Answer:
0.27km
Explanation:
tanA=\(\frac{a}{b}\)
a=btanA
a=(0.75km)tan20
=0.27km
HI PLEASE HELP ON QUESTION ASAP USING AVERAGE (MEAN) TO ANSWER QUESTION! IF UR ANSWER AND EXPLAINATION IS CORRECT ILL RATE YOU FIVE STARS, A THANKS AND MAYBE EVEN BRAINLIEST. PLEASE MAKE SURE YOU ANSWER MY QUESTION USING AVERAGES.
1) a meal for 6 cost £12 per person. as it is one of the diners birthday , the other 5 decided to pay for his meal. how much do each of the five friends need to pay?
Each of the five friends needs to pay £12 to cover the cost of their own meals and contribute towards the birthday person's meal. Using mean allows us to distribute the cost equally among the friends, ensuring a fair division of expenses for the meal.
To determine how much each of the five friends needs to pay, we can use the concept of averages (mean) and divide the total cost by the number of people paying.
In this scenario, the total cost of the meal for 6 people is £12 per person. Since the other 5 friends have decided to pay for the birthday person's meal, they will collectively cover the cost of their own meals plus the birthday person's meal.
To calculate the total cost covered by the five friends, we can subtract the cost of one person's meal (since the birthday person's meal is being paid by the group) from the total cost. The cost of one person's meal is £12.
Total cost covered by the five friends = Total cost - Cost of one person's meal
= (£12 x 6) - £12
= £72 - £12
= £60
Now, to find out how much each of the five friends needs to pay, we divide the total cost covered by the five friends (£60) by the number of friends (5).
Amount each friend needs to pay = Total cost covered by the five friends / Number of friends
= £60 / 5
= £12
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The half-life of a radioactive isotope is 210 d. How many days would it take for the decay rate of a sample of this isotope to fall to 0.58 of its initial rate?
It would take approximately 546 days for the decay rate of the sample of this radioactive isotope to fall to 0.58 of its initial rate.
1. The decay rate of a radioactive isotope is proportional to the number of radioactive atoms present in the sample at any given time.
2. The decay rate can be expressed as a function of time using the formula: R(t) = R₀ * \(e^{(-\lambda t\)), where R(t) is the decay rate at time t, R₀ is the initial decay rate, λ is the decay constant, and e is the base of the natural logarithm.
3. The half-life of a radioactive isotope is the time it takes for half of the radioactive atoms in a sample to decay. In this case, the half-life is given as 210 days.
4. Using the half-life, we can find the decay constant (λ) using the formula: λ = ln(2) / T₁/₂, where ln(2) is the natural logarithm of 2 and T₁/₂ is the half-life.
5. Substituting the given half-life into the formula, we have: λ = ln(2) / 210.
6. Now, we need to find the time it takes for the decay rate to fall to 0.58 of its initial rate. Let's call this time "t".
7. Using the formula for the decay rate, we can write: 0.58 * R₀ = R₀ * e^(-λt).
8. Simplifying the equation, we get: 0.58 = \(e^{(-\lambda t\)).
9. Taking the natural logarithm of both sides, we have: ln(0.58) = -λt.
10. Substituting the value of λ from step 5, we get: ln(0.58) = -(ln(2) / 210) * t.
11. Solving for t, we have: t = (ln(0.58) * 210) / ln(2).
12. Evaluating the expression, we find: t ≈ 546.
13. Therefore, it would take approximately 546 days for the decay rate of the sample of this radioactive isotope to fall to 0.58 of its initial rate.
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A ball is dropped from the top of a building and hits the street below in 4.25 s. How tall is the building? Show work for brainliest.
Answer:
90.3125 m
Explanation:
\(s = ut + \frac{1}{2} a {t}^{2} \)
a = 10m/s^2 (constant)
S=height
U=initial velocity
a= gravitational acceleration
t= time
s = 0 + 1/2 * 10 * 4.25 ^2
u is 0 because it is dropped without velocity
s =90.3125 m
Got it
1. A force of 15 Newtons is applied to an object with a mass of 5 kilograms.
What will be the object's final velocity after 10 seconds?
what is the maximum magnitude of p that can be applied before tipping would occur, assuming the block does not slip? express your answer to three significant figures with appropriate units. ptip
A probabilistic assessment of seismic hazards requires an estimate of the maximum moment intensity M of the largest earthquake that is likely to occur in a given region. The answer is in the image.
