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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Look at this model of an atom. Where are the protons located and how many are there?
Answer:
protons are in the nucleus .
Explanation:
there are 6 protons
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
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]
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
A 782-kg satellite is in a circular orbit about Earth at a height above Earth equal to Earth's mean radius. (a) Find the satellite's orbital speed. 9.82278e7 Incorrect: Your answer is incorrect. Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. m/s (b) Find the period of its revolution. h (c) Find the gravitational force acting on it.
Answer:
a) v = 5.59x10³ m/s
b) T = 4 h
c) F = 1.92x10³ N
Explanation:
a) We can find the satellite's orbital speed by equating the centripetal force and the gravitation force as follows:
[tex] F_{c} = F_{G} [/tex]
[tex]\frac{mv^{2}}{r + h} = \frac{GMm}{(r + h)^{2}}[/tex]
[tex] v = \sqrt{\frac{gr^{2}}{r+h} [/tex]
Where:
g is the gravity = 9.81 m/s²
r: is the Earth's radius = 6371 km
h: is the satellite's height = r = 6371 km
[tex]v = \sqrt{\frac{gr^{2}}{2r}} = \sqrt{\frac{gr}{2}} = \sqrt{\frac{9.81 m/s^{2}*6.371 \cdot 10^{6} m}{2}} = 5.59 \cdot 10^{3} m/s[/tex]
b) The period of its revolution is:
[tex] T = \frac{2\pi}{\omega} = \frac{2\pi (r + h)}{v} = \frac{2\pi (2*6.371 \cdot 10^{6} m)}{5.59 \cdot 10^{3} m/s} = 14322.07 s = 4 h [/tex]
c) The gravitational force acting on it is given by:
[tex] F = \frac{GMm}{(r + h)^{2}} [/tex]
Where:
M is the Earth's mass = 5.97x10²⁴ kg
m is the satellite's mass = 782 kg
G is the gravitational constant = 6.67x10⁻¹¹ Nm²kg⁻²
[tex] F = \frac{GMm}{(r + h)^{2}} = \frac{6.67 \cdot 10^{-11} Nm^{2}kg^{-2}*5.97 \cdot 10^{24} kg*782 kg}{(2*6.371 \cdot 10^{6} m)^{2}} = 1.92 \cdot 10^{3} N [/tex]
I hope it helps you!
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
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]
True/False: The core, mantle, and crust explanation for the Earth's layers is outdated and now we use the 5 layer explanation. *
Answer:
False
Explanation:
We still use the old way. It's easier to understand the old way, and its NOT outdated.
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
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.
A car of mass 1150 kg drives in a circle of radius 44 m. If the car has a speed of 13 m/s, what is the
centripetal force acting on the car?
Answer:
4417
i think because
mv^2/r is centripetal force
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.
b) A satellite with mass m orbits the Earth at a radius r. A second satellite also with mass m orbits the
Earth at twice the radius.
How does the force of Earth's gravity acting on the two satellites
compare? PLEASE HURRY
Answer:
So, given the eqn Fg=G(m1+m2/r^2) where G is the gravitational constant, m is the mass of the satellite and m2 is the mass of the earth and r is the distance from earth to the satellite, the force of earths gravity should be quartered.
Cause (2r)^2 gets turned into (4r^2) where 4r^2 is compared to r^2
Explanation:
Which of the following is an opinion about friction?
It always acts in the opposite direction as the motion of the object.
It stops objects on Earth from staying in motion forever.
It slows objects down too much.
It happens any time two objects are in contact.
Help me out please-
You'll get 40 points
My opinion about friction is that It always acts in the opposite direction as the motion of the object.
What is friction?Friction refers to the resistance of motion of one object that is moving relative to another object. Fricton has many application but it has also many disadvantages.
So we can conclude that friction is always acts in the opposite direction as the motion of the object.
Learn more about friction here: https://brainly.com/question/24338873
Use the following information to answer questions 4 and 5:
A rock is launched vertically into the air at a velocity of 14.75 m/s.
4. Toby claims that the rock must come to rest before it can fall back towards the ground. Is Toby
correct?
A. Toby is correct because the rock is experiencing a negative acceleration, causing its negative
velocity to increase until the rock reaches a velocity of O m/s before becoming positive.
