Answer:
Potential energy: stored energy
Explanation:
Energy is the capacity to do work. It exists in various forms which can be converted from one form to another. It is measured in Joules (J).
The energy possessed by an object at rest is called potential energy. It is a form of mechanical energy. It is a stored energy which can be converted to kinetic energy when the object start to move.
The best match between an established energy type and its use or trait as given in the question is: Potential energy: stored energy
Tonya is modeling the discovery of electromagnetic induction. Which procedure should she use? moving a magnet into a coil of wire in a closed circuit moving a magnet into a coil of wire in an open circuit bringing a compass near a wire that has no electric current bringing a compass near a wire that has an electric current
To model the discovery of electromagnetic induction, Tonya should use the procedure of moving a magnet into a coil of wire in a closed circuit.
Tonya should use the procedure of moving a magnet into a coil of wire in a closed circuit.
Electromagnetic induction refers to the phenomenon of generating an electric current in a conductor by varying the magnetic field passing through it. This concept was discovered by Michael Faraday in the early 19th century. To model this discovery, Tonya needs to recreate the conditions that led to this breakthrough.
In Faraday's experiment, he observed that when a magnet is moved into or out of a coil of wire, it induces an electric current in the wire. This occurs when the magnetic field passing through the coil changes. Therefore, Tonya should use a similar setup to replicate this process.
Out of the given options, the most appropriate procedure for Tonya would be to move a magnet into a coil of wire in a closed circuit. By having a closed circuit, it means that the ends of the wire are connected to form a complete loop. When the magnet is moved into the coil, the changing magnetic field induces an electric current to flow through the wire.
This procedure demonstrates the principle of electromagnetic induction and shows how a changing magnetic field can produce an electric current. It allows Tonya to visually observe the effects of the induced current, which is essential in modeling the discovery of electromagnetic induction.
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Question 4 Multiple Choice Worth 2 points)
(02.07 MC)
A car increases from 15 km/s to 45 km/s in 5 seconds. Calculate the average acceleration of the car during these 5 seconds
Explanation:
ACCELERATION IS THE RATE OF CHANGE OF VELOCITY
i.e a = ΔV/ Δt where ΔV is final velocity – initial velocity and Δt is t final – t initial
a = (45–15)/5= 6 km/s²
The average acceleration of the car during these 5 seconds = a = 6 km/s^2
What is average acceleration ?Average acceleration refers to the rate of change of velocity for that interval per time
given
v(initial) = 15 km/s
v( final ) = 45 km/s
time interval = 5 seconds
a (average acceleration) = (v( final ) - v(initial)) / time interval
a = (45 - 15) / 5
a = 6 km/s^2
average acceleration of the car during these 5 seconds = a = 6 km/s^2
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A spring is resting vertically on a table. A small box is dropped onto the top of the spring and compresses it. Suppose the spring has a
spring constant of 300 N/m and the box has a mass of 1.9 kg. The speed of the box just before it makes contact with the spring is 0.39
m/s.
(a) Determine the magnitude of the spring's displacement at an instant when the acceleration of the box is zero.
(b) What is the magnitude of the spring's displacement when the spring is fully compressed?
(a) The magnitude of the spring's displacement when the acceleration of the box is zero can be determined by equating the initial gravitational potential energy to the elastic potential energy stored in the spring.
(b) The magnitude of the spring's displacement when the spring is fully compressed can be determined by equating the initial gravitational potential energy to the elastic potential energy stored in the spring.
(a) To determine the magnitude of the spring's displacement when the acceleration of the box is zero, we need to apply the principles of conservation of energy.
Initially, the box has gravitational potential energy given by mgh, where m is the mass of the box, g is the acceleration due to gravity, and h is the height from which the box was dropped. The initial gravitational potential energy is converted into the elastic potential energy stored in the compressed spring and the kinetic energy of the box just before it makes contact with the spring.
The gravitational potential energy is given by:
mgh = (1.9 kg)\((9.8 m/s^2)h\)
The elastic potential energy stored in the spring is given by:
1/2 kx^2\(kx^2\), where k is the spring constant and x is the displacement of the spring.
The kinetic energy of the box just before it makes contact with the spring is given by:
\(1/2 mv^2,\) where m is the mass of the box and v is the speed of the box.
Since the acceleration of the box is zero at the instant when the spring's displacement is maximum, the kinetic energy is zero. Therefore, we can equate the initial gravitational potential energy to the elastic potential energy to find the spring's displacement.
mgh = 1/2 \(kx^2\)
Substituting the given values, we have:
\((1.9 kg)(9.8 m/s^2)h = 1/2 (300 N/m)x^2\)
Solving for x, the magnitude of the spring's displacement, we can determine its value at the instant when the acceleration is zero.
