Answer;
2.6
Explanation;
Formular for mechanical advantage is length of the slope divided by the height of the inclined plane.[tex]1.85 \div 0.72 = 2.56[/tex]Approximately 2.6A pail in a water well is hoisted by means of a frictionless winch, which consists of a spool and a hand crank. When Jill turns the winch at her fastest water-fetching rate, she can lift the pail the 28.0 m to the top in 11.0 s. Calculate the average power supplied by Jill's muscles during the upward ascent. Assume the pail of water when full has a mass of 7.30 kg.
Answer:
182.28 W
Explanation:
Here ,
m = 7.30 Kg
distance , d= 28.0 m
time , t = 11.0 s
average power supplied = change in potential energy/time
average power supplied = m×g×d/time
average power supplied = 7.30×9.81×28/11
average power supplied = 182.28 W
the average power supplied is 182.28 W
What is the water cycle ?
Answer:
The water cycle shows the continuous movement of water within the Earth and atmosphere. ... Liquid water evaporates into water vapor, condenses to form clouds, and precipitates back to earth in the form of rain and snow. Water in different phases moves through the atmosphere (transportation).
Explanation:
It's the water cycle.
A waterbed has a force of 1300N on the floor. It exerts 347 Pa of pressure. What is the area of the waterbed?
Answer:
Pressure = Force/Area
347 = 1300/Area
Area = 1300/347
area= 3.47m2
Answer:
I hope the above pic will help you
I will always help you understanding your assingments have a great day
#Captainpower
1. A 15 kg chair initially at rest on a horizontal floor requires 125 N to set it in motion, Ong
the chair is in motion, a 95 kg force keeps it moving at constant veloclty,
a Find the coefficient of static friction between the chair and the floor,
Answer:
μ = 0.849
Explanation:
In order to solve this problem we must remember that the friction force is defined as the product of the coefficient of friction by the normal force. And normal force is defined as the component of force in the opposite direction to the weight of the body (chair).
As in the y axis there is no movement we can say that the sum of the forces on the chair is equal to zero.
∑Fy = 0
[tex]N-W=0[/tex]
where:
N = normal force [N] (units of Newtons)
W = weight of the chair = m*g [N]
m = mass = 15 [kg]
g = gravity acceleration = 9.81 [m/s²]
[tex]N=m*g\\N=15*9.81\\N=147.15 [N][/tex]
Now the key to solving this problem is to understand that we start applying force on the horizontal component until the chair starts to move at this moment the friction component is calculated with the static friction coefficient. As the chair doesn't move we can say that the sum of force in the horizontal direction is equal to zero.
∑Fx = 0
[tex]F -f_{force} = 0[/tex]
F = force applied = 125 [N]
fforce = friction force = μ*N
μ = friction coefficient (static)
N = normal force = 147.15 [N]
[tex]125-u*147.15=0\\u = 125/147.15\\u = 0.849[/tex]
Consider a car engine running at constantspeed. That is, the crankshaft of the en-gine rotates at constant angular velocity whileeach piston moves back-and-forth in its cylin-der according to the rules of simple harmonicmotion.2030 rpm6.95 cmSuppose the two extremal positionsxmaxandxminof a piston are 6.95 cm from eachother.When the crankshaft of the engine rotatesat 2030 rpm (revolutions per minute), what isthe maximal speed|v|maxof the piston?Answer in units of m/s.
Answer:
The value is [tex]|v| = 7.39 \ m/s[/tex]
Explanation:
From the question we are told that
The angular speed is [tex]w = 2030 \ rpm = \frac{2030 * 2 * \pi }{ 60} = 212.61 \ rad/s[/tex]
The distance between the minimum and maximum external position is [tex]d = 6.95 \ cm = 0.0695 \ m[/tex]
Generally the amplitude of the crank shaft is mathematically represented as
[tex]A = \frac{d}{2}[/tex]
=> [tex]A = \frac{0.0695}{2}[/tex]
=> [tex]A = 0.03475 \ m[/tex]
Generally the maximum speed of the piston is mathematically represented as
[tex]|v| = A * w[/tex]
=> [tex]|v| = 0.03475 * 212.61[/tex]
=> [tex]|v| = 7.39 \ m/s[/tex]
19. What energy transformation occurs in a battery?
A. chemical energy to thermal energy
C. electric energy to chemical energy
B. chemical energy to electric energy
D. thermal energy to chemical energy
i think correct answer is b
Answer:
B.chemical energy changes to electric energy.Explanation:
I hope l helped you. ❤❤if an atom was a scale, in which the nucleus is the size of an apple the electron.....
