a) The kinetic energy of the dart after it is thrown is 2.376 J.
b) The speed of the dart is 18.45 m/s.
c) If the dart were thrown straight upwards, the maximum height it would reach is 17.0 m.
a) The work done on the dart by the applied force is given by:
work = force x distance = 4.40 N x 0.54 m = 2.376 J
Since no energy is lost due to friction, all of this work is converted to the kinetic energy of the dart:
kinetic energy = work = 2.376 J
b) The kinetic energy of the dart can also be expressed as:
kinetic energy = (1/2) x mass x velocity^2
Rearranging this equation gives:
velocity^2 = (2 x kinetic energy) / mass
Substituting the values from part a) gives:
velocity^2 = (2 x 2.376 J) / 0.028 kg = 340.29 m^2/s^2
Taking the square root of both sides gives:
velocity = 18.45 m/s
c) When the dart is thrown straight upwards, its initial vertical velocity is zero. The maximum height it will reach can be calculated using the formula:
maximum height = (initial velocity^2) / (2 x acceleration)
where acceleration is the acceleration due to gravity, which is approximately 9.81 m/s^2.
Substituting the speed calculated in part b) gives:
maximum height = (18.45 m/s)^2 / (2 x 9.81 m/s^2) = 17.0 m
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Question 3
A 2,209 kg car travelling at 31 m/s hits the back of a 1,278 kg car that is travelling 5 m/s slower than the other car. The 2,209 kg
car goes 10 m/s slower than it was going before it hit. Both cars are travelling in the same direction. How fast will the car that got
hit from behind be going after the collision?
The car that got hit from behind will be going 48.05 m/s (or about 172.98 km/h) after the collision.
What is Collision?
In physics, a collision is an event where two or more objects come together and interact with each other, causing a transfer of energy and momentum between them. Collisions can be classified into two types: elastic and inelastic.
To solve this problem, we can use the conservation of momentum principle, which states that the total momentum of an isolated system remains constant before and after a collision. We can set up an equation for the conservation of momentum before and after the collision:
Before the collision:
(2209 kg)(31 m/s) + (1278 kg)(26 m/s) = total momentum
After the collision:
(2209 kg)(21 m/s) + (1278 kg)(vf) = total momentum
where vf is the final velocity of the 1,278 kg car after the collision.
Simplifying the equations, we get:
Before the collision: 76,079 kgm/s + 33,228 kgm/s = 109,307 kg*m/s
After the collision: 46,689 kgm/s + 1,278 kgvf = 47,967 kgm/s + 1,278 kgvf
Since the total momentum before and after the collision is the same, we can set the two equations equal to each other and solve for vf:
76,079 kgm/s + 33,228 kgm/s = 46,689 kgm/s + 1,278 kgvf
109,307 kgm/s = 47,967 kgm/s + 1,278 kg*vf
61,340 kgm/s = 1,278 kgvf
vf = 48.05 m/s
Therefore, the car that got hit from behind will be going 48.05 m/s (or about 172.98 km/h) after the collision.
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A student is given a low voltage power supply and 1m of resistance wire. The student uses these and other pieces of equipment to measure the resistance of just 50cm of the resistance wire. Draw a diagram of the circuit that the students should use. Your circuit diagram should identify the pieces of equipment that the student uses
The student should use the power supply to provide a voltage source (V), the resistance wire (R) and an ammeter (A).The circuit diagram is V-A- R (50cm) -V.
What is resistance ?Resistance is the refusal to accept or comply with something. It is the opposition to a particular idea, policy, or course of action. Resistance can be seen in many forms, including physical, psychological, social, and political. Physically, it can be seen in the refusal to comply with a certain rule or law, or in the refusal to engage in a certain activity or behavior. Psychologically, it can be seen in the refusal to accept certain ideas, beliefs, or values. Socially, it can be seen in the refusal to engage in certain social practices or customs.
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Answer the following questions
1- How to Calculate Power?
2- What is the units of Power?
3- Write a solved example?
Answer:
1- How to Calculate Power?
ans; power is defined as " work done per unit time"
therefore calculated by P= Work/time.