Maximum magnitude, an important parameter in calculating seismic hazards, is also a controversial parameter. The choice of value can have a large impact on the final outcome of the results, but it is most likely the magnitude of an earthquake that has not yet occurred in the area under study.
The term size is defined as the number of flocks. For example, the magnitude can be used to describe the speed comparison between a car and a bicycle. It can also be used to describe how far an object has moved or how much an object has in relation to size.
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What's the kinetic energy of an object that has a mass of 30 kilograms and moves with a velocity of 20 m/s?
Question 16 options:
A)
12,000 J
B)
2,940 J
C)
6,000 J
D)
5,880 J
the kinetic energy of an object that has a mass of 30 kilograms and moves with a velocity of 20 m/s is 6,000 J. Option C is correct answer.
The kinetic energy of an object that has a mass of 30 kilograms and moves with a velocity of 20 m/s can be calculated by using the formula:
K.E = 1/2 mv²
Where, K.E = Kinetic energy of the objectm = Mass of the objectv = Velocity of the object
Putting the given values in the above formula:
K.E = 1/2 mv²K.E = 1/2 × 30 kg × (20 m/s)²K.E = 1/2 × 30 × 400K.E = 6000 joules
The correct answer is C.
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What kinds of materials generally have the lowest specific heats?
Answer:
Iron and lead generally have low specific heats.
what are the two reasons for citing sources?
Answer:
Well, you will get in trouble for plagiarism, and you will not get full credit or Maby none
Explanation:
Answer:
1: To make sure people don't think u plagiarized from another person
2: To show that you did good research by listing your sources
what is a asteroid traveling rapidly called
Answer:
meteor
Explanation:
A asteroid stays still and a meteor goes fast
Answer:
meteor
Explanation:
or some people call it a shooting star
10. For the graph shown in the figure, what physical quantity does the slope of the graph represent for ohmic material?
Explain.
The slope of the graph represent for ohmic material is as per the graph is that the current will increases with increase in potential.
What is ohmic material?Ohmic material is defined as anything that complies with Ohm's law, according to which the current flowing through a device is proportional to the applied voltage. Ohmic materials are those that adhere to Ohm's law.
Ohm's Law describes the relationship between voltage and current, and the resistance in a circuit is represented by the slope of the line from a graph of the two quantities. The slope of the distance-time plot, or the speed of the body, is the ratio of the distance traveled by the body to the time required for travel.
Thus, the slope of the graph represent for ohmic material is as per the graph is that the current will increases with increase in potential.
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calculate the electric potential energy in a capacitor that stores 9.40 x 10 to the negative 10 C of charge at 50.0 V
The electric potential energy stored in the capacitor is 4.70 x 10^-8 Joules.
The electric potential energy stored in a capacitor is given by the formula:
U = (1/2) * C * V^2
where U is the potential energy in Joules, C is the capacitance in Farads, and V is the voltage across the capacitor in Volts.
In this case, we are given that the capacitor stores 9.40 x 10^-10 C of charge at 50.0 V. However, we are not given the capacitance value. Therefore, we cannot calculate the potential energy directly using the above formula.
To find the capacitance value, we can use the formula:
C = Q / V
where Q is the charge stored in the capacitor and V is the voltage across the capacitor.
Substituting the given values, we get:
C = 9.40 x 10^-10 / 50.0
= 1.88 x 10^-11 F
Now we can use the formula for electric potential energy to find the energy stored in the capacitor:
U = (1/2) * 1.88 x 10^-11 * (50.0)^2
= 4.70 x 10^-8 J
Therefore, the electric potential energy stored in the capacitor is 4.70 x 10^-8 Joules.
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PLEASE I NEED HELP CLICK ON THIS IMAGE
I believe you are incorrect. A weathered mountain would appear more jagged.
I do believe with a lot of exposure to weather will make the mountain appear somewhat more jagged compared to a mountain that is less weathered.
If this is incorrect, please, don't refrain to tell me.
