Answer:
float
Explanation:
a less dense material will float when placed in a material that is more dense than itself. The reverse is also true, that a denser material will sink when placed into into a less dense material.
The total amount of energy contained in an object.
Answer: see the explanation
Explanation:
The total amount of energy contained in an object is called its energy. Energy can exist in different forms, such as kinetic energy (energy of motion), potential energy (stored energy), thermal energy (heat), chemical energy (energy stored in chemical bonds), and many others.
To calculate the total energy of an object, you need to consider the different forms of energy it possesses. For example, if an object is moving, it has kinetic energy, which depends on its mass and velocity. The equation to calculate kinetic energy is KE = 0.5 * mass * velocity^2, where KE represents kinetic energy, mass is the object's mass, and velocity is its speed.
If an object is at a certain height above the ground, it has gravitational potential energy. The equation for gravitational potential energy is PE = mass * gravity * height, where PE represents potential energy, mass is the object's mass, gravity is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth), and height is the object's height above a reference point.
Additionally, an object can have other forms of energy, such as thermal energy due to its temperature, chemical energy stored in its chemical bonds, or electrical energy if it has an electric charge.
It's important to note that the total energy of an object is the sum of all the different forms of energy it possesses. Each form of energy can be converted into another form, but the total energy remains constant, as stated by the law of conservation of energy.
In summary, the total amount of energy contained in an object is the sum of its different forms of energy, such as kinetic energy, potential energy, thermal energy, chemical energy, and others. To calculate the total energy, you need to consider the specific forms of energy present and use the appropriate equations. The law of conservation of energy states that energy cannot be created or destroyed, only converted from one form to another.
can u tell in a very easy where a small child can also understand
Brainly Ginny character avatar
AI-generated answer
The total amount of energy in an object is all the different kinds of energy that it has. Energy is what makes things happen and allows them to do work. It can come in different forms, like when you're running and have energy to move, or when you have a ball that can bounce and roll.
Imagine you have a toy car that you wind up. When you wind it up, you're putting energy into it. That energy gets stored inside the car. When you let go of the car, it starts moving and uses up that stored energy. This is an example of kinetic energy, which is the energy of motion.
Another kind of energy is potential energy. Let's say you have a ball on top of a hill. The ball has potential energy because it can roll down the hill. When you let the ball go, it starts rolling and its potential energy turns into kinetic energy as it moves.
Objects can also have thermal energy, which is heat energy. When you touch something hot, like a stove, you feel the thermal energy transferring to your hand.
Some objects have chemical energy stored inside them. For example, when you eat food, your body breaks it down and turns it into energy that you can use.
These are just a few examples of the different forms of energy. The total energy of an object is the sum of all the different kinds of energy it has. Energy can change from one form to another, but it cannot be created or destroyed.
So, to put it simply, the total energy of an object is all the different types of energy it has, like the energy of motion, heat, stored energy, and more
Work is the product of ___
_ and an object's displacement.
Answer:
Force
Explanation:
W= F * d
Work is defined in physics as the product of force and an object's displacement. It is expressed mathematically as Work = Force x Distance. The direction of the force and displacement also affect whether the work done is considered positive or negative.
Explanation:In physics, work is defined as the product of force and an object's displacement. It is represented mathematically as Work = Force x Distance. In this equation, Force is the amount of effort exerted on an object, and Distance or displacement is the amount of space over which the force is applied. If the force and the displacement are in the same direction, the work done is positive.
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What is an input force?
the applied force on a system
the net force on a system
the force a simple machine applies to an object
the force a person applies to a simple machine
Answer:
The force a person applies to a simple machine
Explanation:
An input force is that variable that enters a simple machine to perform a particular job by multiplying the value of that input force.
As a typical example we can find a lever where a person introduces an input force, this force multiplies according to the mechanical advantage of the lever resulting in the work of a simple machine with more work.
