A 0.520 kg mass suspended from a spring oscillates with a period of 1.50 s. how much mass must be added to the object to change the period to 2.05 s?

Answers

Answer 1
[tex]Given:\\m_1=0.520kg\\T_1=1.50s\\T_2=2.05s\\\\Find:\\\Delta m=?\\\\Solution:\\\\\Delta m=m_2-m_1\\\\T=2 \pi \sqrt{ \frac{m}{k} } \Rightarrow 2 \pi = \frac{T}{\sqrt{ \frac{m}{k} }} \\\\\frac{T_1}{\sqrt{ \frac{m_1}{k} }} =\frac{T_2}{\sqrt{ \frac{m_2}{k} }} \\\\T_1\sqrt{ \frac{m_2}{k} }} =T_2\sqrt{ \frac{m_1}{k} }} \\\\\frac{T_1^2m_2}{k} =\frac{T_2^2m_1}{k} \\\\T_1^2m_2=T_2^2m_1\Rightarrow m_2= \frac{T_2^2m_1}{T_1^2} \\\\\Delta m=\frac{T_2^2m_1}{T_1^2} -m_1=m_1(\frac{T_2^2}{T_1^2} -1)[/tex]

[tex]\\\\\Delta m=0.520kg( \frac{(2.05s)^2}{(1.50s)^2} -1)\approx 0.4512kg[/tex]

Related Questions

A temperature of 200°F is equivalent to approximately

Answers

93°C or 366 Kelvin. Be a little more specific next time in your questions.

To convert [tex]200^{\circ}F[/tex] to Celsius, subtract 32 from 200 and then multiply the result by 5/9 to get approximately [tex]93.33^{\circ}C[/tex]. To convert this to Kelvin, add [tex]273.15[/tex] to the Celsius result, which gives about [tex]366.48 K[/tex].

Converting [tex]200^{\circ}F[/tex] to Celsius and Kelvin

To convert a temperature of [tex]200^{\circ}F[/tex] to Celsius (°C), use the formula:

[tex]C = \frac{{F - 32}}{9} \times 5[/tex]

Here's the step-by-step conversion:

Subtract 32 from 200: [tex]200 - 32 = 168[/tex]Multiply 168 by 5/9: [tex]168 \times \frac{5}{9} \approx 93.33^\circ \text{C}[/tex]

So, [tex]200^{\circ}F[/tex]  is approximately [tex]93.33^{\circ}C[/tex].

Next, to convert Celsius to Kelvin ([tex]K[/tex]), use the formula:

[tex]K = C + 273.15[/tex]

Add 273.15 to 93.33: [tex]93.33 + 273.15 = 366.48 K[/tex]

Therefore, [tex]200^{\circ}F[/tex] is approximately [tex]366.48 K[/tex].

Jessica stretches her arms out 0.6 m from the center of her body while holding a 2 kg mass in each hand. she then spins around on an ice rink at 1.1 m/s.
a. what is the combined angular momentum of the masses?

Answers

Angular momentum is the measure of the amount of rotation of the body. It is the product of the moment of inertia and the angular velocity. The moment of inertia has the equation I=mr^2, where m is the mass and r is the radius of the circle. In this case, the radius is 0.6 m. Then, I = 2kg * (0.6)^2 = 0.72 kg-m2/s2.

The angular velocity on the other hand is the product of linear velocity and the radius. The equation is ω = rv, where v is the linear velocity. Therefore, ω = 0.6*1.1 = 0.66 rad/s

Therefore, the angular momentum is 

= 0.72 kg-m2/s2*0.66 rad/s
= 0.48 kg-m^2/s

An ideal solenoid having a coil density of 5000 turns per meter is 10 cm long and carries a current of 4.0
a. what is the strength of the magnetic field at its center?