(b) To find the magnitude of the spring's displacement when the spring is fully compressed, we need to consider the conservation of mechanical energy once again.
At maximum compression, all the initial gravitational potential energy is converted into the elastic potential energy stored in the compressed spring.
mgh = 1/2 \(kx^2\)
Substituting the given values and solving for x, the magnitude of the spring's displacement, we can determine its value when the spring is fully compressed.
It's important to note that in both cases, the negative sign of the displacement indicates that the spring is being compressed. The magnitude of the displacement will be a positive value.
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Which statement about RNA polymerase is NOT true?
RNA polymerase reads a template strand of DNA 5' to 3'
RNA polymerase binds to a promoter region to initiate transcription
RNA polymerase adds a ribonucleotide to the 3' end of a growing RNA molecule
During transcription of a gene, RNA polymerase reads only one strand of DNA
Please explain!
Answer:
RNA polymerase reads a template strand of DNA 5' to 3'
Explanation:
RNA polymerase is the enzyme accountable for the transcription of the DNA. It shows one coast of the DNA and transcribed within the RNA. It combines the nucleotide to the 3' conclusion of the expanding series of the RNA. It commences the method by connecting to the promoter area of the gene. The enzyme increases nucleotide, not ribonucleotide.
Therefore, A. RNA polymerase reads a template strand of DNA 5' to 3' is false.
Answer:
RNA polymerase reads a template strand of DNA 5' to 3'.
Explanation:
RNA synthesis is less processive during elongation than during initiation. Synthesis begins with the polymerase binding two rNTP molecules. The polymerase frequently releases the nascent transcript before it reaches 8-10 nucleotides in length.
7. DRAW A PICTURE TO SHOW WORK.
Brandon buys a new Seadoo. He goes 12
km north from the beach. He jumps
wakes for 6 km to the east. Then chases
a boat 12 km south. He then turns and
goes 3 km to the West. What distance
did he cover? What was his
displacement?
the very act of observing a particle has a dramatic effect on its behaviour why do you think this is the case
Answer:
Explanation:
In the microscopic world of quantum mechanics, particles don't behave like familiar everyday objects. They can exist in multiple states simultaneously and behave as both particles and waves. When we try to measure or observe a particle, we typically use light or other particles to interact with it. However, this interaction can disturb the particle's state. Imagine trying to measure the position of an electron using light. Light consists of photons, and when photons interact with the electron, they transfer energy to it. This energy exchange causes the electron's position and momentum to become uncertain. The more precisely we try to measure its position, the more uncertain its momentum becomes, and vice versa. This is known as the Heisenberg uncertainty principle.
So, the act of observing a particle disturbs its state because the interaction between the observer and the particle affects its properties. The very act of measurement or observation introduces a level of uncertainty and alters the particle's behavior. It's important to note that this behavior is specific to the quantum world and doesn't directly translate to the macroscopic world we experience in our daily lives. Quantum mechanics operates at extremely small scales and involves probabilities and uncertainties that are not typically noticeable in our macroscopic observations.
mention the type of motion taking place in, horse pulling a cart which type of motion
Answer:
Motion of a horse pulling a cart on a straight road – Straight line motion. As the horse cart is moving on a straight road. ... Therefore it is oscillatory motion.
Explanation:
please give me brainlist and follow
The amount of energy needed to a power a 0.20kw bulb for one minute would be just sufficient to lift a 2.5 kg object through a vertical distance of
The amount of energy needed to power a 0.20 kW bulb for one minute would be just sufficient to lift a 2.5 kg object through a vertical distance of approximately 29.03 meters.
To calculate the energy required to lift a 2.5 kg object through a vertical distance, we need to consider the gravitational potential energy formula:
Potential energy (PE) = mass (m) × gravity (g) × height (h)
Where:
m = 2.5 kg (mass of the object)
g = 9.8 m/s² (acceleration due to gravity on Earth)
h = ? (height)
First, let's find the height (h) by rearranging the formula:
h = PE / (m × g)
Now, let's calculate the potential energy (PE) needed to lift the object. We are given that the power of the bulb is 0.20 kW, and we want to find the energy required for one minute. To convert kilowatts (kW) to joules (J), we multiply by the conversion factor of 3,600 (60 seconds × 60 minutes):
Energy (E) = power (P) × time (t)
E = 0.20 kW × 1 min × 3,600 J/kW
Now, we can substitute the values into the equation to find the height:
h = (0.20 kW × 1 min × 3,600 J/kW) / (2.5 kg × 9.8 m/s²)
Calculating the expression on the right side:
h ≈ 0.20 × 1 × 3,600 / (2.5 × 9.8) ≈ 29.03 meters (rounded to two decimal places)
Therefore, the amount of energy needed to power a 0.20 kW bulb for one minute would be just sufficient to lift a 2.5 kg object through a vertical distance of approximately 29.03 meters.