Answer:
The force a simple machine applies to an system
Explanation:
While pushing a refrigerator up a ramp, there would be less friction to overcome if you used a dolly because of the wheels. So the efficiency of the ramp would be ________________________ with the use of the dolly.
While pushing a refrigerator up a ramp, there would be less friction to overcome if you used a dolly because of the wheels. So the efficiency of the ramp would be greater with the use of the dolly.
Explanation:
The ramp provides for a wedge setup, so when the refrigerator is being pushed up the ramp, the friction on the ramp would equally distributed to the refrigerator when pushed wholly as the friction applied is a product of the coefficient of friction with the Normal reaction of the weight in contact with the surface.
Therefore, when the dolly is used, the surface in contact becomes divided and thus, the friction applied would become less due to though coefficient of friction remains the same, the normal reaction of the weight becomes small and so does the applied friction. Therefore, efficiency of the ramp increases as the friction is less and work done is more.
can someone please simplify and explain what displacement and instantaneous and also scientific notation and velocity to me in a clear, simplified way basically how you'd explain it to a 5th grader
thanks in advance
Displacement and instantaneous:
Displacement is the distance vector that the object has displaced from its initial position. It is calculated from the starting point to the endpoint in the journey of the object in question. The displacement can be understood as the straight line joining the points mentioned above. Keep in mind that the actual path taken by the object is not related to the displacement. The exact route is the average distance.
Velocity is the speed in a particular direction. If I say the speed of the car was 10mph than it would be speed, but if I say the speed was 10mph in the right direction than it would be velocity. So, the Directional speed is velocity. Velocity is a vector quantity and follows the rules of vector algebra and cannot be added or subtracted. The notation of velocity is a v with an arrow on the top. The arrow just tells that the quantity in question is a vector.
When white light passes through a glass prism, it separates out into different colors. Which of the following best explains why this happens?
A. The light is circularly polarized, causing it to spread out when it passes through glass.
B. Different wavelengths of visible light refract at different angles when passing from air to glass.
C. The light passes through tiny holes in the molecules of glass, causing the light to diffract into different colors.
D. White light causes a chemical reaction when it enters glass, causing the glass to emit different colors.
Answer:
B
Explanation:
When a beam of light hits glass straight on it passes right through it. But the whites that make up the light actually get sloped down by the glass. And only go back to their normal speed when they come out the other side. That slowing down is what causes white light to split into a rainbow of color whenever it hits glass on an angle. it happens because glass slows some colors of light more than others and because slowing down on an angle causes them to slightly bend. All colors get bend somewhere in between. The reason that different colors get split is because they all have different wavelengths. The longest being red and violet being the shortest. The longer the wavelengths, the slower it is.
Different wavelengths of visible light refract at different angles when passing from air to glass.
What is the refraction of light?Refraction is the bending of light (it also happens with sound, water and other waves) as it passes from one transparent substance into another. This bending by refraction makes it possible for us to have lenses, magnifying glasses, prisms and rainbows.
When a beam of light hits glass straight on it passes right through it. But the whites that make up the light actually get sloped down by the glass. And only go back to their normal speed when they come out the other side.
That slowing down is what causes white light to split into a rainbow of color whenever it hits glass on an angle. it happens because glass slows some colors of light more than others and because slowing down on an angle causes them to slightly bend.
All colors get bend somewhere in between. The reason that different colors get split is because they all have different wavelengths. The longest being red and violet being the shortest. The longer the wavelengths, the slower it is.
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Identify the area where convection is taking place.
In this area the convection is taking place inside the water which is inside the utensils.
Explanation:
Convection is the type of heat transfer method which is usually taking place through the liquid and gases. In this convection process, the liquid acts as the medium for the heat transfer. From the given picture we can see both convection and conduction. The conduction process which occurs in the solid objects. Here the heat is directly given to the pan which is a solid conductor so the pan conducts the heat. Inside the pan there happens to be the liquid which favors the convection process and again the eggs are heated by the conduction process as the outer part of the egg is solid.