2- What is the units of Power?
Ans; It is watt denoted by "W"
3- Write a solved example?
Ans; Lets say we move a block from One place to another by using 10joules in 4 seconds.
so put values
P=work/time
P=10/4
P=2.5
Explanation:
A ray of light starting from diamond is incident on the interface separating diamond and water . Draw a labelled diagram to show the refraction of light in this case
Answer & Explanation:
incident ray
|
v
----------
| diamond |
----------
^
|
refracted ray
In this diagram, the incident ray of light is represented by the line pointing downward towards the diamond. The interface between the diamond and water is shown as a horizontal line. The refracted ray of light is represented by the line pointing upward away from the diamond.
When the incident ray of light passes from diamond into water, it will refract or bend due to the change in the speed of light between the two media. The exact angle of refraction depends on the refractive indices of the diamond and water, as well as the angle of incidence.
A ray of light starting from diamond is incident on the interface separating diamond and water is as shown in the figure.
What is refractive index ?When a light is going from medium 1 to medium 2. The refractive index is defined as a ratio of velocity of light in medium 1 to velocity of light in medium 2. Refractive index is the factor which deals with the amount of bending of light. More refractive index means more it will bend in the medium 2. When it is 1 we can say that light has not been bent.
By Snell's law, Refractive index is given by,
sin (i) ÷ sin (r) = μ₂÷μ₁
where i is the the angle of incidence
r is the angle of refraction
μ₂ & μ₁ are refractive index of medium 2 and 1 resp.
Light bends as it passes from diamond to water at an angle due to Refractive index between air and glass.
white light consist of number of colors, each color has its own wavelength. Refractive index of an optical medium changes with the wavelength, therefore each color of white light get splitted from white light this phenomenon is know as dispersion of the light.
Labeled diagram is shown in the figure.
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Determine the maximum axial force p that can be applied to the steel plate. Express your answer to three significant figures and include the appropriate units
We must take into account the relationship between the material's stress and strain, which is characterised by its Young's modulus, in order to establish the maximum axial force p that may be applied to the steel plate (E).
We must take into account the relationship between the material's stress and strain, which is characterised by its Young's modulus, in order to establish the maximum axial force p that may be applied to the steel plate (E). Assume that the cross-sectional area of the steel plate is A.
You can compute the tension on the steel plate as follows:
force x area equals stress
You may compute the strain on the steel plate as follows:
strain is equal to length change / starting length.
Hence, p = yield strength * area can be used to compute the maximum axial force p that can be applied to the steel plate without generating plastic deformation.
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light travels a certain distance in 2000 years. is it possible that an astronaut, traveling slower than light, would go as far in 20 years of her life as light travels in 2000 years?
They will be unable to cover as much distance as light does.
The statement is: Light travels a certain distance in 2000 years. No, it is not possible for an astronaut, traveling slower than light, to go as far in 20 years of her life as light travels in 2000 years because the speed of light is constant and cannot be matched by anything with mass.
The speed of light in a vacuum is 299,792,458 meters per second (m/s), which is incredibly fast. On the other hand, the fastest spacecraft to ever leave Earth was NASA's New Horizons probe, which traveled at a speed of about 16.26 kilometers per second.
It would take this spacecraft 37,200 years to travel 2000 light-years. Astronauts cannot travel faster than the speed of light, and their velocity will always be lower than that of light. As a result, they will be unable to cover as much distance as light does.
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1. A 1.33-kg physics textbook is initially at rest on a steel table.
The textbook is then pushed with a constant force of 4.0 N.
Friction with a magnitude of 2.0 N is exerted on the moving
book by the surface of the table.
Determine the final velocity of the textbook after it has been
pushed 0.75 meter across the table.
The acceleration of the textbook is a = F/m = 2.0 N/1.33 kg = 1.5 m/s². and the final velocity of the textbook is v = 0 + (1.5 m/s²)(0.75 s) = 1.125 m/s.
What is acceleration?Acceleration is the rate at which an object changes its velocity over time. It is a vector quantity, meaning it has both magnitude and direction. An object's acceleration can be calculated by measuring the change in its velocity over time.
