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]
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 real car moving at 10 km/h has more momentum than a toy car moving at the same speed because the real car ____.
A. generates less friction
B. has greater mass
C. has less mass
D. has greater forward motion
Answer:
The answer is B (has greater mass)
The real car has more momentum because it has greater mass.
Explanation:The correct answer is B. The real car has greater mass.
Momentum is defined as the product of an object's mass and its velocity. In this case, both the real car and the toy car are moving at the same speed of 10 km/h. However, since the real car has greater mass, it will have a greater momentum.
For example, let's say the real car has a mass of 1000 kg and the toy car has a mass of 100 kg. The momentum of the real car would be 1000 kg × (10 km/h) = 10,000 kg km/h, while the momentum of the toy car would be 100 kg × (10 km/h) = 1000 kg km/h. Therefore, the real car has more momentum than the toy car.
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Calculate the force of gravity on a 5 kg mass at Earth's surface. The mass of the Earth is 6 x 1024 kg and its radius is
6.4 x 106 m. Do not use scientific notation. Round to a whole number (no decimal).
Force = 49 N
Explanation:
The gravitational force of attraction on the surface of earth F = G M m/R²
Here G = gravitational constant = 6.67 x 10⁻¹¹
M = mass of the earth and m = mass of the body on the surface of earth .
R = radius of earth
In this question
mass of earth = 6 x 10²⁴ kg and its radius = 6 x 10⁶ m
The values are substituted in the above equation
F = 6.67 x 10⁻¹¹ x 6 x 10²⁴ x 5 / ( 6 x 10⁶ )² = 49 N
The mass will be attracted by 49 N of force .
A piece of cork has a volume of 10 cm cube. find the net force on the cork if it is completely submerged and then released.
(density of cork=200kg/m^3)
Answer:
Explanation:
The force required to submerge something underwater can be found from Archimedes principle:
FB=pwVg
Where FB is the buoyant force, pw is the density of water (1g/ml), V is volume of the water displaced, and g is gravity. The key here is V. The volume of water displaced by the cork is equal to the volume of cork. Therefore, the required force is
F=1 g/cm³ x 10 cm³ x 9.8 m/s²= 98 N
While in flight, a hot air balloon decreases its elevation by 83 meters and then increases its elevation by 83.7 meters,
Enter an inequality in the ber to compare the changes in elevation of the hot air balloon while in flight. this is math that i dont get pls help
Explanation:
Let the initial height of the balloon is L .
The lower level is L - 83 , because it goes 83 m downwards
The upper limit is L + 83.7 , because it goes up by 83.7 m
Thus the inequality becomes
L-83 ≤ L ≤ L + 83.7
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 weather is warm and dry.
Which change would a cold front bring?
Answer:
rain or thunder
Explanation:
What does the standard deviation of a set of data tell you?
O
A. The number of experiments that were performed
O
B. How many data points there are in the set
O
C. The largest and smallest data values of the set
O
D. How much each data point differs, on average, from the mean
value of the set
SUBMIT
Answer:D
Explanation:
The standard deviation of a set of data tell you how much each data point differs, on average, from the mean value of the set. The correct option is D.
What is standard deviation?A standard deviation is a measure of how far apart the data is from the mean. A low standard deviation indicates that data is clustered around the mean, whereas a high standard deviation indicates that data is more spread out.
When data is distributed, standard deviation is important because it aids in understanding the measurements. The higher the standard deviation, the more evenly distributed the data is.
To summarize continuous data, the standard deviation is used in conjunction with the mean.
Furthermore, like the mean, the standard deviation is normally only appropriate when the continuous data is not significantly skewed or has outliers.
Thus, the correct option is D.
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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:
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]
Roberta's next door neighbor has a theory that the best time to wash your car is late in the afternoon on Sunday. Is this a scientific theory? A. No, it is an opinion and is not testable. B. Yes, the car will stay clean for more of the week. C. Yes, the neighbor might be a scientist. D. No, it is better to wash cars on Saturday.