Answer:
the nucleus is the size of an apple, approximately 5 cm of radius e, the atom has a radius of R = 5 cm 104 = 50000 cm = 50 km
Explanation:
In the Rutherford experiments it was proved that the atomic nucleus has the volume 10-4 the volume of the atom.
If we make a scale design in which the nucleus is the size of an apple, approximately 5 cm of radius e, the atom has a radius of R = 5 cm 104 = 50000 cm = 50 km
This shows that almost the entire volume of the atom is empty.
A double-slit interference pattern is created by two narrow slits spaced 0.21 mm apart. The distance between the first and the fifth minimum on a screen 61 cm behind the slits is 6.2 mm What is the wavelength of the light used in this experiment?
Answer:
[tex]\lambda =533.6 nm [/tex]
Explanation:
the slits spacing, d = 0.21 mm
distance of screen, D = 61 cm
The condition for minima is given as
[tex]dsin(\theta) = \left ( n+\frac{1}{2} \right )\lambda[/tex]
So, first minima, n = 0
[tex]dsin(\theta_1) = \frac{1}{2}\lambda[/tex]
fifth minima, n = 4
[tex]dsin(\theta_5) = \frac{9}{2}\lambda[/tex]
[tex]d(sin(\theta_5) -sin(\theta_1))= 4\lambda[/tex]
For small angle
[tex]d(tan(\theta_5) -tan(\theta_1))= 4\lambda[/tex]
From the figure:
[tex]d(\frac{y_5}{D}-\frac{y_1}{D})= 4\lambda[/tex]
[tex]\frac{d}{D} (y_5-y_1) = 4\lambda[/tex]
[tex]\lambda = \frac{d}{4D} (y_5-y_1)[/tex]
[tex]\lambda = \frac{0.021}{4(61)} (6.2 \times 10^{-3})[/tex]
[tex]\lambda =533.6 nm[/tex]
"533.5 nm" would be the wavelength of the light used in this experiment.
According to the question,
Slits spacing,
d = 0.21 mmDistance of screen,
D = 61 cmThe condition for minima is given as:
→ [tex]d (sin \Theta) = (n+\frac{1}{2} ) \lambda[/tex]
So,
1st minima, n = 0
→ [tex]d sin(\Theta_1)= \frac{1}{2} \lambda[/tex]
5th minima, n = 4
→ [tex]d (sin (\Theta_5) - sin (\Theta_1) = 4 \lambda[/tex]
For small angle,
→ [tex]d (tan (\Theta_5) - tan (\Theta_1) = 4 \lambda[/tex]
From the figure, we get
→ [tex]d(\frac{y_5}{D} - \frac{y_1}{D} )= 4 \lambda[/tex]
[tex]\frac{d}{D} (y_5 -y_1) = 4 \lambda[/tex]
[tex]\lambda = \frac{d}{4D}(y_5-y_1)[/tex]
[tex]= \frac{0.021}{4\times 61} (6.2\times 10^{-3})[/tex]
[tex]= 533.6 \ nm[/tex]
Thus the above answer is correct.
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10) The coil of transformer is coated by enamel why
Answer:
Enamel is used to coat the wires, it is the thinnest possible insulator. The coils are made up of large number of turns and enamel makes it possible to cram a lot of wires (coils) in much smaller space.
Question 10 of 10
In the photoelectric effect, an electric current forms when light strikes a metal
surface. Which statement explains what causes the current?
O A. Electrons flow from one atom to another because the light acts as
a wave.
O B. The light causes electrons to flow in different directions within an
atom because light acts as a wave.