The net force acting on the textbook is the difference between the pushing force of 4.0 N and the frictional force of 2.0 N, which is 2.0 N.
According to Newton's Second Law, this net force of 2.0 N will cause an acceleration of the textbook given by the equation F = ma, where m is the mass of the textbook (1.33 kg) and a is the acceleration.
Therefore, the acceleration of the textbook is a = F/m = 2.0 N/1.33 kg = 1.5 m/s².
The final velocity of the textbook can then be calculated using the equation v = v0 + at, where v0 is the initial velocity (0 m/s, since the textbook was initially at rest), a is the acceleration (1.5 m/s²), and t is the time the textbook was pushed (0.75 m).
Therefore, the final velocity of the textbook is v = 0 + (1.5 m/s²)(0.75 s) = 1.125 m/s.
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The fastest bird is the spine-tailed swift, which
reaches speeds of 171 km/h. Suppose that you wish
to shoot such a bird with a. 22-caliber rifle that fires
a bullet with a speed of 366 m/s. If you fire at the
instant when the bird is 30 m directly overhead, how
many meters ahead of the bird must you aim the
rifle? Ignore gravity in this problem.
We need to aim the rifle 47.154 meters ahead of the bird's current position to intercept its flight path and hit it.
Since we are ignoring gravity, the horizontal velocity of the bullet will remain constant and equal to the muzzle velocity of the rifle, which is 366 m/s.
To hit the bird, we need to aim the rifle ahead of the bird such that the bullet intercepts the bird's flight path at the same point in space where the bird will be when the bullet arrives.
time = distance / velocity
time = 30 m / 366 m/s
time = 0.08197 s
During this time, the bird will have flown a distance equal to its speed multiplied by the time:
distance = speed x time
distance = 171 km/h x (0.08197 s)
distance = 47.154 m
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When tension is applied to an aluminum rod (Y = 70 x 10^9 Pa) of length 1 m, it stretches by Δ.
1. If the same tension is applied to another aluminum rod with the same cross-sectional area, but of length 2 m, by how much will it stretch?
a) less than Δ
b) Δ
c) more than Δ
2. Now, consider two aluminum rods of length 1 m, one twice as thick as the other. If a compressive force F is applied to both rods, their lengths are reduced by Δthick rod
and Δthin rod, respectively.
The ratio (Δthick rod)/(Δthin rod) is
a) (Δthick rod)/(Δthin rod) < 1
b) (Δthick rod)/(Δthin rod) = 1
c) (Δthick rod)/(Δthin rod) > 1
The answers for the given questions about topic tension:
1. c.) More than ΔL
2. b.) <1
What is aluminium rod?Light and strong, an aluminium rod is highly resistant to corrosion and is ideal for both indoor as well as outdoor use as it can withstand a variety of environmental conditions. Our aluminium rods, which are also referred to as aluminium round bars, are provided in the 6000 series, which has the greatest commercial versatility.
The mechanical sectors can use aluminium alloy wire rods for things like bolts, nuts, nails, needles, rivets, clips, and staples.
1. stress = Y strain
(F / A) = Y (deltaL / L)
deltaL / L = constant (for this problem)
delta(L) / 1 = delta(L') / 2
delta(L') = 2 delta(L)
2. deltaL A = constant
L_thick (2A) = Lthin (A)
L_thick / L_thing = 1/2 < 1
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Figure 1 shows history graphs of two different points on a string as a wave pulse moves along the string. The blue curve is the history graph for the point at x = 1.0 cm , and the green curve is for the point at x = -3.0 cm .
We know that Velocity = delta x /delta t = [-3 -1]cm/[5-0]s = - 0.8 cm/s answer
What is called velocity?Velocity is the direction at which an object is moving and serves as a measure of the rate at which its location is changing as seen from a specific point of view and as determined by a specific unit of time (for example, 60 km/h northbound). In kinematics, the area of classical mechanics that deals with the motion of things, velocity is a basic idea.
A physical vector variable called velocity must have both a value and a direction in order to be defined. Speed is the scalar absolute value (magnitude) of motion; it is a coherent derived unit whose amount is quantified in metres per second (m/s or m/s1) in the SI (metric system).
