The final speed of the roller coaster is 454.6 m/s.
How to determine final speed?To determine the behavior of the roller coaster, we can use the conservation of energy principle, which states that the total energy of a closed system remains constant. The initial energy of the roller coaster is potential energy (due to its height) and kinetic energy (due to its initial speed), and the final energy is potential energy (due to its final height) and kinetic energy (due to its final speed). Assuming no energy losses due to friction or other factors, the initial energy must equal the final energy.
The potential energy of the roller coaster at height h is given by:
Ep = mgh
where m is the mass of the roller coaster, g is the acceleration due to gravity (9.81 m/s²), and h is the height of the roller coaster.
At the top of the roller coaster (where h = 100 m), the potential energy of the roller coaster is:
Ep = (1000.0 kg)(9.81 m/s²)(100.00 m) = 981000 J
The kinetic energy of the roller coaster at the initial speed vi is given by:
Ek = (1/2)mv²
where m is the mass of the roller coaster, and v is its speed.
At the beginning of the roller coaster (where vi = 10.00 m/s), the kinetic energy of the roller coaster is:
Ek = (1/2)(1000.0 kg)(10.00 m/s)² = 50000 J
The total energy of the roller coaster at the beginning of the ride is:
Etotal = Ep + Ek = 981000 J + 50000 J = 1031000 J
At the bottom of the roller coaster, all of the potential energy has been converted to kinetic energy, and the roller coaster has reached its maximum speed. Therefore, the kinetic energy at the bottom of the roller coaster is:
Ek = Etotal - Ep = 1031000 J - 0 J = 1031000 J
The final speed of the roller coaster, vf, is found using the equation:
Ek = (1/2)mv²
Solving for vf:
vf = √(2Ek/m) = √(2(1031000 J)/(1000.0 kg)) = 454.6 m/s
Therefore, the final speed of the roller coaster is approximately 454.6 m/s.
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The complete question is:
a frictionless roller coaster is given an initial speed of vi=10.00m/s , at the initial height h=100:00m,has a mass m=1000.0kg. what is the roller coaster's final speed?
Assume the two radii of the thin convex lens surfaces to be equal for each of the two convex lenses used in this experiment and the index of refraction of their glass to be 1.5. From the relationship given in equation, determine the radius of curvature for each of the two thin convex lenses that you need
The radius of curvature for each surface of the thin convex lenses is 4 times the focal length (f).
A convex lens is what?Two spherical surfaces often make up an optical lens. The lens is referred to as a biconvex lens or just a convex lens if those surfaces are curved outwards. These lenses have the ability to focus an outside light beam to a spot on the opposite side by converging it.
Is the convex lens's radius of curvature positive or negative?The radius of curvature is always positive for convex lenses and always negative for concave lenses.
The relationship between the focal length (f), radius of curvature (R), and index of refraction (n) for a thin convex lens is,
1/f = (n - 1) * (1/R1 - 1/R2)
where R1 and R2 are the radii of curvature of the two surfaces of the lens.
Since the two radii of curvature for each of the two convex lenses are equal, we can simplify the equation to:
1/f = (n - 1) * (2/R)
R = radius of curvature for each surface of the lens.
We can rearrange this equation
R = 2 * f / (n - 1)
Substituting the given values of n = 1.5
R = 2 * f / 0.5
R = 4 * f
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Why does nuclear fusion require high temperatures and high densities? (Select all that apply.)
to overcome the repulsive force between the protons
to overcome attractive forces between protons and electrons
because it produces so much energy
because it occurs in the Sun
so there are enough collisions for fusion to occur
They get enough energy and high temperature to break their equal electric repulsion. The strong nuclear force will defeat the electric barrier once the nuclei are nearer & they can fuse as a final result.
Why is nuclear power so powerful?A strong nuclear force can be used in this situation. Meson exchange between nucleons produces the intense nuclear force between them. This conversation is comparable to two persons striking a tennis ball or ping-pong ball back back and forwards continually.