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anybody from India ?
Answer:
No,why you say that
Explanation:
HELPPPP LATE HOMEWORK DUE TODAY
If F₁ has a greater magnitude than F₂, the box will accelerate backward because the net force is in the backward direction (1st option)
How do i know which direction the box will move to?To obtain the direction in which the box will move, we shall determine the net force acting on the box. This is illustrated below:
Assumption:
Magnitude of force 1 (F₁) = 40 NMagnitude of force 2 (F₂) = 25 NNet force (F) =?Net force = Magnitude of force 1 (F₁) - Magnitude of force 2 (F₂)
Net force = F₁ - F₂
Net force = 40 - 25
Net force = 15 N backward
From the above illustration, we can see that the net force is 15 N backward.
Thus, we can conclude from the box will accelerate backward (1st option)
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Edg 2021
Answer the questions using the drop-down menus.
1. Which statement shows the direction of the transfer of heat in this experiment?
The heat transfer is from the ______ to the ______.
2. Which statement compares the temperatures of the white and black sheets at 1, 2, and 3 minute(s)?
The temperature _________.
3. What conclusion can be made based on this data?
___________
Answer: light bulb, paper, is higher for the black paper, the white paper absorbs less heat.
Explanation: god bless everyone and stay safe!
Answer:
nswer the questions using the drop-down menus.
1. Which statement shows the direction of the transfer of heat in this experiment?
The heat transfer is from the
light bulb
to the
paper
.
2. Which statement compares the temperatures of the white and black sheets at 1, 2, and 3 minute(s)?
The temperature
is higher for the black paper.
.
3. What conclusion can be made based on this data?
The white paper absorbs less heat.
Explanation:
bc i just took the assignment
Polarized sunglasses:
a. block most sunlight because sunlight is polarized
b. are better but work the same way as non-polarized sunglasses
c. are polarized to filter out certain wavelengths of light
d. block reflected light because reflected light is partially polarized.
Polarized sunglasses creates filter of vertical openings for light. The light rays will reach the eyes of human vertically only.
The sun rays will not reach human eye directly which will create a shield for sun light burden on human eye.
Polarized sunglasses are best used for blocking and eliminating certain wavelengths of light.
Therefore the correct answer is option C. Polarizes Sunglasses are polarized and it filter out certain wavelengths of light.
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Hey any physicist or engineer around. am giving brainliest to anyone who will answer this question.
Answer:
N = 167 Newtons
R = 727 Newtons
Explanation:
i) For static equilibrium, moments about any convenient point must sum to zero.
A moment is the product of a force and a moment arm length. Only the force acting perpendicular to a moment arm passing through the pivot point makes a moment.
ii) I will ASSUME the two moment arms are 0.05m and 0.15 m
CCW moments about the fulcrum are
190 N(0.2 m) + 280 N(0.05 m) = 52 N•m
CW moments are (N)N(0.15 m + 90 N(0.3 m) = 27 + 0.15N N•m
For static equilibrium, these must be equal
27 + 0.15N = 52
0.15N = 25
N = 166.6666666...
Sum moments about N to zero
(Same as saying CW and CCW moments must balance)
190(0.2 + 0.15) + 280(0.05 + 0.15) - R(0.15) - 90(0.3 - 0.15) = 0
R = 726.6666666...
We could verify this by summing vertical forces to zero.
R - 190 - 280 - 166.666666 - 90 = 0
R = 726.6666666...
The current flowing through a lamp is 1.5AIt is plugged into a 120 V outletWhat is the resistance of the lamp? Ω
Given the flow of current and the voltage, the resistance of the lamp is 80 Ohms.
What is the resistance of the lamp?Ohm’s law states that the potential difference between two points is directly proportional to the current flowing through the resistance.
V = IR
Where V is the voltage or potential difference, I is the current and R is the resistance.
Given the data in the question;
Current I = 1.5AVoltage V = 120VResistance R = ?Plug the given values into the equation above and solve for R.
V = IR
120 = 1.5 × R
R = 120/1.5
R = 80Ω
Given the flow of current and the voltage, the resistance of the lamp is 80 Ohms.