Answers

The rule that is used to get the strength of magnetic field at the center of solenoid (B) is:
B = µ x n x I where:
µ is the permeability of the medium where the solenoid is based. In this problem, the medium is air which means that µ = µ o = 4 pi x 10^-7 Tm/A
I is the current passing (I = 4 amperes)
n is the number of turns per unit length (5000 turns)

Substituting in the mentioned equation, we find that:
B = 4 x 3.14 x 10^-7 x 5000 x 4 = 25.132 mT

The time a basketball player spends in the air when shooting a basket is called the​ "hang time." the vertical leap l measured in feet is related to the hang time t measured in seconds by the equation lequals=4t2. suppose that a basketball player has a vertical leap of 4 feet 4 inches. find the hang time for this leap.

Answers

I believe that L is in feet while t is in seconds. To find for the hang time, all we have to do is to plug in the value of L in feet in the equation.

4 inches is equivalent to 4/12 feet or 0.33 feet, therefore the total L is:

L = 4.33 ft

Using the equation to find for t:

L = 4 t^2

4.33 = 4 t^2

t = 1.04 s

To calculate the hang time for a basketball player with a vertical leap of 4 feet 4 inches, solve the equation l = 4[tex]t^2[/tex] to find that the hang time is approximately 1.041 seconds.

The vertical leap l is related to the hang time t by the equation l = 4[tex]t^2[/tex]. To find the hang time for a basketball player with a vertical leap of 4 feet 4 inches (which is 4.333 feet), we plug this value into the equation and solve for t:

4.333 = 4[tex]t^2[/tex]

[tex]t^2[/tex] = 4.333 / 4

[tex]t^2[/tex] = 1.08325

t = [tex]\sqrt{(1.08325)[/tex]

t ≈ 1.041

Hence, the hang time for this leap is approximately 1.041 seconds.

Restate the definition of efficiency assuming that the heating properties of a light bulb are more important than the illumination.

Answers

In topics related to power, work or energy, the definition of efficiency is described as:


Efficiency = useful intended output / total input 



Therefore with this definition, we restate that:

Efficiency is energy transferred to light divided by the electrical energy consumed (input).

 

A recent experiment reports that increased lighting during the winter months results in lower depression scores. for this study, what is the dependent variable?

Answers

the weather is the dependent variable

A person riding north on a bike speeds up from 0m/s to 9m/s in 3 seconds. What is the acceleration of the bike

Answers

A=(V-V0)/T
V=9m/s
V0=0m/s
T=3sec

So a=9/3=3m/s^2

The acceleration of the bike that speeds up from 0m/s to 9m/s in 3 seconds is 3m/s². Details about acceleration can be found below.

How to calculate acceleration?

The acceleration of a moving body can be calculated by dividing the change in velocity of the body by the time taken.

According to this question, a bike speeds up from 0m/s to 9m/s in 3 seconds. The acceleration can be calculated as follows:

a = (9m/s - 0m/s)/3 seconds

a = 9m/s ÷ 3s

a = 3m/s²

Therefore, the acceleration of the bike that speeds up from 0m/s to 9m/s in 3 seconds is 3m/s².

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The main difference between turbojets and rocket engines is the fact that A. turbojets carry their own supply of oxygen as oxidizers. B. turbojets are not dependent on oxygen from the air. C. rocket engines need oxygen from the air. D. rocket engines are not dependent on oxygen from the air.

Answers

The main difference between turbojets and rocket engines is the fact that
A. turbojets carry their own supply of oxygen as oxidizers.
B. turbojets are not dependent on oxygen from the air.
C. rocket engines need oxygen from the air.
D. rocket engines are not dependent on oxygen from the air.

D.  rocket engines are dependent on oxygen from the air.


How strong is the electric field between the plates of a 0.86 µf air-gap capacitor if they are 2.0 mm apart and each has a charge of 64 µc?

Answers

The electric field between the plates is equal to the potential difference across the plates divided by the separation of the plates.
The potential difference across the plates is equal to the charge stored divided by the capacitance.

When a sound wave moves through a medium such as air, the motion of the molecules of the medium is in what direction (with respect to the motion of the sound wave?