O C. Electrons are destroyed when light strikes a surface because the
light acts as particles.
D. Electrons are knocked off the surface when light strikes it because
the light acts as particles.
Explanation:
D. I hope i helped it should be right but if it isn't my bad
In the photoelectric effect, an electric current forms when light strikes a metal surface because electrons are knocked off the surface when light strikes it because the light acts as particles, The correct option is D.
What is the photoelectric effect?
It is the process of emission of electrons from the material because of absorption of electromagnetic radiation in form of photons of light waves.
The photoelectric effect explains the particle behavior of the light waves.
The photoelectric effect is responsible when electrons are knocked off the surface when light strikes it because the light acts as particles.
Learn more about the photoelectric effect
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how do you determine half life
Answer:
T= In(2)/___ =__ In(2)
Explanation:
the equation pices arnt on the keyboard so i put the blanks
sorry
jope it helps some. Have a good day ir night! :)
Power lines often carry high voltages. For example, a single power line may carry 100,000 volts. An outlet in a home only carries 120-240 volts. What accounts for this difference in voltage?
- Voltage is decreased due to traveling long distances.
- Voltage is decreased by local transformers.
- Voltage is decreased as it is lost to the environment.
Answer: The second one? C.
Answer:
B. - Voltage is decreased by local transformers.
Explanation:
edge 2021 beep boop
1. A girl drops a ball off the roof of her house. It takes the ball 2 seconds to hit the ground. How tall
is the house?
If the acceleration constant..
you can use the formula s = ut + 1/2at²
Known that :
s = ?
u = 0
t = 2s
a = 10ms-²
Then you can apply the formula
s = ut + 1/2at²
s = 0 + 1/2(10)(2)²
s = 5 × 4
s = 20m
Answer : 20m
Explanation :
The gravity can be 9,8 or 10. Also im not sure how people teach you but in my school, if the ball goes down the gravity is positive and not negative thats why i put 10ms-² and not -10ms-²
s = displacement/distance
u = initial speed
a = acceleration
t = time
sorry if im wrong
The space shuttle releases a satellite into a circular orbit 630 km above the Earth.
How fast must the shuttle be moving (relative to Earth's center) when the release occurs?
Answer:
7,539 m/s
Explanation:
Let's use this equation to find the gravitational acceleration of this space shuttle:
[tex]\displaystyle g=\frac{GM}{r^2}[/tex]We know that G is the gravitational constant: 6.67 * 10^(-11) Nm²/kg².
M is the mass of the planet, which is Earth in this case: 5.972 * 10^24 kg.
r is the distance from the center of Earth to the space shuttle: radius of Earth (6.3781 * 10^6 m) + distance above the Earth (630 km → 630,000 m).
Plug these values into the equation:
[tex]\displaystyle g=\frac{(6.67\cdot 10^-^1^1 \ Nm^2kg^-^2)(5.972\cdot 10^2^4 \ kg)}{[(6.3781\cdot 10^6 \ m)+(630000 \ m)]^2}[/tex]Remove units to make the equation easier to read.
[tex]\displaystyle g=\frac{(6.67\cdot 10^-^1^1 )(5.972\cdot 10^2^4 )}{[(6.3781\cdot 10^6)+(630000 )]^2}[/tex]Multiply the numerator out.
[tex]\displaystyle g=\frac{(3.983324\cdot 10^1^4)}{[(6.3781\cdot 10^6)+(630000 )]^2}[/tex]Add the terms in the denominator.
[tex]\displaystyle g=\frac{(3.983324\cdot 10^1^4)}{[(7008100)]^2}[/tex]Simplify this equation.
[tex]\displaystyle g=8.11045189 \ \frac{m}{s^2}[/tex]The acceleration due to gravity g = 8.11045189 m/s². Now we use the equation for acceleration for an object in circular motion which contains v and r.
[tex]\displaystyle a = \frac{v^2}{r}[/tex]a = g, v is the velocity that the space shuttle should be moving (what we are trying to solve for), and r is the radius we had in the previous equation when solving for g.
Plug these values into the equation and solve for v.