Answer: no, it is an opinion and is not testable (a)
Explanation:
i just got this question on Study Island
What do the lines making a circle around the low-pressure area indicate?
areas of equal altitude
areas of equal pressure
a stationary front
an occluded front
Answer:
Areas of equal pressure.
Explanation:
The line making a circle means equal pressure.
Final answer:
The lines around a low-pressure area on a weather map are isobars, indicating areas of equal pressure crucial for predicting weather conditions.
Explanation:
The lines making a circle around the low-pressure area indicate areas of equal pressure, also known as isobars. These isobars connect places with the same atmospheric pressure measurements, typically in millibars. On a weather map, isobars form almost circular shapes around low-pressure centers, like cyclones, and indicate areas where the pressure decreases towards the center.
Understanding these pressure patterns is essential for meteorologists to describe and predict weather, as they directly affect weather conditions. For instance, the approach of a low-pressure system often brings cloudiness, winds, and precipitation.
Which statement is the best interpretation of the ray diagram shown below?
A) A concave mirror forming a larger, virtual image
Explanation:
The figure is missing; see attachment.
There are two types of mirror:
Concave (converging) mirrors: a concave mirror is a mirror that reflects the light inwardConvex (diverging) mirrors: a convex mirror is a mirror that reflects the light outwardThe image formed by a mirror can also be of two types:
Real image: it is formed on the same side of the object, with respect to the mirrorVirtual image: it is formed on the opposite side of the object, with respect to the mirrorIn the figure of this problem (see attachment), we see that:
- The mirror reflects the light from the object inward --> so it is a concave mirror
- The image is formed on the other side of the mirror --> it is a virtual image
So the correct option is
A) A concave mirror forming a larger, virtual image
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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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which is is not an effective way to gain fitness
Will mark Brainlist!
Which of the following is an example of a wheel and axle?
A. wheel barrow
B. automobile steering wheel
C. jar lid
D. pencil
Answer:
A. Wheel barrow
can't rlly explain-
The correct answer to the question is B. automobile steering wheel, as it represents a wheel and axle system where the steering wheel turns the axle (steering column), steering the vehicle.
A wheel and axle is a simple machine where a wheel is attached to a central rod known as an axle. The combination is designed to amplify force and can be found in many tools and machines. In the context of the provided options, B. automobile steering wheel is the correct answer, as it exemplifies a wheel and axle system. The steering wheel serves as the wheel that, when turned, rotates the axle (steering column) which ultimately steers the vehicle.
Other examples provided, such as a wheelbarrow, jar lid, and pencil, do not fit the definition of a wheel and axle as accurately. The wheelbarrow indeed has a wheel, but the axle's function and setup differ from the wheel and axle mechanism. The jar lid is more similar to a screw, and a pencil lacks the rotational mechanics involved in a wheel and axle system.
In which of the following conditions does
the car not accelerate?
A) A car moves at 80 km/h on a flat,
straight highway.
B) The car slows from 80 km/h to 35 km/h
C) The car turns a corner.
D) The car speeds up from 35 km/h to
80 km/h.
Answer:
The answer is A
Explanation:
If it goes 80km/h on a flat highway than it is not going any faster or slower.
When a car moves at 80 kilometers / hour on a flat, straight highway then the car would not accelerate, therefore the correct answer is option A.
What is acceleration?The rate of change of the velocity with respect to time is known as the acceleration of the object.
As per the second option when the car slows from 80 km/h to 35 km/h, then it would accelerate with negative acceleration.
When the car turns in the corner car would accelerate because there is a change in the velocity of the motion.
Similarly in the last option when a car speeds up from 35 km/h to
80 km/h, then it would generate acceleration because there is a change in the velocity with respect to the time.
The first option is the tye only case when the car would not accelerate because there is no change in the velocity of the car, thus the correct answer is option A.