A 1.35 kg block is pulled across a flat, frictionless floor with a 3.07 n force at 32.0 above horizontal. What is the acceleration of the block
Find the value of n if nc₂ = 15
a stone on the ground has zero energy why
Explanation:
it has no energy when considered with respect to earth ,as it has neither height (i e potential energy) nor velocity (i.e kinetic energy).
an airplane accelerates down a runway at 5.20 m/s^2 for 32.8s until it finally lifts off the ground. determine the distance traveled before takeoff
Answer:
7,272.7m
Explanation:
Our knowns:
a = 5.2m/s^2
t = 32.8s
\(V_{i}\) = 0 m/s
Our Unknowns:
Distance (x): ?
We can use displacement formula:
ΔX = \(V_{i}\) t + \(\frac{1}{2}\) a \(t^{2}\)
Plug in knowns:
X = 0 + 1/2 ((5.2)(32.8))^2
Answer:
ΔX = 7272.7m
(I beleive this should be right) let me know if it helped!
An experiment is set up and collects the following data
Force (N) Acceleration (m/s^2)
30 1.5
70 3.5
85 4.25
What is the mass of the object experimented on in this situation?
A. 10 kg
B. 15 kg
C. 20 kg
D. 25 kg
The mass of the object experimented on in this situations is 20 kg. So, option(C) is correct.
What is force?
A force is something that pushes or pulls an object. The objects' interactions with one another are what causes push and pull. Force can also be expressed using words like stretch and squeeze.
When an object with mass is pushed or pulled, it changes its velocity, according to the definition of force in physics.
The product of mass (m) and acceleration (a) represents the amount of force (F). Mathematically speaking, the force equation or formula can be written as follows:
F = ma
According to given parameters:
Force = 30 N; acceleration = 1.5 m/s². So, mass = 30/1.5 kg = 20 kg.
Force = 70 N; acceleration = 3.5 m/s². So, mass = 70/3.5 kg = 20 kg.
Force = 85 N; acceleration = 4.25 m/s². So, mass = 85/4.25 kg = 20 kg.
Hence, the mass of the object experimented on in this situations is 20 kg.
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1.00 kg of ice at -24.0°C is placed
in contact with a 1.00 kg block of a
metal at 5.00°C. They come to
equilibrium at -8.88°C. What is
the specific heat of the metal?
1.00 kg of ice at -24.0°C is placed in contact with a 1.00 kg block of a metal at 5.00°C. They come to equilibrium at -8.88°C.
We can use the principle of conservation of heat to solve this problem. The heat lost by the metal must equal the heat gained by the ice.
The heat lost by the metal is given by
Q1 = m1c1ΔT1
Where m1 is the mass of the metal, c1 is its specific heat, and ΔT1 is the change in temperature.
The heat gained by the ice is given by
Q2 = m2c2ΔT2
Where m2 is the mass of the ice, c2 is its specific heat, and ΔT2 is the change in temperature.
Since the two objects come to thermal equilibrium, we can set Q1 equal to Q2
m1c1ΔT1 = m2c2ΔT2
Solving for c1, we get
c1 = m2c2ΔT2 / (m1ΔT1)
By putting these values we get
c1 = (1.00 kg)(2.06 kJ/kg·K)(-24.0°C - (-8.88°C)) / [(1.00 kg)(5.00°C - (-8.88°C))]
c1 = 0.902 kJ/kg·K
Hence, the specific heat of the metal is 0.902 kJ/kg·K.
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Compare sound and earthquake waves
When materials vibrate, waves are created that travel through the substance, and this energy is what we hear as sound. Earthquakes are earth vibrations that cause the (potential) energy held within rocks to be released (as a result of their pressure-generating relative positions). Seismic waves are produced by earthquakes.
How do sound waves and earthquakes compare?
The waves lose energy as they move through the air with sound or through the ground with shaking during an earthquake. Therefore, a band can be heard louder close to the stage than farther away, and an earthquake can be felt more strongly close to the fault than farther away.
In actuality, sound in the air cannot match how quickly earthquake waves move. In rock, the compressional or "P" wave of an earthquake moves at the In actuality, sound in the air cannot match how quickly earthquake waves move. The speed of a P wave is typically 10,000 mph. The speed of sound through air is roughly 750 mph.
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An 8.0 Kg mass is placed at = 3 where should a 10 Kg mass be placed along the − so that the center of mass will be located ay = 4.5?
Answer:
Therefore, the 10 kg mass should be placed at x = 5.7 m along the x-axis to achieve a center of mass located at y = 4.5 m.