2. Karen wants to know where in her garden a basil plant will grow the best. She thinks a basil plant will grow best in the corner of the garden that gets the most sunlight. To test her hypothesis, she decided to plant several groups of basil in her garden.
Which of the following variables should Karen change from one group of basil plants to the next?
A. the amount of water she gives the plants
B. the location of the plants
C. the height of the plants
D. the type of plants
Since she is testing where the plant would grow best, the type, height and amount of water does not help the original question. Only moving the plants will help her determine where to plant the basil plants. Option B. the location of the plants
Answer: C. the height of the plants
Explanation:
2. A sailor pushes a 100.0 kg crate up a ramp that is 3.00 m high and 5.00 m long onto the deck of a ship. He
exerts a 650.0 N force parallel to the ramp. What is the mechanical advantage of the ramp? What is the
efficiency of the ramp? Your response should include all of your work and a free-body diagram.
Answer:
Mechanical advantage of the ramp = [tex]\frac{980}{650} = 1.51[/tex]
Efficiency of the ramp = [tex]\frac{Actual\hspace{0.1cm} work\hspace{0.1cm} done}{Work}[/tex] = [tex]\frac{100\times 9.8\times 3}{650\times 5} = \frac{2940}{3250} = 0.9046 = 90.46%[/tex]
Explanation:
i) Mechanical advantage of the ramp = [tex]\frac{980}{650} = 1.51[/tex]
ii) Efficiency of the ramp = [tex]\frac{Actual\hspace{0.1cm} work\hspace{0.1cm} done}{Work}[/tex] = [tex]\frac{100\times 9.8\times 3}{650\times 5} = \frac{2940}{3250} = 0.9046 = 90.46%[/tex]
The mechanical advantage and the efficiency of the ramp are respectively;
330 N and 90%
Mechanical advantage and EfficiencyI have drawn an image of the force diagram on the crate and attached it.
Applying Newton's second law to the force diagram attached, we have;
F_fric + F + N + mg = 0
Projecting forces gives us;
In the x-direction;
F = F_fric + mg*sin α
In the y-direction;
N - mg*cos α = 0
Also;
F_fric = μmg*cos α
Thus;
F = (μmg*cos α) + (mg*sin α)
Mechanical advantage is;
ΔF = mg - F
ΔF = mg - mg((μ cos α) + (sin α))
Since the ramp is 3 m high and 5 m long, then by trigonometric ratios;
(sin α) = 3/5
cos α = 4/5
But we are given that F is 650 N.
Thus;
ΔF = (100 × 9.8) - 650
ΔF = 330 N
Efficiency of the ramp is;
η = (mgh/Fl) × 100%
η = (100 × 9.8 × 3/(650 × 5)) × 100%
η ≈ 90%
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The olive oil in a bottle has a mass of 360 g. If the density of olive oil is 0.9 g/mL, what is its volume?
A. 300 mL
B. 400 mL
C. 500 mL
D. 600 mL
Answer:
B-400 mL
Explanation:
Volume = Mass divided by density
360 / 0.9 = 400
Kinetic energy is the energy of motion. How could you determine how much kinetic energy an object has?
A.
by finding its speed and direction
B.
by finding its mass and speed
C.
by finding its height and width
D.
by finding its position and form
Answer:
B
Explanation:
this is because the formula for calculating 1 half of the mass multiplied by the velocity squared
Answer:
b
Explanation:
You pull a 100 N object up a ramp with only 20 N of force.
Find MA.
Mechanical advantage of the ramp is 5
Explanation:
The Mechanical Advantage (MA) of a simple machine represents the factor of multiplication of the input force applied in the machine; it represents the mechanical advantage of the machine taking into account the energy losses due to internal frictional forces.