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A cylinder at left has balls stacked near its bottom with an arrow leading to a cylinder at right with balls evenly spaced throughout the cylinder. Which change of state is shown in the model? condensation evaporation sublimation deposition
Answer:
SublimationExplanation:
Your description corresponds to the picture attached.
In that model, the spheres represent atoms or molecules (is the same) of a substace. You can call them particles.
The particles tightly packed inside the cylinder of the left represent a substance in solid state whose particles are in a fix position and cannot move freely.
The particles randomly distributed throughout the cylinder on the right model a substance is gas state, where the particles occupy the whole space, moving freely.
Thus, the image depicts the change of a substance from solid state to gaseus phase. Such change is defined as sublimation.
Therefor, the answer is the third choice of your list: sublimation.
The change observed is the process of sublimation in the model. The correct answer is (c) sublimation.
In that model, the spheres represent atoms or molecules (the same) of a substance. You can call them particles.
The particles tightly packed inside the cylinder on the left represent a substance in a solid state whose particles are in a fixed position and cannot move freely.
The particles are randomly distributed throughout the cylinder on the right model a substance is a gas state, where the particles occupy the whole space, moving freely.
Thus, the image depicts the change of a substance from a solid state to the gaseous phase. Such change is defined as sublimation.
Therefore, the answer is the third choice of your list sublimation. The correct answer is (c).
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Estimate how much farther a person can jump on the Moon as compared to Earth if the take off
speed and angle are the same? The acceleration due to gravity on the moon is one-sixth what it
is on Earth.
Explanation:
Let us assume , an Object is thrown with initial Velocity u m/s and angle of θ above the horizontal level. The horizontal and vertical velocities are (x,y)
vₓ = v₀cos θ
[tex]v_{y}[/tex] = v₀ sinθ
now, the time when the object reaches the maximum height can be calculated from
[tex]v_{y}[/tex] = v₀ sinθ - at₀ = 0
t₀ = v₀ sinθ/a
thus, the total time in air is two times higher ; t = 2t₀ = 2 (v₀ sinθ) /a
the maximum distance can be calculated from this equation
X = vₓ t= v₀ cos θ x 2 (v₀ sinθ) /a
it implies x is inversely proportional to a.
we know the acceleration on the Moon is 1/6 th of Earth.the ratio between between maximal distance on the moon and on the earth is 6.
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
Naomi has increased the pressure on a solution of liquid and gas in a closed container. This will _______
amount of gas held in her solution
the
Increase
Explanation:
Naomi increasing the pressure on a solution of liquid and gas in a closed container will increase the amount of gas held in her solution.
Increase in pressure increases the solubility of gases in a solution.
Originally, the gases have their particles far apart from one another They move randomly all about without staying in the solution. Increasing their pressure brings the gases into more frequent collision with the solution. This will lead to an increase in amount of gas held in a solution.learn more:
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Increasing the pressure on a solution of liquid and gas in a closed container will increase the amount of gas held in the solution.
Explanation:Increasing the pressure on a solution of liquid and gas in a closed container will increase the amount of gas held in the solution. This is because an increase in pressure will result in more collisions between gas particles and the container walls, leading to a greater force being exerted on the walls. As a result, the pressure inside the container increases.
Explain why a law is accepted as fact, but a theory is not
In scientific discourse, a law is generally considered a descriptive generalization about how some aspect of the natural world behaves under stated circumstances. A theory, on the other hand, is a well-substantiated explanation of some aspect of the natural world that incorporates facts, laws, inferences, and tested hypotheses. The principal difference is that a law describes what happens and a theory explains why it happens.