B. Toby is correct because the rock is experiencing a negative acceleration, causing its positive
velocity to decrease until the rock reaches a velocity of O m/s before becoming negative.
C. Toby is incorrect because the rock is experiencing a positive acceleration, causing its positive
velocity to increase in magnitude.
D. Toby is incorrect because the rock is experiencing a negative acceleration, causing its positive
velocity to increase in magnitude.
5. Calculate the time it takes for the rock to reach its maximum height.
A. 1.50 seconds
B. 2.47 seconds
C. 3.00 seconds
D. 4.94 seconds
Question 4
B. Toby is correct because the rock is experiencing a negative acceleration, causing its positive velocity to decrease until the rock reaches a velocity of O m/s before becoming negative.
Question 5
At the maximum height, velocity is 0, so:
v = v₀ - gt
0 = 14.75 - 9.8t
t = 14.75/9.8
t = 1.5 s (OPTION A)
4). In the given situation, the assertion that could be made regarding Toby would be:
B). Toby is correct because the rock is experiencing a negative acceleration, causing its positive velocity to decrease until the rock reaches a velocity of O m/s before becoming negative.
5). The time that would be taken by the rock to attain its greatest height would be:
1.5 second
4). Tobby correctly states as rock would be undergoing a -ve acceleration which leads its +ve velocity to fall by the time rock attains the velocity of 0 m/s.
Thus, option B is the correct answer.
5). Given that,
Initial velocity([tex]v_{0}[/tex]) = 14.75 m/s
As we know,
Velocity remains 0 m/s at the greatest height,
So,
Velocity(v) [tex]= v_{0} - gt[/tex]
where
[tex]0 = 14.75 - 9.8t[/tex]
⇒ [tex]t = 14.75/9.8[/tex]
∵ [tex]t = 1.5 s[/tex]
Learn more about "Velocity" here:
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A block that slides on a rough surface slows down and eventually stops. The reverse process never occurs. That is, a block at rest never begins to move and accelerate on a rough surface without the action of an external agent. The second situation is forbidden because it would violate:_________.
a) conservation of total energy
b) conservation of momentum
c) the first law of thermodynamics
d) the second law of thermodynamics
e) both the first and second law of thermodynamics
Gracias.
Answer:
d) the second law of thermodynamics
Explanation:
Here we take an example
The entropy represents a measurement of the energy dispersal in the system. Also, the campfire would an entropy example. The burning of the solid wood and then it became the ash, smoke and gases this all would be spread the energy to the outward as compared to the solid fuel
Therefore as per the given statement, the correct option is d.
A thin, uniform stick of mass M and length L is at rest on a flat, frictionless surface to which one end of it is pinned. A small mass m traveling at speed v collides with and attaches to the stick at a distance 2L/3 away from the end through which it is pinned to the surface. (a) Find an expression for the moment of inertia of the stick mass object after the collision. (b) Find an expression for the final angular speed of the combined object
Answer:
a) I = ([tex]\frac{M}{3}[/tex] + [tex]\frac{4m}{9}[/tex]) L² , b) w = (\frac{27 M}{18 m} + 2)⁻¹ Lv₀
Explanation:
a) The moment of inertia is a scalar that represents the inertia in circular motion, therefore it is an additive quantity.
The moment of inertia of a rod held at one end is
I₁ = 1/3 M L²
The moment of inertia of the mass at y = L
I₂ = m y²
The total inertia method
I = I₁ + I₂
I = \frac{1}{3} M L² + m (\frac{2}{3} L)²
I = ([tex]\frac{M}{3}[/tex] +[tex]\frac{4m}{9}[/tex] ) L²
b) The conservation of angular momentum, where the system is formed by the masses and the bar, in such a way that all the forces during the collision are internal.