How do nuclear weapons get made?The much more fundamental powerful force, also known as the strong interaction, has a byproduct known as the nuclear force. The quarks—elementary particles that make up protons and neutrons—are bound together by the strong interaction, which is an attractive force.
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A student attaches a rope to a 33 kg box, and drags it to the left with constant velocity of 1.11 m/s. The tension in the rope is 283 N at an angle of 33° to the ground.
How much does the box weigh?
323.4N
Find the x and y components of the applied (tension) force:
Fx =
237.34N
Fy =
154.13 N
How much friction must be present?
How much Normal force must be present?
Answer: To find the frictional force and normal force, we need to first find the gravitational force acting on the box, which is equal to its weight. We can find weight by multiplying the mass of the box by the acceleration due to gravity:
Weight = m * g
Weight = 33 kg * 9.8 m/s^2
Weight = 323.4 N
To find the x and y components of the tension force, we can use trigonometry:
Fx = Tension * cos(33°)
Fx = 283 N * cos(33°)
Fx = 237.34 N
Fy = Tension * sin(33°)
Fy = 283 N * sin(33°)
Fy = 154.13 N
Since the box is moving with constant velocity, we know that the net force on the box is zero. Therefore, the frictional force must be equal in magnitude and opposite in direction to the x component of the tension force:
Friction = -Fx
Friction = -237.34 N
The normal force is equal in magnitude and opposite in direction to the y component of the tension force:
Normal force = -Fy
Normal force = -154.13 N
Explanation:
In the same liquid, the pressures are equal at all points that are
A. the same distance below the liquid surface.
B. along the vertical walls of the container.
C. not touching any immersed objects.
D. not in the sunlight.
The correct option is A. which states that in the same liquid, the pressures are equal at all points that are at the same distance below the liquid surface.
This is because the pressure is determined by the weight of the liquid column above it, which is the same for all points at the same depth. The pressure along the vertical walls of the container is not equal because the liquid is in hydrostatic equilibrium which means that the pressure is not the same at all points in the liquid, and since the walls are vertical, the pressure is the same along them. The pressure at any point not touching any immersed objects is not equal to the pressure at any other point not touching any immersed objects because the pressure is determined by the weight of the liquid column above it, which is the same for all points not touching any immersed objects. The pressure is not affected by factors such as sunlight since the pressure at any point in the sunlight is equal to the pressure at any other point not in the sunlight.
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Which above element is the most active nonmetal?
A. cerium (Ce)
B. potassium (K)
C. xenon (Xe)
D. iodine (I)
E. gold (Au)
Answer:
D. iodine (I) is the most active nonmetal in the options given.
I hope you can help me with this problem thank you.
This discussion will require you to interview and talk to an older family member, parent(s), or someone who knew you intimately during the first two years of your life.
You will first need to read "The Developing Person Through the Life Span 11th Edition" chapters 5, 6, and 7 to prepare to respond to the discussion prompt and to interview and talk to individuals who knew you during the first two years of your life.
Consider the first two years of your life with respect to:
- physical development;
- cognitive development; and
- psychosocial development.
Then take this opportunity to talk to individuals who remember this stage of your development, including
- language development;
- memory skills;
- motor skills;
- early emotions and temperament; and
- early attachment.
And finally, what role did your race, ethnicity, gender, and culture play in your development during your first two years of life, and how you were socialized during those years?
The creation of an individual's ethnic identity also includes their self-categorization Thermodynamics within and psychological ties to their ethnic group (s).
How does a child's social maturation depend on their ethnicity?Children's ethnicity gives them a sense of connection and helps them to understand who there are and where she came from. Nonetheless, ethnicity can cause conflicts between people, and children who belong to a minority ethnic group may grow despite looking less significant in society.
What function does ethnicity serve?They point out that ethnicity, as a scientific term, enables researchers to distinguish between different people-groups based on their lineage, language, customs, philosophy, culture, or country without relying on the physical qualities that are essential to the notion of ethnicity (Atkinson et al., 1998).
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Starting from rest at a height equal to the radius of the circular track, a block of mass 24 kg slides down a quarter circular track under the influence of gravity with friction present (of coefficient μ). The radius of the track is 26 m.