Laws are accepted as fact because they are simple, true statements about how things occur in nature, usually summed up in a mathematical formula. They are typically based on empirical evidence from observations and experiments. For example, the Law of Gravity describes the attraction between two objects but doesn’t explain the mechanism. Theories, however, go through rigorous testing and are only sustained after consistent empirical support. They aim to provide the most reasonable explanation based on the evidence at hand. Consider the Theory of Evolution by Natural Selection - it explains the mechanisms behind the changes in species over time. Unlike a law, a theory can be adjusted or discarded if new evidence presents itself that doesn't align with the current theory. This flexibility is why theories, despite being well-supported, are not accepted as unchanging facts, but rather as the best explanations we have based on current knowledge.
A car moves along a horizontal road with constant velocity v0 = v0xi until it encounters a smooth inclined hill, which it climbs with constant velocity v1 = v1xi + v1yj as indicated in the figure. The period of time during which the car changes its velocity is Δt.
Answer:
a ave = ( v1x - v0x ) i/Δt + v1y j/Δt
Explanation:
The acceleration of a body is the rate of change of the velocity of the body
The correct equation and value for the average acceleration vector and magnitude of the acceleration of the car are as follows;
Part (a) The average acceleration vector is [tex]\overset \rightarrow a_{av} =\dfrac{(v_{1x} - v_{0x})}{\Delta t} }\mathbf{i} + \dfrac{v_{iy} }{\Delta t} \mathbf{j}[/tex]
Part (b) The magnitude of the cars acceleration is [tex]\mathbf{ 2.\overline{518} }[/tex] m/s²
The reason the above values are correct is as follows:
Question: The parts of the question that appears to be missing are;
Part (a); The vector expression for the average acceleration in the time periods
Part(b); Find the magnitude of the cars acceleration
Variables:
v₀ₓ = 31 m/s
v₁ₓ = 31 m/s
[tex]v_{1y}[/tex] = 6.8 m/s
Δt = 2.7 s
Solution:
Part (a) The average acceleration vector, [tex]\mathbf{\overset \rightarrow a_{av}}[/tex], is given as follows;
[tex]Average \ acceleration \ vector, \overset \rightarrow a_{av} = \mathbf{\dfrac{\overset \rightarrow v_2 - \overset \rightarrow v_1}{t_2 - t_1}} =\dfrac{\Delta \overset \rightarrow v}{\Delta t}[/tex]
The given parameters in the question;
v₀ = v₀ₓ i
v₁ = v₁ₓ i + [tex]v_{1y}[/tex]j
∴ v₁ - v₀ = v₁ₓ i + [tex]v_{1y}[/tex]j - v₀ₓ i
The average acceleration vector becomes;
[tex]\overset \rightarrow a_{av} = \mathbf{\dfrac{\overset \rightarrow v_1 - \overset \rightarrow v_0}{\Delta t}} =\dfrac{(v_{1x} - v_{0x})\mathbf{i} + v_{iy} \mathbf{j}}{\Delta t}[/tex]
Therefore;
[tex]\mathbf{The \ average \ acceleration \ vector} \overset \rightarrow a_{av} =\dfrac{(v_{1x} - v_{0x})}{\Delta t} }\mathbf{i} + \dfrac{v_{iy} }{\Delta t} \mathbf{j}[/tex]
Part (b) The magnitude of the car's acceleration is given by plugging values of the variables v₀ₓ, v₁ₓ, [tex]\mathbf{v_{1y}}[/tex], and Δt in the above equation as follows;
[tex]\overset \rightarrow a_{av} =\dfrac{(31 \, m/s - 31 \, m/s)\mathbf{i} + 6.8 \, m/s \mathbf{j}}{2.7 \, s} = 2.\overline{518} \ m/s^2 \ \mathbf{j}[/tex]
The magnitude of the cars acceleration, a = [tex]\sqrt {(2.\overline{518} \ m/s)^2 } = \mathbf{ 2.\overline{518} \ m/s^2}[/tex]
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By what mechanical adjustments can you speed up or slow down an old-fashioned grandfather
pendulum clock?