It is given by
[tex]MA=\frac{Load}{Effort}[/tex]
where
Load is the force in output, which is the weight of the object moved
Effort is the input force applied to move the object
For the ramp in this problem, we have:
Load = 100 N
Effort = 20 N
Therefore, the mechanical advantage is
[tex]MA=\frac{100}{20}=5[/tex]
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Solve for the missing values using the inverse square
law. Round to the thousandths (0.001) place.
50 pointssss!!!!
SHOW WORK PLS
Answer:
1 2 3 4 5
New force ( N ) 1.25 0.4166 48 175 150
Explanation:
We know that ,
Force ( f ) ∝ distance ( d )
1 )
initial distance =40 m
initial force = 5 N
F ∝ d
F = k d ( k = proportionality constant )
5 = k * 40
k = (1/8)
new distance = 10 m
new force = ( 1/8 ) * 10 = 1.25 N
2)
d = 72 m
F = 2.5 N
k = 2.5/72
new distance = 12 m
new force = ( 2.5/72 ) * 12 = 0.4166 N
3)
d = 12 m
F = 8 N
k = 2/3
new distance = 72 m
new force = ( 2/3 ) *72 = 48 N
4 )
d = 6 m
F = 25 N
k = 25/6
new distance = 42 m
new force = ( 25/6)*42 = 175 N
5)
d = 10 m
F = 50 N
k = 5
new distance = 30 m
new force = 5 * 30 = 150 N
Specifically, I do not know the answer to 18, but if someone could tell me the answers to all of them that would be great.
Answer:
16. reflected
17. transmitted
18. refracted
Looking at the image below (a roller coaster model), explain why the potential energy went from 100 (at top) to zero, and the kinetic energy from zero to 100 (joules)?
Answer:
Explanation:
The total energy at all times is equal to the sum of kinetic and potential energy.
Eu = Ep + Ek
If an object has reached a finite height point and is stationary, then the potential energy is maximum (100 J) and the kinetic energy is equals to zero.
If the same object started to fall before the impact on the ground itself, the kinetic energy is maximum (100 J) and the potential energy is minimum ie zero.
God is with you!!!
In a model ensemble system, what do meteorologists change each time they run a simulation of the same model?
a) the predicted forecast
B) the mathematical equations used
c) the initial conditions
D) the range of possible outcomes
Answer:
the initial conditions
Explanation:
The rest of the answers are
the duration of seasons on Earth
turn left toward the coast, turn right and head out to sea (in that order)
a warm, dry air mass moving over an area.
The two models assimilate data differently using different equations.
changes in ocean currents
In a model ensemble system, meteorologists change the initial conditions each time they run a simulation of the same model.
What is Ensemble modelling?Ensemble modelling is a process in which multiple diverse models are created to predict an outcome, either by employing a variety of modelling algorithms or by employing a variety of training data sets. The ensemble model then aggregates each base model's prediction, yielding a single final prediction for the unseen data.
The goal of using ensemble models is to reduce prediction generalization error. When the ensemble approach is used, the prediction error of the model decreases as long as the base models are diverse and independent. In making a prediction, the approach seeks the wisdom of the crowds.
Hence, in a model ensemble system, meteorologists change the initial conditions each time they run a simulation of the same model. Option(c) is correct.
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A transverse wave on a long horizontal rope with a
wavelength of 8 m travels at 2 m/s. At t= 0, a
particular point on the rope has a vertical
displacement of +A, where A is the amplitude of
the wave. At what time will the vertical
displacement of this same point on the rope be -A ?
Answer:
2 seconds
Explanation:
The frequency of a wave is related to its wavelength and speed by the equation
[tex]f=\frac{v}{\lambda}[/tex]
where
f is the frequency
v is the speed of the wave
[tex]\lambda[/tex] is the wavelength
For the wave in this problem,
v = 2 m/s
[tex]\lambda=8 m[/tex]
So the frequency is
[tex]f=\frac{2}{8}=0.25 Hz[/tex]
The period of a wave is equal to the reciprocal of the frequency, so for this wave:
[tex]T=\frac{1}{f}=\frac{1}{0.25}=4 s[/tex]
This means that the wave takes 4 seconds to complete one full cycle.