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For a particular cross-sectional area of the wire, 3.00 x [tex]10^{20}[/tex] electrons must go through it in 6.00 x [tex]10^{14}[/tex] seconds.
How can you figure out how long it takes an electron to travel across a wire with a specific cross-sectional area?Q = It, where I is the current, t is the time, and Q is the total charge.
Q = N
N is the quantity of electrons.
The two equations together give us:
Ne = It,
To solve for t, we obtain:
t = Ne/I
Inputting the values provided yields:
t = (3.00× [tex]10^{20}[/tex])
(1.60× [tex]10^{-19}[/tex] C/e) / (80.0× [tex]10^{-3}[/tex] A)
t = 6.00× [tex]10^{14}[/tex] s
For a particular cross-sectional area of the wire, 3.00 x [tex]10^{20}[/tex] electrons must go through it in 6.00 x [tex]10^{14}[/tex] seconds.
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observe where your house is located and from this explain why your house is hot or cold
The temperature inside a house can be influenced by various factors such as the geographic location, orientation of the house, insulation, and the type of construction materials used.
For instance, if a house is located in a hot and humid climate, it may become hot inside due to the external heat and humidity, even with air conditioning.
On the other hand, a house located in a cold climate may become cold inside, especially during the winter season, due to heat loss from the interior to the cold outside environment.
Proper insulation and efficient heating/cooling systems can help regulate the temperature inside a house and improve its energy efficiency.
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A coconut is free-falling vertically from a tree. The gravitational potential energy of the coconut when it starts to fall is 560J
a) Calculate the mechanical energy of the coconut when it begins to fall.
b) Find the kinetic energy of the coconut when it hits the ground.
c) Calculate the kinetic energy, potential energy & mechanical energy of the coconut at a position 1/2 the height when it started to fall.
Question
A coconut of mass m falls from its tree through a vertical distance of s and could reach ground with a velocity of v ms−1 due to air resistance. The work done by air resistance is:
A.) −m/2 (2gs−v2)
B.) −1/2 mv^2
C.) −mgs
D.) mv^2+2mgs
Solution
Correct option is A)
Here, a coconut of mass m falls from its tree through a vertical distance of s, with a velocity of v hence work done by gravity is,
Wg=mgs .......(1)
Change in velocity of coconut is,
E=1/2m(u−v)^2 = −1/2m(v)2 ........(2)
Now, total work done on coconut is equal to change in kinetic energy hence,
Wa+Wg=1/2mv^2
where, Wa is work done by air resistance.
Using (1) and (2), we get
Wa=1/2mv^2−Wg
Wa=1/2mv^2−mgs
Wa=−m/2(2gs−v2)
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Which would have more matter: a 1 cm cube of lead or a 1 cm
cube of rubber?
Answer: 1CM CUBE OF LEAD
Explanation:
A marble is placed in a graduated cylinder, which was filled to the 20 mL mark. The level rises to 40 mL. What happens to the volume of the water?
Answer:
Below
Explanation:
The volume of water remains the same....the new measurement now includes the volume of the marble ( 20 ml)
A stone hits the bottom of an old mineshaft that is 210 m deep. If the temperature in the mineshaft is 10°C, how many seconds pass before the sound is heard at the top of the mine shaft?
The speed of sound in air at 10°C is approximately 343 meters per second. Let's use the formula:
distance = speed x time
We want to find the time it takes for the sound to travel 210 meters to the top of the mineshaft. So we can rearrange the formula to solve for time:
time = distance ÷ speed
Plugging in the values we have, we get:
time = 210 ÷ 343
time ≈ 0.612 seconds
Therefore, it takes approximately 0.612 seconds for the sound to travel from the bottom to the top of the mineshaft.
a 1.60 m m tall person lifts a 1.40 kg k g book off the ground so it is 2.00 m m above the ground. part a what is the potential energy of the book relative to the ground?
27.44 J of the potential energy of the book relative to the ground, when a 1.60 m tall person lifts 1.40 kg of the book off the ground.
A 1.60 m m tall person lifts a 1.40 kg book off the ground so it is 2.00 m m above the ground.