A)By changing the elongation angle of the pendulum
B) By giving the pendulum a slight nudge into or against its motion direction
C) By altering the length of the pendulum
D)
Either of the above works
E) None of the above works
C) By altering the length of the pendulum
Explanation:
The period of a simple pendulum is given by the equation
[tex]T=2\pi \sqrt{\frac{L}{g}}[/tex]
where
L is the length of the pendulum
g is the acceleration due to gravity
In this problem, we are asked which adjustmenet can be done to speed up or slow down the pendulum clock: that means, which adjustment can be done in order to change the period of the pendulum.
From the equation above, we notice that the period of a pendulum depends only on its length (and the acceleration of gravity). Therefore, its period can be changed only by changing the length of the pendulum. And so, the only correct answer is
C) By altering the length of the pendulum
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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:
The average speed of a train is 24.0km/hr. Suppose a train moving at this speed accelerates -0.20 m/s^2 until it reaches a speed of 8.0 km/hr. How long does it take the train to undergo this change in speed?
time = 2.2 sec
Explanation:
The initial speed of train = 24 km/hr = 24 x 1000/3600 = 20/3 m/sec
The final speed of train = 8 km/hr = 8 x 1000/3600 = 20/9 m/sec
The relation of motion
v = u + a x t
final velocity = initial velocity + acceleration x time
20/9 = 20/3 - 2 x t where t is time
Because the acceleration is negative
2 t = 20/3 - 20/9 = 40/9 or t = 20/9 sec = 2.2 sec
The time taken to decrease the speed from 24 km/hr to 8 km/hr is 2.2 sec approx
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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4. Elements that lie along the stair step line of the periodic table are
a. metals
c. liquids
b. metalloids
d. radioactive
The answer is B. metalloids
(boron, silicon, germanium, arsenic, antimony, tellurium, astatine, and polonium)
Final answer:
Elements along the stair step line of the periodic table are metalloids, with properties between those of metals and nonmetals. Metals are to the left and are conductive and malleable, while nonmetals are to the right and are typically poor conductors. Atomic radii decrease across a period and increase down a group. Option b
Explanation:
Elements that lie along the stair step line of the periodic table are known as metalloids. These elements exhibit properties that are intermediate between those of metals and nonmetals. Metals are typically found to the left of the metalloids, and they are generally malleable, shiny, and good conductors of heat and electricity.
On the other hand, nonmetals are located to the right of the metalloids and typically have opposite properties, such as being poor conductors of heat and electricity. The atomic radii of elements tend to decrease from left to right across a period because of the increasing positive charge in the nucleus, which pulls electrons closer. In contrast, atomic radii generally increase as you move down a group due to the addition of energy levels.
100 ml of water is initially at 20°C. 30,000 J of heat is added to the water. What is temperature change for the water?
Answer:
Therefore the new temperature of the water is 91.67°C
Explanation:
Specific heat of water = 4.186 joule /gram °C
The equation to calculate change of temperature
Q=s×m×ΔT
Q = the amount of heat = 30,000 J
s= Specific heat of water = 4.186 joule /gram °C
m = mass of the water = volume ×density=(100×1)gram =100 gram
ΔT = the change of temperature = (T-20)
Therefore,
30000= 4.186×100×(T-20)
⇔(T-20)= 71.67
⇔T = 71.67+20
⇔T = 91.67
Therefore the new temperature of the water is 91.67°C
what might be happening since 1880 for average global temperatures to increase
Answer:
The average global temperatures has increased since 1880 due to the emission of toxic gases in the atmosphere.
Explanation:
In average the global temperature of the earth has increased by 1 degree Celsius (2 degrees Fahrenheit). It includes the combined land and ocean's temperature.The main reason for this increase in global temperature is the emission of gases like carbon dioxide, CFC's and other greenhouse gases.Human activities, industrialization, modernization etc. are majorly responsible for this increment in temperature through the centuries.