Explanation:
To find the position along the x-axis where a 10 kg mass should be placed such that the center of mass is located at y = 4.5, we can use the formula for the center of mass:
x_cm = (m1 * x1 + m2 * x2) / (m1 + m2)
Here, m1 and x1 represent the mass and position of the 8 kg mass, respectively. m2 is the mass of the 10 kg mass, and we need to find x2, its position.
Given:
m1 = 8 kg
x1 = 3 m
x_cm = unknown (to be found)
m2 = 10 kg
y_cm = 4.5 m
Since the center of mass is at y = 4.5, we only need to consider the y-coordinate when calculating the center of mass position along the x-axis.
To solve for x2, we can rearrange the formula as follows:
x2 = (x_cm * (m1 + m2) - m1 * x1) / m2
Substituting the given values:
x2 = (x_cm * (8 kg + 10 kg) - 8 kg * 3 m) / 10 kg
Simplifying:
x2 = (x_cm * 18 kg - 24 kg*m) / 10 kg
Now, we can set the y-coordinate of the center of mass equal to 4.5 m and solve for x_cm:
4.5 m = (8 kg * 3 m + 10 kg * x2) / (8 kg + 10 kg)
Simplifying:
4.5 m = (24 kg + 10 kg * x2) / 18 kg
Multiplying both sides by 18 kg:
81 kg*m = 24 kg + 10 kg * x2
Subtracting 24 kg from both sides:
10 kg * x2 = 81 kg*m - 24 kg
Dividing both sides by 10 kg:
x2 = (81 kg*m - 24 kg) / 10 kg
Simplifying:
x2 = 8.1 m - 2.4 m
x2 = 5.7 m
(brainlest?) ples:(
Answer:
the 10 kg mass should be placed at x = -2.4 m to achieve a center of mass at y = 4.5 m.
Explanation:
To find the position along the x-axis where the 10 kg mass should be placed so that the center of mass is located at y = 4.5, we can use the principle of the center of mass.
The center of mass of a system is given by the equation:
x_cm = (m1x1 + m2x2) / (m1 + m2),
where x_cm is the x-coordinate of the center of mass, m1 and m2 are the masses, and x1 and x2 are the positions along the x-axis.
Given:
m1 = 8 kg,
x1 = 3 m,
m2 = 10 kg,
y_cm = 4.5 m.
To solve for x2, we need to find the x-coordinate of the center of mass (x_cm) by using the y-coordinate:
y_cm = (m1y1 + m2y2) / (m1 + m2),
where y1 and y2 are the positions along the y-axis.
Rearranging the equation and substituting the given values:
4.5 = (83 + 10y2) / (8 + 10).
Simplifying the equation:
4.5 = (24 + 10*y2) / 18.
Multiplying both sides by 18:
81 = 24 + 10*y2.
Rearranging the equation:
10*y2 = 81 - 24,
10*y2 = 57.
Dividing both sides by 10:
y2 = 5.7.
Therefore, the y-coordinate of the 10 kg mass should be 5.7 m.
To find the x-coordinate of the 10 kg mass, we can use the equation for the center of mass:
x_cm = (m1x1 + m2x2) / (m1 + m2).
Substituting the given values:
x_cm = (83 + 10x2) / (8 + 10).
Since the center of mass is at x_cm = 0 (the origin), we can solve for x2:
0 = (83 + 10x2) / (8 + 10).
Rearranging the equation:
83 + 10x2 = 0.
24 + 10*x2 = 0.
10*x2 = -24.
Dividing both sides by 10:
x2 = -2.4.
Astronauts living on the International Space Station have zero gravitational acceleration.
True
False
Which description tells two processes scientists think move Earth's lithospheric plates?
Responses
friction between the plate and the asthenosphere and pressure of magma on the edge of the plate
friction between the plate and the asthenosphere and pressure of magma on the edge of the plate
gravity acting on the edges of plates and convection in the mantle
gravity acting on the edges of plates and convection in the mantle
gravity acting on the edges of plates and friction between the plate and the asthenosphere
gravity acting on the edges of plates and friction between the plate and the asthenosphere
convection in the mantle and pressure of magma on the edge of the plate
The description that tells two processes that scientists think move Earth's lithospheric plates is convection in the mantle and pressure of magma on the edge of the plate.
What is the Earth's lithosphere?The Earth's lithosphere is the rocky outer part of Earth which is made up of the brittle crust and the top part of the upper mantle.