Therefore, the time taken for the wave to go from a point with displacement +A to a point with displacement -A is half the period, therefore for this wave:
[tex]t=\frac{T}{2}=\frac{4}{2}=2 s[/tex]
The time taken by the wave to travel the vertical displacement from the point on the rope to -A is 2 seconds
Given to us:
wavelength λ = 8 m,
Velocity v = 2 m/s,
The frequency of a wave is given by:
[tex]frequency=\dfrac{Velocity}{wavelength}\\f=\dfrac{V}{\lambda}\\\\f=\dfrac{2}{8}\\\\f= 0.25\ \rm Hz[/tex]
Therefore, the frequency of the wave is 0.25 Hz.
The period of a wave is equal to the reciprocal of the frequency,
[tex]{\rm period\ of\ time}(T),\\T=\dfrac{1}{f}\\T=\dfrac{1}{0.25}\\\\T=4\ sec[/tex]
Therefore, It takes 4 seconds to complete one full cycle.
Hence, the time taken by the wave to travel the vertical displacement from the point on the rope to -A is 2 seconds as its is the half distance which is needed to be traveled by the wave.
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I'm big boi confused.
A beam of light traveling in air enters a substance. If the angle of incidence is 35 ∘ and the angle of refraction is 25 ∘ , what is the index of refraction of the substance?
n1sin(theta)1=n2sin(theta)2 So would it be like 1.008*sin(35)=n2*sin(25) ????
Explanation:
Correct. Air has an index of refraction of approximately 1, and the angle of incidence is 35°. The substance has an unknown index of refraction n, and the angle of refraction is 25°.
1 sin 35° = n sin 25°
n = 1.36
In this section of a circuit, resistors R1, R2, and R3 combine for an equivalent resistance of 4.0 ohm. What is R2? Let R1 = 6.0 ohm and R3= 2.0 ohm.
Answer:
R2=10ohm
Explanation:
In this combination
R2 and R3 are in series combination where R1 is in parallel combination with them hence
R2+R3=R`
And
1/R`+1/R1=1/Req
1/R`=1/Req-1/R1
1/R`=1/4-1/6
=1/12
R`=12ohm
Also
R2+R3=R`
R2=R`-R3
R2=12-2
R2=10ohm
A 75 kg pilot flies a plane in a loop. At the top of the loop, where the plane is completely
upside down for an instant, the pilot hangs freely in the seat and does not push against the
seat belt. The airspeed indicator reads 120 m/s. What is the radius of the planes loop?
Answer:
1.47 km
Explanation:
When the pilot hangs freely in the seat and does not push against the seat belt, his centripetal acceleration would counter balance gravitational acceleration g = 9.81m/s2 = a
We can calculate the radius of the loop using velocity v = 120m/s and a
[tex]a = \frac{v^2}{r}[/tex]
[tex]r = \frac{v^2}{a} = \frac{120^2}{9.81} = 1467.89 m[/tex] or 1.46 km
The radius of the plane's loop is approximately 1469.4 meters. This is determined by equating the centripetal force and gravitational force at the top of the loop and solving for radius.
Explanation:The question is about determining the radius of a plane's loop while considering the gravitational force and centripetal acceleration. At the top of the loop, the pilot is not pushed against the belt, which means the gravitational force is providing the necessary centripetal force. We can use the equation of motion for circular motion to solve the problem.
Given that the mass (m) of the pilot is 75 kg and he is travelling with a speed (v) of 120 m/s, and the acceleration due to gravity (g) is approximately 9.8 m/s². Centripetal force (mv²/r) is equal to the gravitational force (mg), hence we can equate mv²/r= mg. The unknown here is r (radius), which we can solve for by rearranging the equation to: r = v²/g. Plugging in the given values gives r = (120 m/s)² / 9.8 m/s² = approximately 1469.4 meters.