The acceleration of gravity is 9.8 m/s2 .
If the kinetic energy of the block at the bottom of the track is 3700 J, what is the work done against friction?
Answer in units of J.
Answer: The initial potential energy of the block is converted into kinetic energy at the bottom of the track, and some work is done against friction. We can use conservation of energy to find the work done against friction:
Initial potential energy = Final kinetic energy + Work against friction
The initial potential energy is mgh, where m is the mass of the block, g is the acceleration due to gravity, and h is the initial height of the block (which is equal to the radius of the track):
Initial potential energy = mgh = (24 kg)(9.8 m/s^2)(26 m) = 60432 J
The final kinetic energy is given as 3700 J.
Plugging these values into the equation above, we can solve for the work done against friction:
Work against friction = Initial potential energy - Final kinetic energy
= 60432 J - 3700 J
= 56732 J
Therefore, the work done against friction is 56732 J
Explanation:
in a car race along a straight race course betv,ieen Yaw and Kofi. both staried from rest but Kofi leaves the statiing line 2.00 s after Yaw does. Yav,; and Kofi maintain acceleration of 4.00 m S2 and 5.00 m S·2 respectively.
We can use the following kinematic equations to solve the problem:
v = u + ats = ut + 1/2 at^2v^2 = u^2 + 2asFor Yaw:
a = 4.00 m/s^2
t = time taken by Kofi + 2.00 s (since Yaw started 2.00 s earlier)
s = distance covered by Yaw when Kofi starts
Using the equation s = ut + 1/2 at^2, we get:
s = 0 + 1/2 (4.00) (2.00)^2
s = 8.00 m
For Kofi:
a = 5.00 m/s^2
We want to find the time when Kofi overtakes Yaw, so we can use the equation:
s = ut + 1/2 at^2
Let t be the time taken by Kofi to overtake Yaw. At that time, their positions will be the same, so the distance covered by Kofi will be equal to the distance covered by Yaw plus 8.00 m. Hence,
1/2 (5.00) t^2 = 1/2 (4.00) (t - 2.00)^2 + 8.00
Simplifying and solving for t, we get:
t = 4.00 s
Therefore, Kofi overtakes Yaw after 4.00 s.
To find the distance Kofi travels before he catches Yaw, we can use the same equation:
s = ut + 1/2 at^2
Using t = 4.00 s and a = 5.00 m/s^2, we get:
s = 0 + 1/2 (5.00) (4.00)^2
s = 40.00 m
Therefore, Kofi travels 40.00 m before he catches Yaw.
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in a car race along a straight race course between Yaw and Kofi. both start from rest but Kofi leaves the starting line 2.00 s after Yaw does. Yav,; and Kofi maintain acceleration of 4.00 m S2 and 5.00 m S·2 respectively.
Calculate the time at which kofi overtakes yaw
Calculate the distance kofi travels before he catches yaw.
a copper water tank of mass 20 kg contains 150 kg of water at 15°C calculate the energy needed to heat the water and the tank to 55°C
copper shc - 385j/kg
water shc - 4200j/kg
Answer: 25230800 Joules
Explanation: We can treat the copper tank and the water inside as two different objects since they have different specific heats. We will utilize Q=Mcdelta(t) in this problem where M is mass, c is specific heat, and delta t is the change in temperature.
Since we are treating the copper and water separately we can make a Mcdelta(t) for each one of them. This gives us Q=(mass of copper)(specific heat of copper)(delta(t))+(mass of water)(specific heat of water)(delta(t)). The delta t will be the same because both the copper and water are at 15 celsius. Now we just do some calculations.
Q=(mass of copper)(specific heat of copper)(delta(t))+(mass of water)(specific heat of water)(delta(t))
Q=(20)(385)(55-15)+(150)(4200)(55-15)
Q=30800+25200000
Q=25230800 J
This number may seem absurdly high but there is 150 kg of water being heated up which is 150 liters(A LOT!).
Hope this helps!