[tex]\displaystyle 8.11045189 \ \frac{m}{s^2} = \frac{v^2}{7008100 \ m}[/tex]Remove units to make the equation easier to read.
[tex]\displaystyle 8.11045189 = \frac{v^2}{7008100}[/tex]Multiply both sides by 7,008,100.
[tex]56838857.89=v^2[/tex]Take the square root of both sides.
[tex]v=7539.154985[/tex]The shuttle should be moving at a velocity of about 7,539 m/s when it is released into the circular orbit above Earth.
A street bridge is 5.5m long if the linear expansion of steel is 0.00001 oc How much will it expand when temperatures is by 10oc? Give answer in Cm
Answer:
[tex]l_o=550.055\ cm[/tex]
Explanation:
Given that,
Length of a street bridge, l = 5.5 m
The coefficient of bridge, [tex]\alpha =0.00001 ^0 C[/tex]
We need to find how much will it expand when temperatures is by 10°C.
The change in length per unit original length is given by :
[tex]\dfrac{\Delta l}{l}=\alpha \Delta T\\\\\Delta l = l\alpha \Delta T\\\\=5.5\times 0.00001 \times 10\\\\\Delta l=0.00055\\\\(l_o-l)=0.00055\\\\l_o=0.00055+5.5\\\\=5.50055\ m\\\\l_o=550.055\ cm[/tex]
Hence, the length will expanded 550.055 cm.
The ancestors of horses possess feet with five digits . Over time with the development of grassland the digits fused and former hooves . What evolutionary advantage did this transformation serve
Answer:
It enabled them to run faster from predators.
Explanation:
The evolution of hooves from a five-digit feet enabled horses to run faster from predators as well as support their larger weights and longer legs. Hope this helped and have an awesome day! :)
It enabled them to run faster from predators. ]
Explanation: The evolution of hooves from a five-digit feet enabled horses to run faster from predators as well as support their larger weights and longer legs.
Assume that, when we walk, in addition to a fluctuating vertical force, we exert a periodic lateral force of amplitude 25 NN at a frequency of about 1 HzHz. Given that the mass of the bridge is about 2000 kgkg per linear meter, how many people were walking along the 144-mm-long central span of the bridge at one time, when an oscillation amplitude of 75 mmmm was observed in that section of the bridge
Complete Question
The complete question is shown on the first uploaded image
Answer:
Explanation:
From the question we are told
The amplitude of the lateral force is [tex]F = 25 \ N[/tex]
The frequency is [tex]f = 1 \ Hz[/tex]
The mass of the bridge per unit length is [tex]\mu = 2000 \ kg /m[/tex]
The length of the central span is [tex]d = 144 m[/tex]
The oscillation amplitude of the section considered at the time considered is [tex]A = 75 \ mm = 0.075 \ m[/tex]
The time taken for the undriven oscillation to decay to [tex]\frac{1}{e}[/tex] of its original value is t = 6T
Generally the mass of the section considered is mathematically represented as
[tex]m = \mu * d[/tex]
=> [tex]m = 2000 * 144[/tex]
=> [tex]m = 288000 \ kg[/tex]
Generally the oscillation amplitude of the section after a time period t is mathematically represented as
[tex]A(t) = A_o e^{-\frac{bt}{2m} }[/tex]
Here b is the damping constant and the [tex]A_o[/tex] is the amplitude of the section when it was undriven
So from the question
[tex]\frac{A_o}{e} = A_o e^{-\frac{b6T}{2m} }[/tex]
=> [tex]\frac{1}{e} =e^{-\frac{b6T}{2m} }[/tex]
=> [tex]e^{-1} =e^{-\frac{b6T}{2m} }[/tex]
=> [tex]-\frac{3T b}{m} = -1[/tex]
=> [tex]b = \frac{m}{3T}[/tex]
Generally the amplitude of the section considered is mathematically represented as
[tex]A = \frac{n * F }{ b * 2 \pi }[/tex]
=> [tex]A = \frac{n * F }{ \frac{m}{3T} * 2 \pi }[/tex]
=> [tex]n = A * \frac{m}{3} * \frac{2\pi}{25}[/tex]
=> [tex]n = 0.075 * \frac{288000}{3} * \frac{2* 3.142 }{25}[/tex]
=> [tex]n = 1810 \ people[/tex]
What is unique regarding the abdominal muscle when is compared to other muscle in the body?
