum according to equation (I) equals to:[tex]L=\sqrt{1(1+1)}h=\sqrt{2h}[/tex]The 5f subshell has an orbital quantum number of 3 . This means that the angular momentum according to equation (I) equals to:[tex]L=\sqrt{3(3+1)}h=\sqrt{12}h=2\sqrt3h[/tex]To know more about momentum visit:
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if the frequency is doubled to 80 khz and the current is kept the same, what will be the peak out-of-phase voltage?
The peak out of phase voltage also becomes doubled with increase in frequency .
The frequency of the incident light must exceed a particular frequency a for photoemission to occur cut-off frequency .No matter how bright the light is, photoemission would not occur if the frequency were lower than that. If the initial frequency is assumed to be higher than the cut-off frequency, doubling the frequency will also result in photoemission and non-zero photocurrent.The intensity, on the other hand, is a measurement of the quantity of incident photons per second per unit area. If the frequency is greater than the cut-off frequency, which we have already assumed, then doubling its value will also double the probability of collision with atoms. Frequency=80KHz with current constant makes no effect due to independent factor of intensity.To study more about probability of collision -
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Give an example of a sport where shoes with a high coefficient of friction would be advantageous.
An example of sport where shoes with a high coefficient of friction would be advantageous : rugby. This is played in deep mud and needs a high level of friction so they don't slip, so boots for this condition are big.
Why shoes of rugby players shoes have high coefficient of friction?Rugby players play in deep mud so they need a high level of friction so that they do not slip and fall. Therefore, boots for this condition are also big and rounded studs so they stick and sink into the ground and give grip.
In sports, high friction avoids slipping and permits grip of a surface better. This permits faster movements but, if the friction is excessive, overload is produced in joints and injuries may occur.
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two straight rods 50-cm long with axes 1.5-mm apart in a current balance carry currents of 15 a each in opposite directions. what mass must be placed on the upper rod to balance the magnetic force of repulsion?
After doing the equation the total mass is 1.53×10^-3kg .
What is the magnetic force of attraction?
Similar poles or charges will typically repel one another. Thus, the two magnets will push against one another. Repulsion is the name given to a force that causes objects to move apart from one another.
between two or more comparable or similar charges there is a force. Similar charges are attracted to one another. Charges that share a similar appearance separate. Chemical bonding is characterized by repulsive forces.
Create a formula for the magnetic force to equal the normal force, and then enter the necessary values into the expression to obtain the mass.
FN=F
mg=µo I1 I2 L÷2πr
m=µo I1 I2 L÷2πrg
= 4π×10^-7T-m/A (15A) (15A)(0.50m)÷2π(0.0015m)(9.8m/s²)
= 1413÷0.0923×10^-7
= 1.53×10^-3kg
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A carousel with a radius of 4.0 m spins at 7.2 revolutions per minute. What centripetal force would a child with a mass of 45 kg feel when standing 1.0 m from the outer edge of the carousel
The centripetal force that a child with a mass of 45 kg feel when standing 1.0 m from the outer edge of the carousel is 127.9 N.
What is the centripetal force of the child?
The centripetal force of the child is the inward force that must maintain the circular motion of the child at the given point in the circular axis without falling.
Mathematically, the formula for centripetal force is given as;
Fc = ma
where;
m is the mass of the childa is the centripetal acceleration of the childThe centripetal acceleration of the child is calculated as;
a = v²/r
where;
v is the linear speed of the childr is the radius of the circular path from point of the childa = (ω²r²) / r
a = ω²r
where;
ω is angular speed of the childr is the distance from the circle center to point of the child = 4 m + 1 m = 5 mω = 7.2 rev/min = 7.2 rev/min x 2π rad/rev x 1 min/60s = 0.754 rad/s
Fc = ma
Fc = m(ω²r)
Fc = 45(0.754² x 5)
Fc = 127.9 N
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1. What is the atomic mass of the new atom?