A
consists of a period of non-strenuous activity that slowly
prepares the body for more vigorous exercise.
The period of non-strenuous activity that slowly prepares the body for more vigorous exercise is called a warm-up. A warm-up is an essential part of any exercise routine as it helps to prepare the body physically and mentally for more intense physical activity.
Explain non-strengthening activity that gradually prepares the body for more strenuous exercise?
During a warm-up, the body's muscles, heart, and lungs gradually increase their activity levels, and the body's temperature begins to rise. This gradual increase in activity and temperature helps to reduce the risk of injury and improves performance during more intense exercise.
A typical warm-up can last between 5 to 15 minutes, depending on the intensity of the upcoming exercise. Some common warm-up activities include light aerobic exercises like jogging or cycling, dynamic stretching, and mobility exercises.
It is important to note that a warm-up should not be too strenuous activity , as this can cause fatigue and decrease performance during the main workout. Instead, it should be a gentle and gradual increase in activity level to prepare the body for the upcoming exercise.
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30 POINTS - the cone moves with simple harmonic motion and it emits
The cone emits a single-frequency sound of 100 Hz and moves in a straightforward harmonic manner. The cone moves a maximum of 2.0 millimetres when it is making a loud sound.
What moves with simple harmonic motion?Simple harmonic motion is a particular type of periodic motion of a body that arises from a dynamic equilibrium between an inertial force that is proportional to the acceleration of the body away from the static equilibrium position and a restoring force on the moving object that is directly proportional to the magnitude of the object's displacement and acts towards the object's equilibrium position.
In mechanics and physics, SHM is sometimes used to refer to this motion. If friction or any other energy dissipation is not present, it leads to an oscillation that is represented by a sinusoid and that lasts indefinitely.
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A rifle with a weight of 35 N fires a 5.5g bullet with a speed of 270m/s. Find the recoil speed of the rifle
The recoil speed of the 35N rifle is 0.42 meters per second.
What is the recoil speed of the rifle?To find the recoil speed of the rifle, we can use the principle of conservation of momentum.
According to this principle, the total momentum before firing the bullet is equal to the total momentum after firing the bullet.
Initially, the rifle and bullet are at rest, so their total momentum is zero.
p_initial = 0
After firing the bullet, the momentum of the bullet is:
p_bullet = m_bullet × v_bullet
p_bullet = ( 5.5 / 1000 )kg × 270m/s
p_bullet = 1.485 kg m/s
By conservation of momentum, the momentum of the rifle in the opposite direction is also equal to 1.485 kg m/s.
Let the recoil speed of the rifle be v_recoil. Then:
p_rifle = m_rifle × v_recoil
v_recoil = p_rifle / m_rifle
Note that weight of the rifle = 35N, then mass = 35/9.8 kg
v_recoil = 1.485 kgm/s / ( 35/9.8 kg )
v_recoil = 0.42 m/s
Therefore, the recoil speed of the rifle is 0.42 m/s.
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Which angle (A,B, or C) is the diffraction angle?
B because it’s closest to the center line
As waves come into contact with a barrier or aperture, they experience the phenomenon known as diffraction, which causes them to bend and disperse.
Which diffraction angle has the highest value?Diffracted light has maximum intensities at angles m given by dsinm=m when light is usually incident on a diffraction grating. Thus, the 3rd-order maxima can arise at 90° (or a smaller angle) and there won't be any 4th-order maxima because the maximum angle for diffraction maxima is 90°.
What factors affect angle of diffraction?Light's wavelength determines the amount of diffraction, with longer wavelengths diffracted at a greater angle than shorter ones (in effect, red light are diffracted at a higher angle than is blue and violet light).
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Answer:
it is B
Explanation:
How to solve it please i need explanation
Answer:
8 N
Explanation:
The net force formula is F = m×a
a = 2 m/s^2, m2 = 4 kg
So, now we can find F:
F = 4 × 2 = 8 N
The VR(and so IMA) of the inclined plane
ANSWER 5 QUESTIONS FOR 35 POINTS PLS!!!