(A) it is a very large muscle
(B) it does not develop easily
(C) it can move the body either from the ribcage or the pelvis.
(D) it can get injured easily if you perform a lot os repetitions.
(E) none of the above
a 2 kg block is attached to a horizontal ideal spring with a spring constant 200N/m. when the
If a sinusoidal electromagnetic wave with intensity 18 W/m2 has an electric field of amplitude E, then a 36 W/m2 wave of the same wavelength will have an electric field of amplitude?
a. 4E
b. 2 underroot 2E
c. 2E
d. underroot E
Answer:
The correct option is D
Explanation:
From the question we are told that
The intensity of the first electromagnetic wave is [tex]I = 18 \ W/m^2[/tex]
The amplitude of the electric field is [tex]E_{max}_1 =A[/tex]
The intensity of the second electromagnetic wave is [tex]I = 36 \ W/m^2[/tex]
Generally the an electromagnetic wave intensity is mathematically represented as
[tex]I = \frac{1}{2} * \epsilon_o * c * E_{max}^2[/tex]
Looking at this equation we see that
[tex]I \ \ \alpha \ \ E^2_{max}[/tex]
=> [tex]\frac{I_1}{I_2} = [ \frac{ E_{max}_1}{ E_{max}_2} ] ^2[/tex]
=> [tex]E_{max}_2 = \sqrt{\frac{x}{y} } * E_{max}_1[/tex]
=> [tex]E_{max}_2 = \sqrt{\frac{36}{18} } * E[/tex]
=> [tex]E_{max}_2 = \sqrt{2 } E[/tex]
Why did scientist struggle for thousands of years to accurately describe the solar system
Answer: C- The planets appeared to move backward in the sky occasionally.
A ball of mass 4kg moving with a velocity of 20m/s collides with another ball of mass 15kg moving with a velocity of 15m/s in the same direction. Calculate the velocity of the 5kg ball if the collision is perfectly inelastic.
Answer:
velocity = 16.05 m/s
Explanation:
inelastic collision formula:
m1u1 + m2u2 = (m1 + m2)v
m1 = 4kg
u1 = 20m/s
m2 = 15kg
u2 = 15m/s
find v ?
m1u1 + m2u2 = (m1 + m2)v
(4×20) + (15×15) = (4+15)v
80 + 225 = 19v
305 = 19v
19v = 305
v = 305/19
v = 16.05 m/s
giving brainiest to correct answer.
Imagine a 0.2 kg ball moving at 5 m/s colliding with a 0.3 kg ball moving at 2 m/s in the same direction. After the collision the 0.2 kg green ball stops moving and the 0.3 kg purple ball continues moving in the same direction.
giving brainiest to correct answer.
Answer:
[tex]5.33\ m/s[/tex]
Explanation:
[tex]We\ know\ that,\\Momentum=Mass*Velocity\\p=mv\\Hence,\\Lets\ first\ consider\ the\ case\ of\ the\ two\ balls\ 'Before\ Collision':\\\\Mass\ of\ the\ green\ ball=0.2\ kg\\Initial\ Velocity\ of\ the\ green\ ball=5\ m/s\\Initial\ Momentum\ of\ the\ green\ ball=5*0.2=1\ kg\ m/s\\\\Mass\ of\ the\ pink\ ball=0.3\ kg\\Initial\ Velocity\ of\ the\ pink\ ball=2\ m/s\\Initial\ Momentum\ of\ the\ pink\ ball=0.3*2=0.6\ kg\ m/s\\\\Total\ momentum\ of\ both\ the\ balls\ 'Before\ Collision'=1+0.6=1.6\ kg\ m/s[/tex]
[tex]Hence,\\Lets\ now\ consider\ the\ case\ of\ the\ two\ balls\ 'After\ Collision':\\\\Mass\ of\ the\ green\ ball=0.2\ kg\\Final\ Velocity\ of\ the\ green\ ball=0\ m/s\\Final\ Momentum\ of\ the\ green\ ball=0\ kg\ m/s\\\\Mass\ of\ the\ pink\ ball=0.3\ kg\\Final\ Velocity\ of\ the\ pink\ ball=v\ m/s\\Final\ Momentum\ of\ the\ pink\ ball=0.3*v=0.3v\ kg\ m/s\\\\Total\ momentum\ of\ both\ the\ balls\ 'After\ Collision'=0+0.3v=0.3v\ kg\ m/s[/tex]
[tex]As\ we\ know\ that,\\Through\ the\ law\ of\ conservation\ of\ momentum,\\In\ an\ isolated\ system:\\Total\ Momentum\ Before\ Collision=Total\ Momentum\ After\ Collision\\Hence,\\1.6=0.3v\\v=\frac{1.6}{0.3}=5.33\ m/s[/tex]
If forces acting on an object are unbalanced, the object could experience a change in ________.