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A solution in which [H +] = 10-8 M has a pH of ____ and is
A. 8, basic
B. 6, basic
C. -6,basic
D. -8, acidic
Yo sup??
To solve this question we must learn that
pH=-log([H+])
in the question its given that
[H+]=10^(-8)
therefore
pH=-log(10^(-8))
=-(-8)log10
=8
Since pH>7 therefore its basic
Hence the correct answer is option A ie
A.8, basic
Hope this helps.
Answer: 8 basic
Explanation:
These are equal and opposite forces that do not cause a change in position or motion.
Please answer quickly!
In this section of a circuit, a current of 2.6 A flows across R1. What is the potential difference V between point x and point y (across R2)? Let R1 = 4.0 ohm, R2 = 8.0 ohm, and R3 = 1.0 ohm.
Answer:
V=21V
Explanation:
In series combination current is same
I=2.6A
R2=8ohm
V2=2.6×8
V2=20.8
V2=21V
Answer:
Explanation:
21 v
refractive index of Glass sample is 1.52 and date of Ruby is 1.71 if the speed of light in vacuum b 3 into 10 to the power 8 metre per second find the speed of light in glass in Ruby and also calculate the refractive index of air with respect to glass
The speed of light in glass [tex]1.97 \times 10^{8}\ \mathrm{m} / \mathrm{s}[/tex]
The speed of light in Ruby is [tex]1.75 \times 10^{8} \mathrm{m} / \mathrm{s}[/tex]
The refractive index of air with respect to glass is 0.666
Explanation:
The refractive index is the degree of diffraction of a light beam passing from one medium to another. It can also be defined as the ratio of the speed of light in an empty space to the speed of light in a material. The equation is given as
[tex]\text {refractive index, n\ or } \mu=\frac{\text c}{\text {v}}[/tex]
Given data:
[tex]\mu_{\text {glass}}=1.52[/tex]
[tex]\mu_{r u b y}=1.71[/tex]
Velocity of light in vacuum, c = [tex]3 \times 10^{8} \mathrm{m} / \mathrm{s}[/tex]
We need to find velocity of glass, ruby and refractive index ratio of air and glass
To find velocity of glass,
[tex]1.52=\frac{3 \times 10^{8}}{\text {velocity of glass}}[/tex]
[tex]\text {velocity of glass}=\frac{3 \times 10^{8}}{1.52}=1.97 \times 10^{8} \mathrm{m} / \mathrm{s}[/tex]
To find velocity of ruby,
[tex]1.71=\frac{3 \times 10^{8}}{\text {velocity of Ruby}}[/tex]
[tex]\text {velocity of Ruby}=\frac{3 \times 10^{8}}{1.71}=1.75 \times 10^{8}\ \mathrm{m} / \mathrm{s}[/tex]
To calculate the refractive index of air with respect to glass: = [tex]\frac{\mathrm{n}_{\text {air}}}{\mathrm{n}_{\text {glass}}}[/tex]
We know, the value of the refractive index of air is 1
The value of the refractive index of glass is 1.5
So, the ratio of them should be [tex]\frac{1}{1.5}=0.666[/tex]
A mechanical engineer launched an arrow with a speed of 800.0 m/s at an angle of 75.0 degree to the horizontal . If it landed on a target 450.0 m away at the same height from which it was fired , for how long was the arrow in the air ?