1. The problem in correlating the rock layers of location D is that there are no clear index fossils that can be used to determine the relative age of the rock layers.
2. Yes, there can be a problem in determining the time span of any rock layers without the use of index fossils. The age of a rock layer can only be estimated by comparing it to the ages of other rock layers in the area, which is done by examining the sequence of the layers and the type of fossils found in them. However, this method only provides a relative age range and not an exact age.
3. While fossils can provide important clues to the relative age of rock layers, they cannot be used to determine the exact age of a layer. This is because the age of a rock layer is determined by the decay of radioactive isotopes in the rock, which is a process that occurs over a long period of time.
4. The feature(s) of the fossils that make them ineffective in dating the relative age of rock layers is that they are not index fossils. Index fossils are usually species that have a widespread distribution and existed for a short period of time, making them useful for dating rock layers over a large area. The fossils listed (clam, nautilus, fusulina, sea urchin, gingko, and snail) may have existed for long periods of time, making them less useful for dating the relative age of rock layers.
What are fossil?Index fossils are distinctive fossils that are used to establish and compare the relative ages of rock layers in different locations. Without index fossils, it becomes difficult to determine which layers are older or younger relative to each other.
The "missing" rock layer could have been eroded away or never deposited in that location. This can occur due to natural processes such as erosion or deposition in a different location, or due to human activity such as mining or excavation. Without the missing layer, it becomes more difficult to accurately date the other rock layers in the area.
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1. What was the problem in correlating the rock layers of location D? Explain.
2. Was there a problem in determining the time span of any rock layers? Explain.
3. Why can't you determine the EXACT age of a layer of rock by simply observing fossils in a rock layer? What constraints you in making this determination?
4. There are fossils in location D that are not index fossils. What feature(s) of these fossils make them ineffective in dating the relative age (as a range of time) of rock layers? Note: The names of the fossils are listed below. What "problem" most likely occurred that led to the missing rock layer? Explain
QUESTION 1 A travel agency has advertising signage of a globe suspended by frame as shown Some data are provide as follows: Weight W = 20N a = 25⁰ B = 60° x= 5m What is the force in the member BC - give your answer in N. Tension = +ve Compression = -ve B a X В 4
Therefore, the force in member BC is equal to the vertical component of the force at joint B, which is: F_BC = -V_BC = -28.37 N.
What is force?In physics, force is defined as an influence that causes an object to undergo a change in motion or to experience deformation. It is a vector quantity, which means it has both magnitude and direction. The SI unit of force is the Newton (N). According to Newton's laws of motion, a force is required to change the motion of an object. The first law states that an object at rest will remain at rest, and an object in motion will remain in motion at a constant velocity, unless acted upon by an unbalanced force. The second law states that the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass (F = ma). The third law states that for every action, there is an equal and opposite reaction.
Here,
To solve this problem, we can use the method of joints to analyze the forces acting on the joints of the frame. The method of joints involves analyzing the forces acting on each joint of a structure in order to determine the internal forces (tension or compression) in the members.
We will start by analyzing joint B, since it has only two unknown forces (the force in member BC and the horizontal force in member AB). We can apply the equations of static equilibrium to this joint:
ΣFx = 0: H_AB = 0
ΣFy = 0: V_AB + V_BC - W = 0
where H_AB and V_AB are the horizontal and vertical components, respectively, of the force in member AB, V_BC is the vertical component of the force in member BC, and W is the weight of the globe.
From the given data, we can determine the values of V_AB and W:
V_AB = -W sin(a) = -20 sin(25°) ≈ -8.37 N
W = 20 N
Substituting these values into the equations of static equilibrium, we can solve for V_BC and H_AB:
V_BC = W - V_AB = 20 + 8.37 = 28.37 N
H_AB = 0
F_BC = -V_BC = -28.37 N
Note that the negative sign indicates that the force in member BC is in compression, which means it is being pushed inward by the forces acting on the structure.