The potential energy of the book relative to the ground would be:
PE = mgh
Where PE is the potential energy,
m is the mass,
g is the acceleration due to gravity, and
h is the height
The acceleration due to gravity is constant and is 9.8 m/s²
mass m = 1.40 kg
Height h = 2.00 m
mgh = 1.40 × 9.8 × 2.00 = 27.44 J
Ans: The potential energy of the book relative to the ground is 27.44 J.
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What are the temperature and energy changes for segment A (red line) on the heating curve for water?
The region marked segment A occurs at 100 degrees Celsius and is the latent heat of vaporization.
What is the latent heat of vaporization?The latent heat of vaporization is the amount of heat energy required to change the state of a substance from a liquid to a gas (vapor) at a constant temperature and pressure.
During the phase transition, the energy supplied to the substance is used to overcome the intermolecular forces of attraction between the particles, which allows the particles to escape from the liquid phase and enter the gaseous phase. This results in an increase in the internal energy of the substance, but with no change in temperature.
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. Mention a few uses of magnets in our daily life.
Explanation:
Magnets are used to make a tight seal on the doors to refrigerators and freezers. They power speakers in stereos, earphones, and televisions. Magnets are used to store data in computers, and are important in scanning machines called MRIs (magnetic resonance imagers), which doctors use to look inside people's bodies
A faulty model rocket moves in the xy-plane (the positive y-direction is vertically upward). The rocket's acceleration has components ax(t)=αt2
and ay(t)=β−γt
, where α
= 2. 50 m/s4
, β
= 9. 00 m/s2
, and γ
= 1. 40 m/s3. At t=0
the rocket is at the origin and has velocity v⃗ 0=v0xi^+v0yj^
with v0x
= 1. 00 m/s
and v0y
= 7. 00 m/s
A pulley system is such that a person pulls down with 10 N of force to lift a 20 N object. The
machanical advantage is.
(MA = Fout/Fin)
O 0. 5
O 2
O
30
Please help me
Two is the mechanical benefit of the pulley mechanism.
The mechanical advantage of a pulley system is the ratio of the output force to the input force. In this case, the person is pulling down with a force of 10 N to lift a 20 N object. Therefore, the mechanical advantage can be calculated as follows:
MA = output force / input force
MA = 20 N / 10 N
MA = 2
The mechanical advantage of the pulley system is 2. This means that for every 1 unit of force the person applies, the object is lifted with 2 units of force. In other words, the pulley system allows the person to lift the object with less force than would be required without the pulley system.
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Dos esteras conductoras, cargadas y de igual radio, se apoyan en soportes no conductores. Sus cargas respectivas son-3 C y +7 MC. Si ambas esteras se ponen en contacto y luego son separadas, entonces las cargas respectivas de cada estera son:
A. -Z UC Y +2 MC
В. +1 МС У -3 МС
C. +2 C y +2 MC
D. -1 MC y - 1 MC
The correct option is B. The respective charges on each mat are +1 MC y -3 MC.
Charge refers to a fundamental property of matter that describes how objects interact electromagnetically. The charge can be positive or negative and is measured in Coulombs (C). Objects with the same charge repel each other, while objects with opposite charges attract each other.
Electric charge can be transferred from one object to another through processes such as friction, contact, or induction. The movement of electric charge is the basis for electric current, which is the flow of charge through a conductor.
A charge is also a conserved quantity in physics, meaning that it cannot be created or destroyed, only transferred or redistributed. This conservation of charge is a fundamental principle in many areas of physics, including electromagnetism and quantum mechanics.
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Complete Question:
Two charged conductive mats of equal radius are supported by non-conductive supports. Their respective charges are -3 C and +7 MC. If both mats come into contact and are then separated, then the respective charges on each mat are:
A. -Z UC Y +2 CM
В. +1 MS У -3 MS
C. +2 C and +2 MC
D. -1 MC and - 1 MC
A wave has a frequency of 12,000 Hz. What does this mean
It means that wave vibrates 12,000 times about its mean position per second.
Humans can hear sounds between about 20 Hz and 20,000 Hz (depending on the human!).