The Earth's lithosphere deflects the convections and as the convections churn clockwise of anticlockwise, they drag the lithosphere with it via friction an this is what is stipulated to cause tectonic plate movements.
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Answer: convection in the mantle and pressure of magma on the edge of the plate
Explanation: I took the unit test
A driver of a car traveling 14.6 m/s must slam on the brakes to avoid hitting a black bear crossing the road. If it takes 3.00 seconds for the vehicle to slow down to a stop at 0.0 m/s, what is the acceleration over the three seconds?
Answer:
a = (V2 - V1) / t = (0 - 14.6) / 3 = -4.87 m/s^2
It might be useful to convert 14.6 m/s to mph
14.6 m/s * 39.37 in/m = 575 in /s
575 in/s / 12 in/ft = 47.9 ft/sec
47.9 ft/s / 88 ft/sec * 60 mph = 32.6 mph
The following are four electrical components.
A. A component which obeys ohm's law
B. Another component which obeys ohm's law
but which has higher resistance than A
A filament lamp
C.
D. A component, other than a filament lamp,
which does not obey ohm's law.
a. For each of these components, sketch current-
voltage characteristics, plotting current on the
vertical axis, and showing both positive and
negative values. Use one set of axes for A and
B, and separate sets of axes for C and for D.
label your graphs clearly.
b.
Explain the shape of the characteristic for C
c. Name the component you have chosen for D.
For the following are four electrical components:
a. For components A and B, both of which obey Ohm's law, the current-voltage characteristics would be a straight line passing through the origin. The slope of the line for component B would be steeper than that of component A, indicating higher resistance.
b. The shape of the characteristic for component C, the filament lamp, can be explained by its construction. A filament lamp consists of a filament made of a resistive material, typically tungsten, which heats up and emits light when an electric current passes through it.
c. The component chosen for D, which does not obey Ohm's law, could be a diode. A diode is a two-terminal electronic component that allows the current to flow in only one direction.
For the following are four electrical components:
a. Sketches of current-voltage characteristics:
For components A and B, both of which obey Ohm's law, the current-voltage characteristics would be a straight line passing through the origin. The slope of the line for component B would be steeper than that of component A, indicating higher resistance.
Current (I)
^
| B
| /
| /
| /
| /
| /
| /
| /
| /
| /
|/
+------------------> Voltage (V)
Current (I)
^
| A
| /
| /
| /
| /
| /
| /
| /
| /
| /
|/
+------------------> Voltage (V)
For component C, a filament lamp, the current-voltage characteristic would be a curve that is not linear. It would exhibit a non-linear increase in current with increasing voltage. At lower voltages, the lamp would have low resistance, but as the voltage increases, the resistance of the filament also increases due to the phenomenon of thermal self-regulation. This leads to a slower increase in current at higher voltages.
For component D, a component that does not obey Ohm's law, the current-voltage characteristic could be any non-linear curve depending on the specific component chosen. Examples of components that do not obey Ohm's law include diodes and transistors.
b. The shape of the characteristic for component C, the filament lamp, can be explained by its construction. A filament lamp consists of a filament made of a resistive material, typically tungsten, which heats up and emits light when an electric current passes through it. As the voltage across the filament increases, the temperature of the filament increases as well, causing its resistance to increase. This increase in resistance results in a slower increase in current with increasing voltage, leading to the characteristic non-linear curve observed.
c. The component chosen for D, which does not obey Ohm's law, could be a diode. A diode is a two-terminal electronic component that allows the current to flow in only one direction. It exhibits a non-linear current-voltage characteristic where it conducts current only when the voltage is above a certain threshold, known as the forward voltage. Below this threshold, the diode has a high resistance and blocks current flow in the reverse direction. The characteristic curve of a diode would show negligible current flow until the forward voltage is reached, after which it exhibits a rapid increase in current with a relatively constant voltage.
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If a person wanted to engineer a new type of communication device, what field of study would be the most useful?
A ) electrical engineering
B ) chemical engineering
C ) optical engineering
D ) mechanical engineering
Answer: Option A: electrical engineering.
Explanation: The field of electrical engineering, sometimes called electronics engineering, mostly outside the US, is a field of engineering that covers a number of subtopics that include large scale power systems, electronics, control systems, signal processing and telecommunications. In this case the engineer would specifically have to know about electronics (computer chips), signal processing (cell signals) and telecommunications.