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Bumblebees are skilled aerialists, able to fly with confidence around and through the leaves and stems of plants. In one test of bumblebee aerial navigation, bees in level flight flew at a constant 0.40 m/s, turning right and left as they navigated an obstacle-filled track. While turning, the bees maintained a reasonably constant centripetal acceleration of 4.0 m/s2
a) What is the radius of curvature for such a turn?
b) How much time is required for a bee to execute a 90∘ turn?
The turn's radius of curvature is 0.04 meters. A 90 degree turn is completed by the bee in 0.628 seconds on average.
How is the radius of curvature for such a turn determined?The radius of curvature of the turn can be calculated using the centripetal acceleration equation:
a = v² / r
where r is the radius of curvature, v is the speed, and an is the centripetal acceleration. When we rearrange this equation to account for r, we obtain:
r = v² / a
Inputting the values provided yields:
0.04 m is equal to r = (0.40 m/s)2 / 4.0 m/s2.
As a result, the turn's radius of curvature is 0.04 meters.
How long does it take a bee to complete a 90-degree turn?We can use the equation for the circumference of a circle to determine how long it takes the bee to complete a 90-degree turn:
C = 2πr
C/4 = (2πr)/4 = πr/2
The result of substituting the r value we discovered before is:
πr/2 = (π/2) (0.04 m) = 0.063 m
We can divide the distance travelled by the speed to determine the required amount of time:
t = d/v
t = (2πr)/v
When we replace the values we discovered above, we obtain:
t = (2π)(0.04 m) / 0.40 m/s = 0.628 s
As a result, the bee needs about 0.628 seconds to complete a 90-degree turn.
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what are some ways that electric fields are simular to magnetic fields
Answer:
Obey inverse square law obey superposition principlelong range forces.linear current source Idl produces magnetic field just as linear charge source produces electric field.pls mrk me brainliest
the angle at which sunlight hits earth is different on different parts of the globe. the diagrams show how sunlight hits two places on earth on the same day in winter.
Which two statments are most likely true.
Sunlight reflects off of Earth's curving surface at an angle that crosses the equator. Farther than the equator, sunlight is less concentrated or intense, which results in less warming of the Earth's surface.
Why did the Earth begin to warm up?More carbon dioxide, methane, & nitrous oxide are present in the upper orbit today than they have been in the previous 800,000 years. These releases of greenhouse gases have amplified the greenhouse effect and raised the earth's surface temperature.
When was the planet last noticeably warmer than it is now?Based on paleoclimatic information from fossil records, ice cores, sediments, and other methods of studying Earth's past, Gavin Schmidt, a climate scientist with NASA, estimated that it was approximately 125,000 years ago.
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why does a person at the depth of the lake doesn't burst
Answer:
Because the body regulates water pressure well because we are mostly composed of water
I need help writing the expression. There is no option for Req as a whole term.
the answer to Ibatt is 2.2A
2) Write an expression for the current through resistor 2.
answer to I2 is 0.68 A
Answer:
R2 + R3 = R2 R3 / (R2 + R3) = R23 R2 and R3 in parallel
R1 + R23 = R1 R23 / (R1 + R23) R1 in parallel with R2 and R3
R = R1 R23 / (R1 + R23)
R23 = 147 * 163 / (147 + 163) = 77.3 Ω
R = 77.3 * 140 / (77.3 + 140) = 49.8 Ω
I = 212 / 49.8 = 4.26 amps thru circuit
R23 = 77.3
I23 = 212 / 77.3 = 2.74 amps thru R23
I1 = 212 / 140 = 1.51 thru R1
I1 + I23 = 1.51 + 2.74 = 4.25 current thru entire circuit
Current thru R2 current thru R23 = 2.74 amps
8. A unique property of water because of its chemical structure is that it's _____ dense when it's a solid than when it's a liquid.
A. less
B. equally
C. inversely
D. more
A unique property of water because of its chemical structure is that it's A. less dense when it's a solid than when it's a liquid.
What is water?Water is an incredibly unique substance, and its physical properties are largely due to its chemical structure. Water is a polar molecule, meaning it has a positively charged end and a negatively charged end, which creates an attraction between molecules of water that is known as hydrogen bonding.