Answer: 2.17 s
Explanation:
The described situation is related to projectile motion (also known as parabolic motion). So, this kind of motion has a vertical component and a horizontal component; however, in this case we will only need the equation related to the horizontal displacement [tex]x[/tex]:
[tex]x=V_{o}cos \theta t[/tex]
Where:
[tex]x=45 m[/tex] is the arrow's horizontal displacement
[tex]V_{o}=800 m/s[/tex] is the arrow's initial velocity
[tex]\theta=75\°[/tex] is the angle
[tex]t[/tex] is the time the arrow is in the air
Isolating [tex]t[/tex]:
[tex]t=\frac{x}{V_{o}cos \theta}[/tex]
Solving with the given data:
[tex]t=\frac{45 m}{800 m/s cos(75\°)}[/tex]
[tex]t=2.17 s[/tex] This is the time the arrow is in the air
The three classes of rocks are sedimentary, metamorphic, and igneous. How are rocks classified into one of these three groups?
Answer:
according to the method of their formation
Explanation:
A sphere of mass m" = 2 kg travels with a velocity of magnitude υ") = 8 m/s toward a sphere of mass m- = 3 kg initially at rest, as shown in the figure. The collision of the two spheres is elastic and the length of the rope is l = 4 m. a) Apply the conservation of the momentum for the system of the two spheres and calculate the speed of the sphere m- just after the collision. b) Calculate the maximum height of the mass m-. c) What is the value of the angle θ at the maximum height of the mass m-? d) If the sphere m- is instantaneously at rest at its maximum height, calculate the tension in the string. e) When the height of the sphere of mass m- from its lowest position is 1 m, calculate its speed. f) What is the tension in the string when the sphere of mass m2 is 1 m above its lowest position?
a) 6.4 m/s
b) 2.1 m
c) [tex]61.6^{\circ}[/tex]
d) 14.0 N
e) 4.6 m/s
f) 37.9 N
Explanation:
a)
Since the system is isolated (no external forces on it), the total momentum of the system is conserved, so we can write:
[tex]p_i = p_f\\m_1 u_1 = m_1 v_1 + m_2 v_2[/tex]
where:
[tex]m_1 = 2 kg[/tex] is the mass of the 1st sphere
[tex]m_2 = 3kg[/tex] is the mass of the 2nd sphere
[tex]u_1 = 8 m/s[/tex] is the initial velocity of the 1st sphere
[tex]v_1[/tex] is the final velocity of the 1st sphere
[tex]v_2[/tex] is the final velocity of the 2nd sphere
Since the collision is elastic, the total kinetic energy is also conserved:
[tex]E_i=E_k\\\frac{1}{2}m_1 u_1^2 = \frac{1}{2}m_1 v_1^2 + \frac{1}{2}m_2 v_2^2[/tex]
Combining the two equations together, we can find the final velocity of the 2nd sphere:
[tex]v_2=\frac{2m_1}{m_1+m_2}u_1=\frac{2(2)}{2+3}(8)=6.4 m/s[/tex]
b)
Now we analyze the 2nd sphere from the moment it starts its motion till the moment it reaches the maximum height.
Since its total mechanical energy is conserved, its initial kinetic energy is entirely converted into gravitational potential energy at the highest point.
So we can write:
[tex]KE_i = PE_f[/tex]
[tex]\frac{1}{2}mv^2 = mgh[/tex]
where
m = 3 kg is the mass of the sphere
v = 6.4 m/s is the initial speed of the sphere
[tex]g=9.8 m/s^2[/tex] is the acceleration due to gravity
h is the maximum height reached
Solving for h, we find
[tex]h=\frac{v^2}{2g}=\frac{(6.4)^2}{2(9.8)}=2.1 m[/tex]
c)
Here the 2nd sphere is tied to a rope of length
L = 4 m
We know that the maximum height reached by the sphere in its motion is
h = 2.1 m
Calling [tex]\theta[/tex] the angle that the rope makes with the vertical, we can write
[tex]h = L-Lcos \theta[/tex]
Which can be rewritten as
[tex]h=L(1-cos \theta)[/tex]
Solving for [tex]\theta[/tex], we can find the angle between the rope and the vertical:
[tex]cos \theta = 1-\frac{h}{L}=1-\frac{2.1}{4}=0.475\\\theta=cos^{-1}(0.475)=61.6^{\circ}[/tex]
d)
The motion of the sphere is part of a circular motion. The forces acting along the centripetal direction are:
- The tension in the rope, T, inward
- The component of the weight along the radial direction, [tex]mg cos \theta[/tex], outward
Their resultant must be equal to the centripetal force, so we can write:
[tex]T-mg cos \theta = m\frac{v^2}{r}[/tex]
where r = L (the radius of the circle is the length of the rope).