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Answer:
80 is the answer
Explanation:
If you want to make a strong battery, should you pair two metals with high electron affinities, low electron affinities, or a mix? Explain your answer.
A blow-dryer and a vacuum cleaner each operate with a voltage of 120 V. The current rating of the blow-dryer is 13 A, while that of the vacuum cleaner is 4.8 A. Determine the power consumed by (a) the blow-dryer and (b) the vacuum cleaner. (c) Determine the ratio of the energy used by the blow-dryer in 15 minutes to the energy used by the vacuum cleaner in 40 minutes.
Answer:
(a) 1560 W
(b) 576 W
(c) 1.01
Explanation:
Voltage, V = 120 V
Current in dryer, I = 13 A
current in vacuum cleaner, i' = 4.8 A
(a) Power consumed by dryer,
P = V I = 120 x 13 = 1560 W
(b) Power consumed by vacuum cleaner
P' = V I' = 120 x 4.8 = 576 W
(c) Energy consumed by dryer
E = P x t = 1560 x 15 x 60 = 1404000 J
Energy consumed by the vacuum cleaner
E' = P' x t' = 576 x 40 x 60 = 1382400 J
the ratio of energies is
E : E' = 1404000 : 1382400 = 1.01
prepare a report on why a vehicle needs to be maintained/serviced after a certain period of time. How is servicing different in a petrol/diesel and electric vehicle?
Vehicles need to be serviced for several reasons such as preventing costly repairs and improving fuel economy.
Why should cars be maintained and / or serviced ?First, regular maintenance can help to prevent costly repairs down the road. Second, maintenance can help to improve fuel economy and emissions. Third, maintenance can help to keep your vehicle safe and reliable.
The servicing requirements for petrol/diesel and electric vehicles differ in a number of ways. Petrol/diesel vehicles require oil changes more frequently than electric vehicles. This is because petrol/diesel engines use oil to lubricate the moving parts, while electric motors do not. Petrol/diesel vehicles also require tune-ups more frequently than electric vehicles.
This is because petrol/diesel engines have more moving parts that need to be synchronized, while electric motors have fewer moving parts.
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In a ballistic pendulum experiment, suppose the digital timer shows 0.02 s for the time of flight of the projectile. The manufacturer information about the precision of the timer is nowhere to be found. What error would you quote on your measurement
Answer:
The value is \(\Delta t = 0.01 \ s\)
Explanation:
From the question we are told that
The time of flight is \(T = 0.02 \ s\)
Given that the value of the time of flight is in three decimal place then the error quote is
\(\Delta t = 0.01 \ s\)
A roller coaster is at a peak of 20m and has a mass of 900kg. What is the potential energy of the roller coaster?
O 100000 J
10000 J
O 9.8 J
O 176400 J
The potential energy of the roller coaster is 176,400 J (joules).
The potential energy of an object is given by the formula PE = mgh, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height or vertical position of the object.
In this case, the roller coaster is at a peak of 20m and has a mass of 900kg. The acceleration due to gravity, g, is approximately 9.8 \(m/s^2\).
Using the formula, we can calculate the potential energy:
PE = mgh
= (900 kg)(9.8 \(m/s^2\))(20 m)
= 176,400 J
Therefore, the potential energy of the roller coaster is 176,400 J (joules).
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To measure the capacitance C of a capacitor, you attach the capacitor to a battery and wait until it is fully charged. You then disconnect the capacitor from the battery and let it discharge through a resistor of resistance R. You measure the time T1/2 that it takes the voltage across the resistor to decrease to half its initial value at the instant that the connection to the capacitor is first completed. You repeat this for several different resistors. You plot the data as T1/2 versus R and find that they lie close to a straight line that has slope 7.50 μF.
What is the capacitance C of the capacitor?
The RC circuit, which is utilized in this experiment, is one of the most basic circuits that make use of a capacitor. When two conductors are linked to a charging device, the charge is passed from one conductor to the other.
When two conductors are connected to a charging device (such as a battery), the charge is transferred from one conductor to the other until the potential difference between the terminals of the charging device and the potential difference between the conductors are equal.
Capacitors are objects that have the capacity to hold electrical charge and energy. Capacitors have a wide range of uses, such as filters in DC power supplies and energy banks for pulsed lasers. Since capacitors only pass AC current and not DC current, they are used to block the DC component of a signal so that the AC component of the signal may be detected.
Plasma physics makes use of the energy-storage capabilities of capacitors. In plasma physics, short energy bursts with extremely high voltages and currents are frequently needed. A capacitor can be softly charged to the necessary voltage and then quickly discharged to yield the necessary energy.