This hydrogen bonding is responsible for a number of the unique properties of water, one of which is its density. Water is less dense when it is a solid than when it is a liquid. This is counterintuitive to most substances, which are more dense when they are solid than when they are liquid. The explanation for this is that when water freezes, the hydrogen bonds between the molecules force them to move further apart, resulting in a decrease in density.
This is why ice floats on top of liquid water, and it is why bodies of water don’t freeze from the bottom up.
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Using P = M x V what is the momentum of an object with a mass of 750 kg and velocity of 15 m/s
Answer:
p = 11250 kg·m/s
Explanation:
Explanation:
it goes like this p=MV which is
M=750,V=15
p= 750x15=11250n
Complete the following:
When light is incident parallel to the principal axis and then strikes a converging lens,
A. the light will remain parallel after refracting through the lens
B. the light will remail parallel after refracting backwards from the lens
C. the light will refract through the focal point on the opposite side of the lens
D. the light will refract through the focal point on the same side as the object
Answer:
c
Explanation:
trust
Challenge: Draw a complex circuit. This circuit should have four light bulbs (two in parallel and
two in series), two switches (one to turn off series lights and one to turn off parallel lights), and
one battery.
The circuit would have one battery with a positive and negative terminal. Connected to the positive terminal would be one switch and then two light bulbs in series. The other end of the two light bulbs in series would be connected to the negative terminal of the battery. Connected in parallel to the two light bulbs in series would be another two light bulbs. The positive end of the first parallel light bulb would be connected to the positive end of the second parallel light bulb. The other ends of both parallel light bulbs would be connected to the negative terminal of the battery. The first switch would be connected to the two light bulbs in series and would turn off only those two light bulbs when switched. The second switch would be connected to the two light bulbs in parallel and would turn off only those two light bulbs when switched.
What is a series connection?In electronics, a series connection refers to a circuit in which the components (such as resistors, capacitors, or light bulbs) are connected end-to-end in a single path, so that the same current flows through each component in turn.
In a series connection, the voltage applied to the circuit is divided among the components according to their individual resistance or impedance values. The total resistance of a series circuit is equal to the sum of the individual resistances of each component.
In a series connection, the total voltage across the circuit is equal to the sum of the individual voltage drops across each component.
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Normal air has a density of 1.22 kg/m^3. Air that has been heated in a hot air balloon has a density of 0.95 kg/m^3. The hot air balloon has a total volume of 3000 m^3.
a. What is the mass of air in the balloon? (1 point)
b. What is the buoyant force acting on the balloon? (1 point)
c. If the basket and riders in the balloon have a mass of 400 kg, what is the acceleration of the balloon? (1 point)
d. What is the minimum volume the balloon can have before it goes downward instead of upward? (1 point)
e. As the balloon rises, the lower air pressure causes the air around the balloon to become less dense. How does this affect the buoyancy of the balloon? (1 point)
f. As the balloon rises, the atmospheric pressure decreases, causing the volume of the balloon to increase. How does this affect the buoyancy of the balloon? (1 point)
a) The mass of air in the balloon is 2850 kg.
b) The buoyant force acting on the balloon is 93258.6 N.
c) The acceleration of the balloon and the riders is 24.8 m/s².
d) the minimum volume the balloon can have before it goes downward instead of upward is 14118.5 m³.
e) The balloon will start to rise more slowly or may even stop rising altogether.
f) The balloon will rise more quickly or may even accelerate.
a. The mass of air in the balloon can be calculated by multiplying the density of the air by the volume of the balloon:
Mass of air = Density of air × Volume of balloon
Mass of air = 0.95 kg/m³ × 3000 m³
Mass of air = 2850 kg
Therefore, the mass of air in the balloon is 2850 kg.
b. The buoyant force acting on the balloon can be calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object:
Buoyant force = Density of fluid × Volume of fluid displaced x Gravity
Buoyant force = (Density of air - Density of balloon) × Volume of balloon × Gravity
Buoyant force = (1.22 kg/m³ - 0.95 kg/m³) × 3000 m³ × 9.81 m/s²
Buoyant force = 93258.6 N
Therefore, the buoyant force acting on the balloon is 93258.6 N.