Answers

A sound wave is a pressure wave that results from the vibration of the particles o the medium from the source. The motion of the particles in the medium is parallel to the direction of the energy transport. The type of wave formed by a sound wave is the longitudinal wave. A longitudinal wave is characterized by rarefactions. A longitudinal wave is a wave motion wherein the particles in the wave medium are displaced parallel to transport. When motion is detected from the source, the particle next to it vibrates from its rest position and a progressive change in phase vibration is observed at each particle within that wave. The result is that the energy is transported from one region to the other. These combined motions result in the movement of alternating regions of rarefaction in the direction of propagation.      

a body of mass 1 kg is placed at a distance of 2 m from another body of mass 10 kg. At what distance from the body of mass 1 kg, another body must be placed so that the net gravitational force acting on the body of mass 1 kg is zero

Answers

To answer this problem, we will use the formula for gravitational force:

F = G m1 m2 / r^2

Where,

G = gravitational constant (6.67 * 10^-11)

m = mass of a body

r = distance between two bodies

To have a net gravitational force equal to zero acting on body of mass 1 kg, then the forces of 1 kg and 10 kg bodies and 1 kg and 5 kg bodies should be equal.

F1 (1 kg and 10 kg) = F2 (1 kg and 5 kg)

Therefore,

(1 kg) (10 kg) / (2 m)^2 = (1 kg) (5 kg) / r2^2

Calculating for r2 (distance of another body 5 kg from body of mass 1 kg):

r2^2 = 2

r2 = 1.41 m       (ANSWER)

Therefore another body of mass 5 kg should be placed 1.41 m from body of mass 1 kg to have a net gravitational force equal to zero.

A uniform 300-n trapdoor in a floor is hinged at one side. find the net upward force needed to begin to open it and the total force exerted on the door by the hinges (a) if the upward force is applied at the center and (b) if the upward force is applied at the center of the edge opposite the hinges. 11.5 .. raising a ladder. a ladder carried

Answers

The force body diagrams are shown in the picture for the two different cases.

In part a, there are 4 forces acting on the system. Two x and y forces in the point of the hinge on the rightside corner. One force pointing downwards for the weight of the trapdoor which is 300 N. One force pointing up which is what is asked. Let's denote this as x. To find this, we have to know the length of the trapdoor. Since it is not given, let's assume it to be 6 meters. Hence, the distance from the hinge to the center is 3 meters. Using the law of conservation of momentum, 

Summation of Moment = 0
Summation of Moment = x(3)  - 300(3) = 0
x = 300 N

In part b, the upward force is at the leftside corner instead of at the center. Using the same procedure,

Summation of Moment = x(6)  - 300(3) = 0
x = 150 N
Final answer:

This problem is about the physics of rotation and equilibrium. To open the trap-door, an upward force that counteracts the door's weight is necessary. The total force exerted on the door equals the applied force minus the net upward force. If the force is applied farther from the door, More force is required due to the increased torque.

Explanation:

The net upward force to open the door is the force that counteracts the gravitational force acting on the door, which can be calculated using the door’s mass and the acceleration due to gravity. The total force exerted on the door by the side is equal to the total force applied on the door minus this net upward force.

In case (a), where the force is applied at the center of the door, the force required to start opening is equal to the weight of the door distributed over the two sides. In case (b), where the force is applied at the center of the edge opposite the door, the force required is larger because the distance from the door to the point where the force is applied is greater, increasing the torque.

In the case of the ladder problem, an analysis of the torques and the net forces, considering the ladder’s weight and the friction with the floor, would be necessary.

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A speedboat moving at 31.0 m/s approaches a no-wake buoy marker 100 m ahead. the pilot slows the boat with a constant acceleration of −4.00 m/s2 by reducing the throttle. (a) how long does it take the boat to reach the buoy? s (b) what is the velocity of the boat when it reaches the buoy? m/s

Answers

u = 31 m/s, the initial speed of the boat
s = 100 m, distance to the buoy
a = -4 m/s², the acceleratin (actually deceleration)

Part (a)
Let t = time required to reach the buoy.
Use the formula ut + (1/2)at² = s.
(31 m/s)*(t s) - (1/2)*(4 m/s²)*(t s)² = (100 m)
2t² - 31t + 100 = 0

Solve with the quadratic formula.
t = (1/4) [31 +/- √(31² - 800)]
  = 10.92 s or 4.58 s
Before selecting the answer, we should determine the velocity at the buoy.