However, when the sphere is at the highest point, it is at rest, so
v = 0
Therefore we have
[tex]T-mg cos \theta=0[/tex]
So we can find the tension:
[tex]T=mg cos \theta=(3)(9.8)(cos 61.6^{\circ})=14.0 N[/tex]
e)
We can solve this part by applying again the law of conservation of energy.
In fact, when the sphere is at a height of h = 1 m, it has both kinetic and potential energy. So we can write:
[tex]KE_i = KE_f + PE_f\\\frac{1}{2}mv^2 = \frac{1}{2}mv'^2 + mgh'[/tex]
where:
[tex]KE_i[/tex] is the initial kinetic energy
[tex]KE_f[/tex] is the kinetic energy at 1 m
[tex]PE_f[/tex] is the final potential energy
v = 6.4 m/s is the speed at the bottom
v' is the speed at a height of 1 m
h' = 1 m is the height
m = 3 kg is the mass of the sphere
And solving for v', we find:
[tex]v'=\sqrt{v^2-2gh'}=\sqrt{6.4^2-2(9.8)(1)}=4.6 m/s[/tex]
f)
Again, since the sphere is in circular motion, the equation of the forces along the radial direction is
[tex]T-mg cos \theta = m\frac{v^2}{r}[/tex]
where
T is the tension in the string
[tex]mg cos \theta[/tex] is the component of the weight in the radial direction
[tex]m\frac{v^2}{r}[/tex] is the centripetal force
In this situation we have
v = 4.6 m/s is the speed of the sphere
[tex]cos \theta[/tex] can be rewritten as (see part c)
[tex]cos \theta = 1-\frac{h'}{L}[/tex]
where in this case,
h' = 1 m
L = 4 m
And [tex]r=L=4 m[/tex] is the radius of the circle
Substituting and solving for T, we find:
[tex]T=mg cos \theta + m\frac{v^2}{r}=mg(1-\frac{h'}{L})+m\frac{v^2}{L}=\\=(3)(9.8)(1-\frac{1}{4})+(3)\frac{4.6^2}{4}=37.9 N[/tex]
2. How does the medium vibrate in a transverse wave?
A at right angles to the direction the wave travels
B with half the force of the energy provided
C parallel to the direction the wave travels
D with twice the force of the energy provided
ANSWER :
(A) AT RIGHT ANGLES TO THE DIRECTION THE WAVE TRAVELS.
EXPLANATION :
TRANSVERSE WAVES IS THAT IN WHICH THE PARTICLES VIBRATE WITH AN UP-AND-DOWN MOTION. THE PARTICLES IN A TRANSVERSE WAVE MOVE ACROSS OR PERPENDICULAR TO THE DIRECTION THAT THE WAVE IS TRAVELING OR AT RIGHT ANGLES TO THE DIRECTION THE WAVE TRAVELS.
A softball is thrown straight up. To what height will it go if it takes 2.0 sec to reach the highest point?
Answer:
4.4 m
Explanation:
Given:
v = 0 m/s
a = -9.8 m/s²
t = 2.0 s
Find: Δy
Δy = vt − ½ at²
Δy = 0 − ½ (-9.8) (2.0)²
Δy = 4.4 m
an experiment was done to see which colored sand would heat up the most when placed in the sun. The sand samples were white, red, green, and black. allsamples were the same amount placed in independent containers left in the sun the same amount of time and the temperature was measured with the same thermometer. what is the independent variable the dependent variable the control and the constant?