mass, speed, or direction
negative acceleration or mass
direction, mass, or both
speed, direction, or both
D) Speed, direction, or both
Mass doesn’t just CHANGE like that.
The skateboarder weighs 75 kilogram. Calculate the potential energy of the skateboarder sliding on the track when his height above the ground is 5 meters. (Assume that acceleration due to gravity is 9.81m/s2.)
Answer:F(of gravity) = MA
F(normal force) = MA * cos(angle)
F = 72 * 9.81 * cos28
Don't have a calculator, so can't really do all the math right there. So just plug that in
Explanation:
i dont really know
Potential energy of a body is the product of its mass, height and acceleration due to gravity. The potential energy of 75 Kg skateboard sitting at 5 meter high is 3675 J.
What is potential energy?
Potential energy of a body is generated by virtue of the position of the body. It is dependent on the mass of the body and the height at which it is placed and the acceleration due to gravity.
Whereas kinetic energy of an object is a form of energy generated by virtue of the motion of the object. Kinetic energy is dependent on the mass and velocity of the body.
It is given that the mass of the object is 75 Kg and the height from the surface is 5 m. Acceleration due to gravity on earth is 9.8 m/s².Thus, the potential energy is calculated as follows:
p = m g h
= 75 Kg × 9.8 m/s² × 5 m
= 3675 J.
Therefore, the potential energy of the skateboard is 3675 J.
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A high-resistance material is used as an insulator between the conductors of a length of coaxial cable. The resistance material, which forms a hollow tube, has an inner radius a and an outer radius b, and the insulator provides a resistance R between the conductors. If a second insulator, made of the same material and having the same length, is made with double both the inner radius and the outer radius of the first, what resistance would it provide between the conductors
This question is incomplete, the complete question is;
A high-resistance material is used as an insulator between the conductors of a length of coaxial cable. The resistance material, which forms a hollow tube, has an inner radius a and an outer radius b, and the insulator provides a resistance R between the conductors. If a second insulator, made of the same material and having the same length, is made with double both the inner radius and the outer radius of the first, what resistance would it provide between the conductors
a) (In2)R
b) 4R
c) R/(In2)
d) 2R
e) R
Answer: Option e) R is the correct answer.
Explanation:
Given that;
Inner radius = a
Outer radius = b
Conical Cylinder
∫dR = ∫(edr/2πrL)
R = e/2πL In e |ᵇₐ
R = e/2πL In(b/a) ------------- let this be equation 1
Taking a look at the second cone
a' = 2a
b' = 2a
R' = e/2πL In(2b/2a)
{L = L'}
R' = e/2πL In(b/a) -------let this be equation 2
now lets compare the two equation
R = e/2πL In(b/a)
R' = e/2πL In(b/a)
so R' = R
Therefore Option e) R is the correct answer.