Part (b)
When t = 10.92 s, the velocity at the buoy is
v = (31 m/s) - (4 m/s²)*(10.92 s) = -12.68 m/s
Because of the negative value, this value of t should be rejected.

When t = 4.58 s, the velocity at the buoy is
v = (31 m/s) - (4 m/s²)*(4.58 s) = 12.68 m/s
This value of t is acceptable.

Answer (to nearest tenth): 
(a) The time is 4.6 s 
(b) The velocity is 12.7 m/s
Final answer:

The boat takes 7.75 seconds to reach the buoy and its velocity when it reaches the buoy is 0 m/s.

Explanation:

To solve this problem, we can use the equations of motion under constant acceleration. Let's start with part (a).

Given:

Initial velocity, v0 = 31.0 m/s

Final velocity, v = 0 m/s (since the boat reaches the buoy and stops)

Acceleration, a = -4.00 m/s2

We can use the equation:

v = v0 + at

Substituting the given values, we have:

0 = 31.0 - 4.00t

4.00t = 31.0

t = 7.75 s

Therefore, it takes the boat 7.75 seconds to reach the buoy.

Now, let's move on to part (b).

To find the final velocity, we can use the same equation:

v = v0 + at

Substituting the known values:

v = 31.0 - 4.00(7.75)

v = 31.0 - 31.0

v = 0 m/s

Therefore, the velocity of the boat when it reaches the buoy is 0 m/s.

A thin film of polystyrene is used as an antireflective coating for fabulite (known as the substrate). the index of refraction of the polystyrene is 1.49, and the index of refraction of the fabulite is 2.409. what is the minimum thickness of film required? assume that the wavelength of the light in air is 500 nanometers.

Answers

To solve this problem, we assume that the wavelength of the light in air is 500 nanometers.

For this case we only need the refractive index of the polystyrene. For an antireflective coating, we need a quarter of wave thickness at the wavelength in the air. Which means that the antireflective coating needs to be as thick as 1/4 of the wavelength, divided by the coating’s refractive index. This is expressed mathematically in the form:

x = λ / (4 * n)

where,

x = thickness

λ = wavelength of light

n = index of refraction of polystyrene

Substituting:

x = 500 nm / (4 * 1.49)
x = 500 nm / 5.96
x = 83.90 nm

The minimum thickness of the film required assuming that the wavelength of the light in air is 500 nanometers is; 83.9 nm

Calculations about Destructive Interference

We are given;

Index of refraction of polystyrene; η_p = 1.49

Index of refraction of Fabulite; η_f = 2.409

Wavelength of the light in air; λ = 500 nm

In this question, it will be discovered that light will first of all be reflected two times, first from the upper layer of coating and then from the interface between the coating and the polystyrene material.

The additional path travelled by the light in coating is 2t while the path difference is 2tη_p.

Thus, minimum thickness of film required will be gotten from the formula used in destructive interference which is;

2tη_p = λ/2

t = λ/2 * 1/2η_p

t = λ/(4η_p)

t = 500/(4 * 1.49)

t = 83.9 nm

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A semicircular plate ft in diameter sticks straight down into fresh water along the surface find the force exerted by the water on one side of the plate

Answers

You would need to know the diameter of the plate (not in the question). This would tell how much of the plate is in the water. Then you'd need to know the speed of the water current. These two figures would let you calculate the force exerted on the submerged portion of the plate.

In order to induce electrical energy into a conductor or generator, what three factors must be present?

Answers

The electricity produced by a generator works through the concepts of the following three factors; magnetic field, voltage and current. When a conductor with current flowing in it is placed in a magnetic field, it will cause the electrons to move in a direction perpendicular to the magnetic field. When working with generators, the guide for this direction is Fleming's Right Hand Rule. Since the electron move in perpendicular motion with magnetic field all the time, it would cause it to spin in a helical direction. These turns would then induce voltage and create electricity.