c. The net force acting on the balloon and the riders is equal to the buoyant force minus the weight of the system:
Net force = Buoyant force - Weight of system
Net force = 93258.6 N - 400 kg × 9.81 m/s²
Net force = 88836.6 N
The acceleration of the system can be calculated using Newton's second law:
Net force = Mass of system × Acceleration
Acceleration = Net force / Mass of system
Acceleration = 88836.6 N / (400 kg + 2850 kg)
Acceleration = 24.8 m/s²
Therefore, the acceleration of the balloon and the riders is 24.8 m/s².
d. The minimum volume the balloon can have before it goes downward instead of upward can be calculated by setting the buoyant force equal to the weight of the system:
Buoyant force = Weight of system
(Density of air - Density of balloon) × Volume of balloon × Gravity = (Mass of air + Mass of system) × Gravity
Volume of balloon = (Mass of air + Mass of system) / (Density of air - Density of balloon)
Volume of balloon = (2850 kg + 400 kg) / (1.22 kg/m³ - 0.95 kg/m³)
Volume of balloon = 14118.5 m³
Therefore, the minimum volume the balloon can have before it goes downward instead of upward is 14118.5 m³.
e. As the balloon rises, the lower air pressure causes the air around the balloon to become less dense. This means that the density of the fluid that the balloon displaces decreases, which reduces the buoyant force acting on the balloon. As a result, the balloon will start to rise more slowly or may even stop rising altogether if the density of the displaced air becomes equal to the density of the balloon.
f. As the balloon rises, the atmospheric pressure decreases, causing the volume of the balloon to increase. This expansion of the balloon increases the volume of air that it displaces, which in turn increases the buoyant force acting on the balloon. As a result, the balloon will rise more quickly or may even accelerate if the expansion of the balloon is significant enough.
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A concave mirror has a focal length of 8.0 cm. A candle is located at a distance of 5.0 cm from the mirror. Calculate the image distance.
A -13.3 cm
B -3.0 cm
C 00.075 cm
D 3.1 cm
The distance of the image from the concave mirror is -13.3 cm. So, A is the correct option.
What is meant by a concave mirror ?Concave mirror is defined as the type of mirror, that has a reflecting surface which is curved inwards. It is also known as converging mirror.
Here,
Focal length of the mirror, f = 8 cm
Distance of the candle from the mirror, u = -5 cm
According to the mirror formula,
1/f = 1/v + 1/u
where v is the image distance.
Applying the values of f and u in the equation,
1/-8 = 1/v + 1/-5
1/v = (1/-8) - (1/-5)
1/v = 1/5 - 1/8
1/v = 3/40
Therefore,
v = 40/3 = 13.33 cm
Image distance, v = -13.3 cm
Hence,
The distance of the image from the concave mirror is -13.3 cm.
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a frictionless roller coaster is given an initial speed of vi=10.00m/s , at the initial height h=100:00m,has a mass m=1000.0kg
Answer: Using conservation of energy, we can find the final speed of the roller coaster at the bottom of the hill:
Initial energy (at the top) = Potential energy + Kinetic energy
1/2 * m * vi^2 + m * g * h = 1/2 * m * vf^2 + m * g * 0
where m = 1000.0 kg is the mass of the roller coaster, vi = 10.00 m/s is the initial speed, h = 100.00 m is the initial height, g = 9.81 m/s^2 is the acceleration due to gravity, and vf is the final speed at the bottom of the hill.
Simplifying and solving for vf:
vf = sqrt(2 * g * h + vi^2)
Substituting the given values:
vf = sqrt(2 * 9.81 m/s^2 * 100.00 m + (10.00 m/s)^2)
vf = sqrt(1962.2)
vf ≈ 44.3 m/s
Therefore, the final speed of the roller coaster at the bottom of the hill is approximately 44.3 m/s.