Below 20 Hz is called infrasound ("infra" means below), and above 20,000 Hz is ultrasound ("ultra" means beyond).
We are most sensitive to sounds between 1,000 and 4,000 Hz:
As we get older we are less sensitive to higher frequency sounds (a limit around 12,000 Hz is normal for an adult).
Vibration refers to the back-and-forth motion of an object or system about its equilibrium position. This motion can be periodic or random and can occur in a variety of mediums, including solids, liquids, and gases. Vibration is caused by a force or disturbance that creates an oscillation within the system.
Vibration can be both beneficial and detrimental. Beneficial vibrations can be used to create sound, power tools, and even musical instruments. On the other hand, detrimental vibrations can cause damage to structures, machinery, and even the human body. For example, exposure to high levels of vibration can cause hand-arm vibration syndrome or whole-body vibration syndrome, which can result in numbness, tingling, and even long-term health problems.
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If a net force of 24 N is applied to an object with a mass of 6 kg, then what will the resulting
acceleration be according to Newton's second law of motion?
a
b
C
d
6 m/s²
0.25 m/s²
24 m/s²
4 m/s²
Answer:
d. 4m/s²
Explanation:
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The torque vs. rotations graph above describes the effects of an increasing unbalanced torque due to a force that acts tangentially along the edge of an object with a moment of Inertia of 0.0025 kg m^2.
Which of the following is the angular velocity of the disc after 2.0 seconds if the disc starts from rest?
The graph is just a torque vs rotations graph. I'm more so looking for an explanation of this.
100 rad/s
200 rad/s
300 rad/s
50 rad/s
150 rad/s
The angular velocity of the disc after 2.0 seconds if the disc starts from rest based on the torque rotation graph is 100 rad/s.
What is the graph about?A torque versus rotations graph is a visual representation of the relationship between the torque applied to an object and the resulting rotations produced by that torque.
Typically, the torque is plotted on the vertical axis, while the rotations are plotted on the horizontal axis. The resulting graph usually shows a linear relationship between torque and rotation, with the slope of the line indicating the object's rotational inertia or resistance to rotation.
The graph can be used to determine the amount of torque required to produce a certain amount of rotation in an object. Based on the graph, the correct option is A.
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Most people store much of their personal information digitally on a computer.
What happens to this information if it is accidentally deleted?
A. The information is backed up, but it is an inferior copy.
O
B. If the information is overwritten, it cannot be recovered.
C. The information is changed and becomes a computer virus.
O
D. The information is automatically backed up as analog storage.
SUBMIT
The correct option is A. If personal information is accidentally deleted from a computer, The information is backed up, but it is an inferior copy.
Information can be defined as a measure of the degree of uncertainty reduction obtained by receiving a message or measuring a system. It is a fundamental concept in many areas of physics, including thermodynamics, quantum mechanics, and information theory.
In thermodynamics, information is related to the entropy of a system, which quantifies the degree of disorder or randomness. The more information we have about a system, the lower its entropy and the more ordered it becomes.
In quantum mechanics, information is closely related to the concept of entanglement, where two or more particles become so strongly correlated that their states cannot be described independently. The amount of information that can be transmitted through an entangled system is limited by the laws of quantum mechanics.
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answer the following questions: which block has a higher temperature? iron does the hotter block have more energy inside? look closely! yes how would you explain that after putting in the same amount of heat, the two blocks have different temperatures? different
Yes, the hotter block has more energy inside. This is due to the fact that the materials of the two blocks have different heat capacities. Heat capacity is the amount of heat energy that must be added to a material to increase its temperature by 1°C. Generally speaking, materials with higher heat capacities will require more heat to raise their temperature by 1°C than materials with lower heat capacities.
For example, if two blocks, one made of iron and one made of aluminum, were both placed in a fire and given the same amount of heat energy, the block made of aluminum would be hotter than the block made of iron. This is because iron has a higher heat capacity than aluminum, meaning it takes more energy to heat it up. Therefore, the aluminum block has absorbed more heat energy and has a higher temperature than the iron block.