An electron at Earth's surface experiences a gravitational force meg. How far away can a proton be and still produce the same force on the electron?

Answers

I will discuss what is a gravitational force since no figures are attached or given. An objects weight is dependent upon its location in the universe because they exhibit gravitational waves. For example, the earth is a massive planet. Because of its massiveness, it exhibits a strong gravitational force within it. In turn, the objects near the earth will be attracted to it and thereby feels a much stronger gravity on earth. That is why bodies of water, despite its liquid features, stick to the earth. The heavier the body is, the stronger its gravitational pull. Another example is the Milky Way Galaxy, there is a gravitational pull because it is to other galaxies. Also, other galaxies are heavier than the earth and therefore, it is attracted to the Milky Way galaxy because of its gravitational pull. 

The proton could be 5 m far away from electron.

Further explanation

Newton's gravitational law states that the force of attraction between two objects can be formulated as follows:

[tex]\large {\boxed {F = G \frac{m_1 ~ m_2}{R^2}} }[/tex]

F = Gravitational Force ( Newton )

G = Gravitational Constant ( 6.67 × 10⁻¹¹ Nm² / kg² )

m = Object's Mass ( kg )

R = Distance Between Objects ( m )

Let us now tackle the problem!

Given:

me = 9.11 × 10⁻³¹ kg

qp = qe = 1.6 × 10⁻¹⁹ kg

Unknown:

R = ?

Solution:

[tex]F_e = F_p[/tex]

[tex]m_e \times g = k \times \frac{q_e \times q_p}{R^2}[/tex]

[tex]9.11 \times 10^{-31} \times 9.81 = 9 \times 10^9 \times \frac{(1.6 \times 10^{-19})^2}{R^2}[/tex]

[tex]R \approx 5 ~ m[/tex]

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Answer details

Grade: High School

Subject: Physics

Chapter: Gravitational Field

Keywords: Gravity , Unit , Magnitude , Attraction , Distance , Mass , Newton , Law , Gravitational , Constant

A circuit contains a 6.0-v battery, a 4.0-w resistor, a 0.60-µf capacitor, an ammeter, and a switch all in series. what will be the current reading immediately after the switch is closed?

Answers

You are given a circuit that contains a 6.0-v battery, a 4.0 ohm resistor, a 0.60 micro farad capacitor, an ammeter, and a switch all in series. You are asked to find the current reading after the switch is closed. Apply ohms law where V = IR where V is the voltage, I is the current and R is the resistor.

V = IR
I = V/R
I = 6 volts / 4 ohms
I = 1.5A

When the switch is closed, the cathode side plate begins to fill up with electrons when it was originally empty before the switch was closed. When it fills up the cathode side of the circuit, the current decreases. And when the capacitor cannot hold more electrons, the current will stop. The higher the capacitance, the higher is the capacity to store electrons.

Answer:

I = 0.667 A

Explanation:

A capacitor behaves like a short circuit at t = 0 immediately after the switch is closed, therefore we can discard it from the equation, the resistance is given in watts or power units equivalent to current by voltage and the ammeter behave like a short circuit by nature.

Considering all of the above, the circuit looks like a battery in series with a resistor, therefore, we can use the power equation to solve the problem as follow:

P = I*V

4W = I*6V

I = 0.667 A  

Two point charges of values +3.4 and +6.6 μc are separated by 0.10 m. what is the electrical potential at the point midway between the two point charges? (

Answers

Final answer:

The electrical potential midway between two point charges is determined by adding the potentials due to each charge, calculated using the formula V = kq/r, where V is potential, k is Coulomb's constant, q is charge, and r is the distance to the point.