2. What is the atomic number of the new atom?
3. What is the symbol of the new atom?
4. What type of decay is demonstrated here?
1. The atomic mass of the new atom be 223. Option (d) is correct.
2. The atomic number of the new atom be 88. Option (g) is correct.
3. The symbol of the new atom be Ra. Option (e) is correct.
4. Beta decay is demonstrated here. Option (c) is correct.
What is Beta decay?A proton inside the radioactive sample's nucleus can change into a neutron or vice versa through a process known as beta decay. Because of processes like beta decay and alpha decay, the radioactive sample's nucleus is able to get as close as practical to the optimum neutron/proton ratio.
A beta particle, which can either be an electron or a positron, is released by the nucleus during this process. Think about the potential for a proton or neutron to decay into another particle. The production of the electron and positron adheres to the law of charge conservation. Beta-decay is the outcome of weak interaction.
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Max is moving boxes in his house from one room to another. Max has
two different floor surfaces in his house, one carpeted and the other wood
floor. What can you correctly conclude about moving the boxes in Max's
house?
A.The boxes will slide more easily on the carpeted floor due to lower friction.
B.The boxes will slide more easily on the wood floor due to higher friction.
C. The boxes will slide more easily on the wood floor due to lower friction
D.The boxes will slide more easily on the carpeted floor due to higher friction.
The conclusion about moving the boxes in Max's house is as follows: The boxes will slide more easily on the carpeted floor due to lower friction (option A).
What is friction?Friction is the force that resists the relative motion or tendency to such motion of two bodies in contact.
According to this question, Max is moving boxes in his house from one room to another. Max has two different floor surfaces in his house, one carpeted and the other wood floor.
The carpeted floor will have a lesser friction than the wooden floor when moving the object. This makes it easier to move the boxes on the carpeted floor.
Therefore, option A is correct.
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Which of the following is not a benefit of stressing
a. Poor circulation
b. Increase speed and power
c.Increased flexibility
d. Minimized change injuries
Poor circulation is not a benefit of stretching.
How many minutes of stretching should a person perform before participating in physical activities?
Stretching for 5 to 10 minutes is probably enough for most activities. It's important, however, to adequately stretch all the muscles you'll be using. Three benefits of stretching before a workout include increased blood flow.
What are the 5 benefits of stretching?
Improve your performance in physical activities.Decrease your risk of injuries.Help your joints move through their full range of motion.Increase muscle blood flow.Enable your muscles to work most effectively.Improve your ability to do daily activities.Which benefit comes with flexibility?
Activities that lengthen and stretch muscles can help you prevent injuries, back pain, and balance problems. A well-stretched muscle more easily achieves its full range of motion.
Thus, poor circulation is the correct option.
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1. jupiter has a mass approximately 300 times greater than earth's and a radius about 11 times greater. how will the gravitational acceleration at the surface of jupiter compare to that at the surface of the earth?
surface gravity formula
[tex]g=\frac{GM}{r^{2} }[/tex]
[tex]g[/tex] is the surface gravity in m/s²
[tex]G[/tex] is the gravitational constant 6.67408x10⁻¹¹ m³/kgs²
[tex]M[/tex] is the mass of the object in kg
[tex]r[/tex] is the radius of the object in m
The Earth’s mass is 5.972x10²⁴kg,
Jupiter’s mass is 1.898x10²⁷ kg,
the Earth’s radius is 6371 km,
Jupiter’s radius is 69911 km
Calculation for earth's surface gravity[tex]g=\frac{6.67408X10^{-11}X5.972X10^{24} }{(6.371X10^{6} )^{2} }[/tex]
[tex]g=9.82 m/s^{2}[/tex]
Calculation for Jupiter's surface gravity[tex]g=\frac{6.67408X10^{-11}X1.898X10^{27} }{(6.9911X10^{7} )^{2} }[/tex]
[tex]g=25.92 m/s^{2}[/tex]
conclusion
[tex]\frac{25.92}{9.82} = 2.63[/tex]
the surface gravity of Jupiter is 2.63 times that of Earth.