Recall that impulse = momentum (FAt = Ap and that Ap is just mx v). How long (time) must a group of people pull with a force of 600N on a stalled 1500kg car to give it a velocity of 1.5m/s? Report your answer to the nearest hundredth (X.XX)
The time taken for the group of people to pull the car, giving it a velocity of 1.5 m/s is 3.75 s
Momentum is simply defined as the product of mass and velocity i.e
Momentum = mass × velocity
To answer the question given, we'll begin by calculating the change in momentum. This can be obtained as follow:
Mass = 1500 Kg
Initial velocity (u) = 0 m/s
Final velocity (v) = 1.5 m/s
Change in momentum =?Change in momentum = m(v – u)
Change in momentum = 1500 (1.5 – 0)
Change in momentum = 1500 × 1.5
Change in momentum = 2250 Kg•m/sFinally, we shall determine the time
Change in momentum = 2250 Kg•m/s
Force (F) = 600 N
Time (t) =?Impulse = Ft = change in momentum
FT = change in momentum
600 × t = 2250
Divide both side by 600
t = 2250 / 600
t = 3.75 sThus, the time required is 3.75 s
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A 1.10-kg object slides to the right on a surface having a coefficient of kinetic friction 0.250 (Figure a). The object has a speed of vi = 2.60 m/s when it makes contact with a light spring (Figure b) that has a force constant of 50.0 N/m. The object comes to rest after the spring has been compressed a distance d (Figure c). The object is then forced toward the left by the spring (Figure d) and continues to move in that direction beyond the spring's unstretched position. Finally, the object comes to rest a distance D to the left of the unstretched spring (Figure e).
The right end of a horizontal spring labeled k is attached to a wall. Five images show five configurations as a block labeled m approaches, compresses, and then moves away from the spring.
In figure a, the block is to the left of the spring, and an arrow above the block points to the right.
In figure b, the block is just touching the uncompressed spring, and an arrow labeled vector vi above the block points to the right.
In figure c, the block has compressed the spring by a distance d, and a label indicates vector vf = 0.
In figure d, the block is just touching the uncompressed spring, and an arrow labeled vector v above the block points to the left.
In figure e, the block is a distance D away from the spring, and a label indicates vector v = 0.
(a)
Find the distance of compression d (in m).
m
(b)
Find the speed v (in m/s) at the unstretched position when the object is moving to the left (Figure d).
m/s
(c)
Find the distance D (in m) where the object comes to rest.
m
(d)
What If? If the object becomes attached securely to the end of the spring when it makes contact, what is the new value of the distance D (in m) at which the object will come to rest after moving to the left?
m
Answer:
(a) Approximately \(0.335\; \rm m\).
(b) Approximately \(1.86\; \rm m\cdot s^{-1}\).
(c) Approximately \(0.707\; \rm m\).
(d) Approximately \(0.228\; \rm m\).
Explanation:
\(v_i\) denotes the velocity of the object in the first diagram right before it came into contact with the spring. Let \(m\) denote the mass of the block. Let \(\mu\) denote the constant of kinetic friction between the object and the surface. Let \(g\) denote the constant of gravitational acceleration.Let \(k\) denote the spring constant of this spring.(a)Consider the conversion of energy in this object-spring system.
First diagram: Right before the object came into contact with the spring, the object carries kinetic energy \(\displaystyle \frac{1}{2}\, m \cdot {v_{i}}^2\).
Second diagram: As the object moves towards the position in the third diagram, the spring gains elastic potential energy. At the same time, the object loses energy due to friction.
Third diagram: After the velocity of the object becomes zero, it has moved a distance of \(D\) and compressed the spring by the same distance.
Energy lost to friction: \(\underbrace{(\mu \cdot m \cdot g)}_{\text{friction}} \cdot D\). Elastic potential energy that the spring has gained: \(\displaystyle \frac{1}{2}\,k\, D^2\).The sum of these two energies should match the initial kinetic energy of the object (before it comes into contact with the spring.) That is:
\(\displaystyle \frac{1}{2}\, m \cdot {v_{i}}^{2} = (\mu\cdot m \cdot g) \cdot D + \frac{1}{2}\, k \cdot D^2\).