Initial instant. Before the crash
L₀ = I₂ w₀
angular and linear velocity are related
w₀ = y v₀
w₀ = [tex]\frac{2}{3}[/tex]L v₀
L₀ = I₂ y v₀
Final moment. After the crash
[tex]L_{f}[/tex] = I w
how angular momentum is conserved
L₀ = L_{f}
I₂ y v₀ = I w
substitute
m ([tex]\frac{2L}{3}[/tex])² (\frac{2L}{3} v₀ = ([tex]\frac{M}{3}[/tex] +[tex]\frac{4m}{9}[/tex] ) L² w
[tex]\frac{6}{27}[/tex] m L³ v₀ = ([tex]\frac{M}{3}[/tex] +[tex]\frac{4m}{9}[/tex] ) L² w
[tex]\frac{6}{27}[/tex] m L v₀ = ([tex]\frac{M}{3}[/tex] +[tex]\frac{4m}{9}[/tex] ) w
L v₀ = [tex](\frac{27 M}{18 m} + 2)[/tex] w
w = (\frac{27 M}{18 m} + 2)⁻¹ Lv₀
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.
hita's Question Bank- CTEVT
Baishakh] Q.No. 12 What is radiocarbon dating?
VER QUESTIONS
"Radiocarbon dating is a method for determining the age of an object containing organic material by using the properties of radiocarbon."
Answer:
well for me I think
Explanation:
The use of carbon 12 to tell the age of substances
How do the potential and kinetic energy change as the sled moves down the slope?
IF YOU DID SLED WARS WORKSHEET HELP ME PLEASE
Answer:
when a sled is moving, the kinetic energy is changing beacuse of the speed and mass. its cause the sled to move, and changes because you aren't at a constant speed. potential energy changes when you get on. because you are adding more weight causing the gravity to change.
Please help! What kind of energy is produce when solar panel to lightbulb filament?
Answer:
electrical energy
Explanation:
sorry I'm really tired but trust me on this one
Answer:
electrical to thermal and light
Explanation:
The FitnessGram Pacer Test is a multistage aerobic capacity test that progressively gets more difficult as it continues. The 20 meter pacer test will begin in 30 seconds. Line up at the start. The running speed starts slowly, but gets faster each minute after you hear this signal. A single lap should be completed each time you hear this sound. Remember to run in a straight line, and run as long as possible.
Select the correct answer.
Derick has been working as a first responder since many years. His primary responsibility at a crime scene is to question witnesses and gather
useful information from the scene. Which of these first responder career roles does Derick fit into?
OA paramedic
OB. police officer
Oc. fire truck driver
OD. firefighter
Answer:
Police officer
Explanation:
Because police officers wants to gather information on what happens and question people to know everything. That is what Derick is doing
2. Using Graph 2, calculate the net force experienced by the particle between 4 and 6 seconds. The
particle has a mass of 0.25 kg.
A +5.0 N
B. +0.5 N
C. -0.5 N
D. -2.0 N
Using Newtons Second Law:
F = m×a
F = (0.25 kg)(-2 m/s²)
F = -0.5 N
The correct option is CWhat are some ways that the Greeks demonstrated their passion for public life?
Answer:
The Greeks had drama and arts competitions that were considered very popular, and important in society.
Explanation:
hope it helps!
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.
To find more on potential energy, refer here:
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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]
A 300 g bird flying along at 6.0 m/s sees a 10 g insect heading straight toward it with a speed of 30 m/s. the bird opens its mouth wide and enjoys a nice lunch. What is the bird's speed immediately after swallowing?
Answer:
6.77m/s
Explanation:
Using the law of conservation of momentum
m1u1 + m2u2 = (m1+m2)v
m1 and m2 are the masses of the object
u1 and u2 are the velocities before collision
v is the final collision
Given
m1 = 300g = 0.3kg
u1 = 6.0m/s
m2 = 10g = 0.01kg
u2 = 30m/s
Required
The bird's speed immediately after swallowing v
Substitute the given values into the formula
m1u1 + m2u2 = (m1+m2)v
0.3(6) + 0.01(30) = (0.3+0.01)v
1.8+0.3 = 0.31v
2.1 = 0.31v
v = 2.1/0.31
v = 6.77m/s
Hence the bird's speed immediately after swallowing is 6.77m/s
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]
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 spiral spring of 8cm extended to 9.2cm when a load of 1.6N is applied. what is the force constant of the spring, provided the elastic is not exceeded.
Explanation:
By Hooke's Law, Fe = kx.
Since Fe = 1.6N and x = 9.2cm - 8cm = 1.2cm,
k = Fe/x = 1.6N/1.2cm = 1.33N/cm.