Explanation:

The question asks about the electrical potential at the point midway between two point charges of values +3.4 and +6.6 μC (microcoulombs) separated by 0.10 m. To solve this, we can use the formula for electric potential due to a point charge, V = kq/r, where V is the electric potential, k is Coulomb's constant (approximately 8.987 × 10^9 Nm^2/C^2), q is the charge in coulombs, and r is the distance from the charge to the point in question. At the midpoint between the two charges, the potentials due to each charge add up algebraically because they are both positive charges.


The distance from each charge to the midpoint is 0.05 m. Thus, the total potential at the midpoint is V_total = V_1 + V_2 = (kq_1/r_1) + (kq_2/r_2) = (8.987 x 10^9 Nm^2/C^2)(3.4 x 10^-6 C/0.05 m + 6.6 x 10^-6 C/0.05 m). Simplifying, the electric potential at the midpoint is calculated to be the sum of the individual potentials from each charge.

Which describes how to generate a real image of an object using a concave mirror?

Answers

A concave mirror is curved inward in the middle, more like a cave. Because the mirror is curved inward, the angle of the light surface can be focused similar to that of the camera. They can form real images that are projected out in front of the mirror at the place where light focuses. When the object is located at the center of the curvature the image formed will also be at the curvature. The image will be inverted and the magnification value is equal to 1 which will become a real image because the ray of light converges at the location of the formed image.

Answer:

The object must be farther from the mirror than the focal point

Explanation:

gradpoint lesson

An athlete does one push-up. In the process, she moves half of her body weight, 250 newtons, a distance of 20 centimeters. This distance is the distance her gravity moves when she fully extends her arms. How much work did she do after one push-up?

Answers

We know that an athlete moves half of her body weight 250 N a distance of 20 cm.
So:  F = 250 N,  d = 20 cm = 0.2 m
The work formula:
W = F * d
W = 250 N * 0.2 m
W = 50 J
Answer: Her work after one push-up is 50 J.

A rectangular gasoline tank can hold 36.0 kg of gasoline when full. what is the depth of the tank (in m) if it is 0.450 m wide by 0.900 m long? m (b) what is the volume of the tank (in gal)? (it is suitable for a passenger car.) gal

Answers

Let h =  depth of the rectangular tank.
Its volume is
V = (0.450 m)*(0.900 m)*(h m)
   = 0.405h m³

The density of gasoline is about 0.77 kg/L = 719.7 kg/m³.
Because the mass of gasoline is given as  36.0 kg, its volume is
V = (36.0 kg)/(719.7 kg/m³)
    = 0.05 m³

Therefore,
0.405h = 0.05
          h = 0.1235 m 

The capacity of the tank in gallons is
(36 kg)/(0.77 kg/L) = 46.75 L
Because 1 L = 0.264 gal, the capacity is
(46.75 L)/(1/0.264 L/gal) = 177.1 gal.
A typical passenger can hold between 12 and 17 gallons, so this tank is too large.

Answer:
The depth is 0.1235 m.
The volume is 0.05 m³.
The tank is too large for a passenger car.

When you eat a candy bar and then decide to go for a walk, energy transformations take place. beginning with the food energy in the candy bar, describe the forms of energy used and the changes in energy that occur as you decide to walk and as you do the walking?

Answers

When we eat a candy bar and then decide to go for a walk, we get instant energy in the body due to the food energy in the candy and that is called carbohydrates. The carbohydrates in the candy give our body some instant energy due to which we feel more energetic and do the walk or another physical thing with a boost.  
Our potential energy somewhat increases after eating the candy and when we walk, it gets transformed into kinetic energy

A boy jumps at a speed of 20.0 m/s at an angle of 25.0o above the horizontal. what is the horizontal component of the boy's velocity?

Answers

Given:
Launch velocity  = 20 m/s
Launch angle = 25° above he horizontal.

The horizontal component of velocity is by definition
Vx = 20*cos(25°) = 18.13 m/s

Answer:  18.13 m/s (nearest hundredth)

Give three examples from your life of magnetic force.

Answers

headphones, refrigerator magnets, and compasses

Hope that was helpful.
Magnets,popsocket, and a car

A man whose weight is 650 N is standing on the ground. The force the ground exerts on him is _____.

Answers

The force the ground exerts on him is 650 N.