Assume that \(g = 9.81\; \rm m \cdot s^{-2}\). In the equation above, all symbols other than \(D\) have known values:
\(m =1.10\; \rm kg\).\(v_i = 2.60\; \rm m \cdot s^{-1}\).\(\mu = 0.250\).\(g = 9.81\; \rm m \cdot s^{-2}\).\(k = 50.0\; \rm N \cdot m^{-1}\).Substitute in the known values to obtain an equation for \(D\) (where the unit of \(D\!\) is \(m\).)
\(3.178 = 2.69775\, D + 25\, D^2\).
\(2.69775\, D + 25\, D^2 + 3.178 = 0\).
Simplify and solve for \(D\). Note that \(D > 0\) because the energy lost to friction should be greater than zero.
\(D \approx 0.335\; \rm m\).
(b)The energy of the object-spring system in the third diagram is the same as the elastic potential energy of the spring:
\(\displaystyle \frac{1}{2}\,k\, D^2 \approx 2.81\; \rm J\).
As the object moves to the left, part of that energy will be lost to friction:
\((\mu \cdot m \cdot g) \, D \approx 0.905\; \rm J\).
The rest will become the kinetic energy of that block by the time the block reaches the position in the fourth diagram:
\(2.81\; \rm J - 0.905\; \rm J \approx 1.91\; \rm J\).
Calculate the velocity corresponding to that kinetic energy:
\(\displaystyle v =\sqrt{\frac{2\, (\text{Kinetic Energy})}{m}} \approx 1.86\; \rm m \cdot s^{-1}\).
(c)As the object moves from the position in the fourth diagram to the position in the fifth, all its kinetic energy (\(1.91\; \rm J\)) would be lost to friction.
How far would the object need to move on the surface to lose that much energy to friction? Again, the size of the friction force is \(\mu \cdot m \cdot g\).
\(\displaystyle (\text{Distance Travelled}) = \frac{\text{(Work Done by friction)}}{\text{(Size of the Friction Force)}} \approx0.707\; \rm m\).
(d)Similar to (a), solving (d) involves another quadratic equation about \(D\).
Left-hand side of the equation: kinetic energy of the object (as in the fourth diagram,) \(1.91\; \rm J\).
Right-hand side of the equation: energy lost to friction, plus the gain in the elastic potential energy of the spring.
\(\displaystyle {1.91\; \rm J} \approx (\mu\cdot m \cdot g) \cdot D + \frac{1}{2}\, k \cdot D^2\).
\(25\, D^2 + 2.69775\, D - 1.90811\approx 0\).
Again, \(D > 0\) because the energy lost to friction is greater than zero.
\(D \approx 0.228\; \rm m\).
The energy transferred between the object and the spring as a closed system, therefore, conserved are;
(a) The distance of compression, d ≈ 0.3354 meters
(b) The speed in the un-stretched position wen the object is sliding to the left, v ≈ 1.8623 m/s
(c) The distance where the object comes to rest, D ≈ 0.7071 m
(d) The distance the object will come to rest attached to the spring, D ≈ 0.2278 m
The reason the above values are correct are as follows;
The known parameters are;
Mass of the object, m₁ = 1.10 kg
Coefficient of friction, μ = 0.250
The initial speed of the object, \(v_i\) = 2.60 m/s
Force constant of the spring, K = 50.0 N/m
Distance the spring is compressed by the object = d
(a) Conservation of energy principle
\(Kinetic \ energy = \dfrac{1}{2} \cdot m\cdot v^2\)
Work done = Force × Distance
Friction force, \(F_f\) = W × μ
Weight, W = m·g
Weight = Mass × Acceleration
Energy transferred by object = Work done by spring + Work done by friction
\(Energy \ transferred \ by \ object = Kinetic \ energy = \dfrac{1}{2} \times 1.10\times 2.60^2 = 3.718\)
Energy transferred by object = 3.718 J
\(Work \ done \ by \ spring = \dfrac{1}{2} \cdot k\cdot x^2\)
\(Work \ by \ spring \ to \ bring \ object \ to \ rest, \ W_{spring} = \dfrac{1}{2} \times 50\times d^2\)
\(W_{spring}\) = 25·d²
Work done by friction, \(W_{friction}\) = 1.10×9.81×0.250×d = 2.69775·d
Therefore;
3.718 = 25·d² + 2.69775·d
25·d² + 2.69775·d - 3.718 = 0
Solving gives
The distance of the compression d ≈ 0.3354 m
(b) The energy given by the spring = 25·d²
The work done by friction, \(W_{friction}\) = 2.69775·d
Kinetic energy given to object = 0.55·v²
0.55·v² = 25·d² - 2.69775·d
0.55·v² = 25×0.3354² - 2.69775×0.3354
∴ v = √(3.4682) = 1.8623
The velocity of the object at the un stretched position, v ≈ 1.8623 m/s
(c) The kinetic energy, K.E. of the object on the way left is given as follows;