In conclusion, after receiving the same amount of heat energy, the two blocks have different temperatures because they have different heat capacities. The block with the higher heat capacity (iron) requires more energy to raise its temperature, resulting in a lower temperature than the block with the lower heat capacity (aluminum).
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A car accelerates from a stop at a rate of 2 m/s² for 20 s, then con- tinues at a constant speed for 40 s. Graph the speed vs. time of the car. What is the car's speed at 10 s? What is its final speed?
The car's speed at 10 s would be 20 m/s, and the final speed would be 40 m/s.
Velocity-time graphDuring the first 20 s, the car accelerates at a rate of 2 m/s², so its speed increases linearly. We can calculate the final speed at 20 s as follows:
a = 2 m/s²
t = 20 s
v = a * t = 2 m/s² * 20 s = 40 m/s
From 20 s to 60 s, the car continues at a constant speed, so the graph is a horizontal line at 40 m/s.
Therefore, the car's speed at 10 s is:
t = 10 s
v = a * t = 2 m/s² * 10 s = 20 m/s
And its final speed is 40 m/s
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a ball player wishes to determine pitching speed by throwing a ball horizontally from an elevation of 5 m above the ground. the player sees the ball land 20 m down range. what is the player's pitching speed?
The pitching speed of the player to cover a horizontal distance of 20 m when the ball is thrown horizontally from a height of 5 m is 19.82 m/s.
To find the pitching speed, we need to use the kinematic equation, which relates the distance traveled by an object to its initial velocity and the time it takes to travel that distance.
Since the ball is thrown horizontally, we can assume that the initial velocity of the ball is horizontal and the acceleration of the ball is vertical due to the force of gravity.
Using the equation of motion for the horizontal motion:
distance = speed × time
Since the ball is thrown horizontally, there is no initial vertical velocity, so the initial velocity is zero.
Therefore, distance = speed × time
time = distance/speed
Using the equation of motion for the vertical motion:
[tex]distance = initial \ velocity \times time + (1/2) \times acceleration \times time^2[/tex]
Since the ball is thrown horizontally, the initial vertical velocity is zero, and the acceleration due to gravity is 9.81 m/s² (since it is acting downward).
Therefore, [tex]distance = (1/2) \times (9.81) \times time^2[/tex]
[tex]time^2 = 2 \times distance/9.81[/tex]
[tex]time = \sqrt{2 \times distance / acceleration}[/tex]
Substituting the values
[tex]time = \sqrt{2\times(5/9.81)} = 1.009 s[/tex]
Now, substituting the value of time in the horizontal motion equation:
[tex]speed = distance/time[/tex]
[tex]speed = 20/1.009 = 19.82\ m/s[/tex]
Speed = 19.82 m/s
Therefore, the player's pitching speed is 19.82 m/s.
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2. A person walks 20 m [N 20E], then
120 m [N 50W], then 150 m [W] and finally
30 m [S 75E]. Find the person final
displacement using trigonometric methods
The person's final displacement is approximately 227 meters at an angle of 17.9 degrees North of West.
The first displacement of 20 m [N 20° E] can be broken down as follows,
The x-component is 20 cos(20°) = 18.8 m to the East
The y-component is 20 sin(20°) = 6.8 m to the North
The second displacement of 120 m [N 50° W],
The x-component is 120 cos(50°) = -91.9 m to the West
The y-component is 120 sin(50°) = 92.2 m to the North
The third displacement of 150 m [W] has no y-component, and the x-component is simply -150 m to the West.
The fourth displacement of 30 m [S 75° E],
The x-component is 30 cos(75°) = 7.4 m to the East
The y-component is 30 sin(75°) = -28.6 m to the South
The total x-component is 18.8 m - 91.9 m - 150 m + 7.4 m = -215.7 m to the West. The total y-component is 6.8 m + 92.2 m + 0 m - 28.6 m = 70.4 m to the North
To find the magnitude of the resultant vector,
|d| = sqrt((-215.7 m)^2 + (70.4 m)^2) ≈ 227 m
To find the direction of the resultant vector,
θ = tan^-1(70.4 m / 215.7 m) ≈ 17.9° N of W
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