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A particle is moving along the x axis such that its position is given by x² =3t²-16t+8. What are the velocity and acceleration of the particle at t = 4s? At what time is the particle stationary?
Answer:
Below
Explanation:
Usually, position is given by x(t) =.......
if x^2 = 3t^2 - 16t+ 8 then
x = ( 3t^2 - 16t + 8)^1/2 ( I do not think this is what you want....but it IS what was posted)
Velocity will be given by the derivative : (3t-8) / ( 3t^2-16t+ 8)^1/2
at t = 4 this equals an imaginary number....
so I think your question equation is incorrect
The answer above this one used x(t) = 3t^2-16t+8 as the position function and is likely the correct way to do it
then velocity = dx/dt = 6t-16 at t = 4 this is 8
the particle is stationary when this = 0 at t = 16/6 = 2.67 s (NOT 4s as posted in the other 'verified' answer !!!!!)
Acceleration = dv/dt = 6
at t= 4 the velocity would be 8 units/s
and the accel would be 6 units/s^2
and when v= 0 would occur at t = 2.67 s
The mean weight of 500 college students is 70 kg and the standard deviation is 3 kg. Assuming that the weight is normally distributed, students who weigh between 60 kg and 75 kg is 476.
It is true that when weights is normally distributed, students who weigh between 60 kg and 75 kg is 476.
Mean is the average of given observations and we can calculate mean by dividing sum of observation by the total number of observation.
A standard deviation shows how much data is dispersed in relation to mean. Low deviation indicates that data are clustered and high deviation means data are scattered.
Mean weight is 70 kg and standard deviation is given 3 kg.
α1 = 75 - 70 / 3 = 1.67
α2 = 60- 70/3 = 3.33
So, P( α2- α1) = 0.9375- (1- 0.9666)
= 0.9371
The number = 500 ×0.9371
= 467
So, the statement is true.
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Question 58
Which of the following numbers correctly express "thirty two micro meter" in scientific notation?
3.2 x 10-7 m
3.2 x 10-6 m
C) 3.2 x 10.⁹ m
3.2 x 10-8 m
3.2 x 10-5 m
In scientific notation "thirty two micro meter" can be expressed as 3.2 x 10^-5 m.
What is a micrometer?Micrometer, often known as micron, is a unit of length in the metric system equal to 0.001 mm, or roughly 0.000039 inch. m is its symbol.
The micrometer is frequently used to gauge the size of small items like colloidal particles and bacteria. Micrometers are also used to describe extremely small distances, like the infrared radiation's wavelengths.
So, 1 micrometer = 10^-6 meter.
∴ thirty two micrometer = 32 × 10^-6 meter = 3.2 × 10^-5 meter.
Hence, in scientific notation "thirty two micro meter" can be expressed as 3.2 x 10^-5 m.
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2 The speed-time graph shows the movement of a car.
speed
0
0
T
time
Which feature of the graph represents the distance travelled by the object whilst
moving at a constant speed?
A
area S
B
area S+ area T
C
area T
D the gradient at point X
Area T represents the distance travelled by the object whilst moving at a constant speed. Option (C) is correct.
What is speed?The distance an object travels in a unit of time is its speed. Speed is a scalar quantity since it has simply magnitude and no direction. SI unit of speed is meter per second.
Hence, mathematically:
Speed = distance travelled/time interval.
Distance travelled = speed × time interval.
In the given graph, area T represents constant speed × time interval. Hence, area T is equal to the distance travelled by the object moving at a constant speed.
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what is the spring constant of a spring that stores 25 j of elastic potential energy when compressed by 7.5 cm?
Answer:
8. 9×10³N/m
Explanation:
k=2U /x²
= 2(25J) / 0.075m²
=8. 9×10³N/m