K.E. = 0.5 × 1.10 kg × 3.4682 m²/s² = 1.90751 J
The work done by friction before object comes to rest = 2.69775·D
\(D = \dfrac{1.90751 \, J}{2.69775 \, N} \approx 0.7071 \, m\)
The distance where the object comes to rest, D ≈ 0.7071 m
(d) The work done on spring, \(W_{spring}\) = 25·D'²
Work done on friction, \(W_{friction}\) = 2.69775·D'
Kinetic energy of object, K.E. ≈ 1.90751 J
K.E. = \(W_{spring}\) + \(W_{friction}\)
1.90751 ≈ 25·D'² + 2.6775·D'
25·D'² + 2.6775·D' - 1.90751 = 0
Solving with a graphing calculator gives;
D' ≈ 0.2278 m
The new value of the distance D = 0.2278 m
Learn more about the energy conservation principle here:
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Seismic waves are the waves that transport energy away from the focus of an
earthquake. Seismometers, such as the one shown here, measure the
shaking of the Earth as a result of earthquakes. The black arrows show the
relative motion of the sensor on the seismometer. What characteristic of a
seismic wave is this motion showing?
OA. The period of the seismic wave
OB. The amplitude of the seismic wave
4
The characteristic of a seismic wave that the motion shown by the sensor on the seismometer represents is the amplitude of the seismic wave.
Seismic waves are waves that transport energy away from the focus of an earthquake, and they cause the ground to shake. Seismometers are instruments that measure the shaking of the Earth caused by seismic waves. The black arrows in the picture show the relative motion of the sensor on the seismometer. The sensor moves back and forth as the ground shakes, and the amplitude of this motion represents the intensity of the seismic wave.The amplitude of a seismic wave is a measure of the strength or energy of the wave. It is the maximum displacement of the ground from its resting position during the passage of the wave. The greater the amplitude of the seismic wave, the stronger the shaking of the ground and the more damage it can cause. The amplitude of a seismic wave is usually measured in millimeters or centimeters.In summary, the motion shown by the sensor on the seismometer represents the amplitude of the seismic wave. This is an important characteristic of a seismic wave as it determines the intensity of the shaking and the potential damage that the earthquake can cause. Seismologists use this information to study earthquakes and to understand their effects on the Earth.
for such more questions amplitude
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A person of mass 100kg runs up a staircase with a vertical height of 10m. If the trips takes 5 seconds to complete, calculate the person's power ( acceleration due to gravity =10m/s²)
Answer:
Power = 2000J/s
Explanation:
Power= Total Work done/Time
Given
mass = 100kg
distance(height) = 10m
time = 5s
acceleration due to gravity = 10m/s²
Work done = force × distance
Finding Force
Force = mass × acceleration due to gravity
Force = 100kg × 10m/s²
Force = 1,000N
Finding work done
Work done = Force × distance
Work done = 1,000N × 10m
Work done = 10,000J
Finding Power
Power = work done/time
Power = 10,000J/5s
Power = 2,000J/s
Therefore Power is 2,000J/s
Help please
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FOREBRAIN: (front)
Includes: cerebrum, thalamus, hypothalamus, pituitary gland, limbic system, and the olfactory bulb.
Example: THE PITUITARY GLAND carries out some of our most basic functions. This part of the brain controls one'sons metabolism, growth,reproduction, and it even affects the way we store energy from the foods we eat.
MIDBRAIN:(middle)
Includes: cranial nerve nuclei, tectum, tegmentum, colliculi, and crura cerebi.
Example: THE TECTUM; works as a neural processor. It controls swift eye movements, avoidance movements, and takes notice at your own or other's movements.
HINDBRAIN: (back)
Includes: pons, cerebellum, and medulla oblongata.
Example: THE CEREBELLUM, the part of the brain responsible for balance. Subtly it helps our bodies shift in ways to keep us balanced, spanning from posture to how we walk or stand.
Hopefully this helps, Have an amazing day
~JET