What is force?

The push or pull on an object with mass that causes it to change its velocity.

According to law of newton

"Every action has an equal and opposite reaction."

This means that the ground is exerting the same amount of force as the man, 650 N.

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Which of newton's laws could we have used to predict that the forces in parts b and e are equal and opposite?

Answers

That's the The third Newton's Law.

What are the components of earths life support system

Answers

The four major components of the earth's life-support system are the atmosphere (air), the hydrosphere (water), the geosphere (rock, soil, and sediment), and the biosphere (living things).

The components of Earth's life support system are air, water, soil, and living organisms.  

What is a Life support system?

The life support system is necessary for living organisms. It elements are necessary to promote living organisms and give sustainable life to living organisms.

It is a system that provides all the substances which is essential for the living. It is the combination of equipment that allows the survival in environment.

Life support systems offer food, oxygen, water, and the disposition of carbon and wastes. It includes the atmosphere(air), hydrosphere (water), biosphere (living organisms), and geosphere (soil).

The atmosphere offers air (oxygen) for living organisms to breathe. Hydrosphere offers water for living organisms and the geosphere offers shelter for living organisms.

Hence the components of Earth's life support system are air, water, soil, and oxygen.

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A balloon is released from a tall building. the total mass of the balloon including the enclosed gas is 2.0 kg. its volume is 5.0 m3. the density of air is 1.3 kg/m3. will the balloon rise, fall, or remain stationary; and why?

Answers

Given:
m = 2.0 kg, mass of the balloon and enclosed gas
V = 5.0 m³, volume of balloon.

Calculate the effective density of the balloon.
ρ = m/V
   = 2/5 
   = 0.4 kg/m³

The density of air is 1.3 kg/m³, which is denser than the balloon. Therefore the balloon will rise.

Answer: The balloon will rise because its density is less than that of air.

1. A 0.828-nm photon collides with a stationary electron. After the collision, the electron moves forward and the photon recoils backwards.
a) Find the momentum of the electron.

b) Find the kinetic energy of the electron.

Answers

a) Find the momentum of the electron.

The momentum would be as follows:
p = E / c 
p= (h(c) / (wavelength)) / c 
p = h / wavelength
p = 6.626x10^-34 J s / 0.828x10^-9 m 
p = 8.00 x 10^-25 kg m/s 

b) Find the kinetic energy of the electron.

Assuming this is a head-on collision, then cosine of the angle would be -1. 
wavelength (after) - wavelength (before) = 2(h / m(e) c) 
wavelength (after) = 2(h/m(e) c) + wavelength (before) 
wavelength (after) = 0.00485 nm + 0.828 nm 
wavelength (after) = 0.83385 nm 

E = h(c)/wavelength 
E(before) = h c / 0.828x10^-9 = 2.4x10^-16 J
E(after) = h c / 0.83385 x10^-9 = 2.38 x10^-16 J 
Total change in E = 2.4x10^-16 J - 2.38 x10^-16 J 
Total change in E = 3.16x10^-17 J
Final answer:

To find the momentum of the electron after collision with a photon, the momentum of the photon must be calculated first using Planck's constant and the wavelength of the photon. The kinetic energy of the electron depends on the specific details of the conservation of energy and momentum in the collision, which are not provided.

Explanation:

The question involves calculating the momentum of the electron and the kinetic energy of the electron after it collides with a photon. This scenario is explored in the context of compton scattering, which is a common topic in high school and college physics classes.

To find the momentum of the electron, we use the relationship for the momentum (p) of a photon, which is given by p = h/λ, where h is Planck's constant (6.63 × 10-34 m² kg/s) and λ is the wavelength of the photon. For an 0.828-nm photon, this yields a momentum that the electron will take after the collision.

However, without additional information on the scattering angle or final energy/wavelength of the photon, we cannot accurately determine the momentum or the kinetic energy of the electron, as these values depend on the specifics of the conservation of energy and momentum in the collision process.

Learn more about Compton scattering here:

https://brainly.com/question/13435570

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