As an astronaunt travels from the surface of the earth to a postion that is four times
as far away from the center of the earth, the astronaut's
a) mass decreases
b)
mass remains the same
c) weight increases
d) weight remains the same
Answer: mass remains the same
Explanation:
My teacher gave me the answer
As an astronaut travels from the surface of the earth to a position that is four times as far away from the center of the earth, the astronaut's:
B. Mass remains the sameAccording to the given question, we can see that an astronaut is on a journey to a new location which is four times further from the center of the earth. We need to find out if there is a change to the mass of the astronaut.
As a result of this, we can see that the mass of the astronaut remains the same as he travels to a position which is four times further from the center of the earth, because the gravitational forces are the same.
Therefore, the correct answer is option B
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Define specific vision??
Answer:an inspirational statement of an idealistic emotional future
Explanation:
I don't know if it's right tho
Answer:
The document that state tge currentand future objectives of an organization.
An astronaut floating at rest in space throws a wrench in one direction and subsequently recoils back with a velocity in the opposite direction. Which of the following statements is/are true?
I. The velocity of the wrench is equal and opposite to the velocity of the astronaut.
Il. The momentum of the wrench is equal and opposite to the momentum of the astronaut.
III. The impulse applied to the wrench is equal and opposite to the impulse applied to the astronaut
a) ll and ill only
b) I only II only
c) I, II, and III
d) I and Il only
Answer:
a) ll and Ill only
Explanation:
Let the mass of the wrench = m
and the mass of the astronaut = M
Initially, the velocity of the astronaut and wrench are zero.
The astronaut throws the wrench in one direction and subsequently recoils back with a velocity in the opposite direction.
Let v and V be the velocity of the wrench and the velocity of the astronaut respectively.
In space, there is no external force acting, the momentum must be conserved.
So, m(0)+M(0)=m(v)+M(V)
So, 0=mv+MV
[tex]\Rightarrow mv=-MV[/tex] ...(i)
Here, the momentum of the wrench = mv, and the momentum of the astronaut= MV. The negative sign showing that both the momentum are in opposite direction.
Therefore, the momentum of the wrench is equal and opposite to the momentum of the astronaut.
According to Newton's second law, the rate of change of momentum = applied force.
Let it take [tex]\Delta t[/tex] seconds to change the momentum.
So, for the wrench
[tex]m(v-0)/\Delta t= F_w \\\\\Rightarrow m(v-0)=F_w\Delta t \\\\\Rightarrow mv=F_w\Delta t \cdots(ii)[/tex]
Here, [tex]F_w\Delta t[/tex] is the impulse applied to the wrench.
Similarly, for the astronaut
[tex]M(-V-0)/\Delta t= F_a[/tex] [negative sign (-V) for opposite direction]
[tex]\Rightarrow M(-V-0)=F_a\Delta t \\\\\Rightarrow -MV=F_a\Delta t[/tex]
Here, [tex]F_a\Delta t[/tex] is the impulse applied to the astronaut.
So, the impulse on the astronaut.
By using equations (i) and (ii)
[tex]F_a\Delta t=F_w\Delta t[/tex]
Therefore, the impulse applied to the wrench is equal and opposite to the impulse applied to the astronaut.
Hence, option (a) is correct.
A 100 kg gymnast comes to a stop after tumbling. Her feet do 5,000 J of work to stop her.
Which of the following was the girl's velocity when she began to stop?
Answer:10 m/s
Explanation:
A 100 kg gymnast comes to a stop after tumbling. Her feet do 5,000 J of work to stop her. The girl's velocity when she began to stop is 10 m/sec.
What is velocity?When an item is moving, its velocity is the rate at which its direction is changing as seen from a certain point of view and as measured by a specific unit of time. Velocity is vector quantity.
Uniform motion an object is said to have uniform motion when object cover equal distance in equal interval of time within exact fixed direction. For a body in uniform motion, the magnitude of its velocity remains constant over time. Here in the question velocity is changing by using work energy theorem we have,
work done = change in kinetic energy
5000 = (.5).m.v² , where v is velocity.
5000 = (.5).100.v²
v = 10 m/sec
A 100 kg gymnast comes to a stop after tumbling. Her feet do 5,000 J of work to stop her. The girl's velocity when she began to stop is 10 m/sec.
To learn more about velocity refer the link:
brainly.com/question/18084516
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