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Which of the following is not an effect that might have originated via catastrophic collision?
Uranus has an axial tilt of 98° with respect to its orbit.
The Moon of Earth is extremely large and only slightly younger than Earth itself.
Venus has an extremely high surface temperature, in fact, the highest on average of any planet in the solar system.
Mercury's crust is extremely small compared to the size of its nickel-iron core.
Some moons of Neptune possess retrograde or highly eccentric orbits.
B, Venus has an extremely high surface temperature, in fact, the highest on average of any planet in the solar system is not an effect that might have originated via catastrophic collision.
What describes a catastrophic collision?This is not an effect that might have originated via catastrophic collision. Venus's high surface temperature is due to its thick atmosphere, which is composed mostly of carbon dioxide. The carbon dioxide traps heat from the sun, causing the planet to warm up.
The other effects listed are all possible effects of catastrophic collisions. Uranus's axial tilt of 98° with respect to its orbit could have been caused by a collision with another planet-sized object.
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True or false: cinnamon rolls grow bigger when baked because they absorb water from the hot air in the oven.
Answer:
THAT IS FOR SURE CORRECT
Explanation:
I USE TO COOK THEM ALL THE TIME LOL
PLSSS MARK ME BRAINLIEST
PLEASE HELP!!!How would you describe the motion of a transverse wave?
Answer:
The motion of a transverse wave would be described as perpendicular to the wave direction.
Explanation:
The motion of a transverse wave is perpendicular to the wave propagation.
What is transverse wave?
A transverse wave is an oscillating wave in physics that advances in the opposite direction of its oscillations. A longitudinal wave, on the other hand, moves in the direction of its oscillations. Transverse waves include water waves.
The waves that can be made on a horizontal length of string by anchoring one end and moving the other end up and down provide a straightforward example. The waves that are produced on a drum's membrane serve as another illustration. Each point in the membrane moves up and down, perpendicular to the membrane plane, as the waves move in directions parallel to the membrane plane.
Another example of a transverse wave is light, which has electric and magnetic fields as oscillations.
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What is the impact of the imagery used in paragraph six on the meaning of "On a Mountain Trail"?
The impact of the imagery used in paragraph six on the meaning of "On a Mountain Trail" emphasizes the fear and uncertainty of the narrator as the pack surrounds the sleigh on the trail.
The imagery in paragraph 6 paints a vivid and powerful picture of a pack of wolves surrounding the sled. Because of the narrator's inability to count the number of wolves present, this description adds to the feeling of anxiety and uncertainty. The scene reinforces the emotional impact of the scene and helps convey the protagonist's sense of vulnerability and danger.
Therefore, the correct option is C.
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What happens to the temperature of a substance while it is changing state?
A. It decreases first and then remains constant.
B. It increases first and then decreases.
C. It remains constant.
D. It varies randomly.
The temperature remains constant while the substance is changing state.The correct answer is option C.
When a substance undergoes a change of state, such as melting, boiling, or condensing, the temperature of the substance remains constant during the phase transition. The process of changing state requires the absorption or release of heat energy without a change in temperature.
For example, when a solid is heated, its temperature increases until it reaches the melting point. At this point, the substance starts to change from a solid to a liquid, but the temperature remains constant until all the solid has melted.
The absorbed heat energy is used to break the intermolecular forces holding the particles together, rather than increasing the kinetic energy of the particles.
Similarly, during the process of condensation or freezing, a substance releases heat energy as it changes state. This released energy is used to form intermolecular forces and convert the substance from a gas to a liquid or a liquid to a solid. The temperature remains constant until the phase transition is complete.
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Forensic Entomology
Forensic Entomology
The study of the life cycle of insects that feed on the flesh to the dead, to establish time of death and occasionally identify chemicals present in a person's body at the time of death.
Time since death
Arrive a few hours after a death and are active through decomposition process. They feed on larvae and other insects rather than the corpse itself.
Larvae that feed on human excrement and remains, and are found late in the decomposition process.
Forensic Entomology is the study of life cycles of insects that feed on the flesh of dead, to establish time of death and occasionally identify chemicals present in a person's body at time of death
What is meant by Forensic Entomology?The scientific study of the colonization of dead body by arthropods is called forensic entomology .
Larvae and adults feed on dry skin and hairs of corpse and arrive later in decomposition process : Carpet Beetles
Time since death : postmortem Interval.
Rove Beetles : Arrive a few hours after death and are active throughout decomposition process. They feed on larvae and other insects rather than the corpse itself.
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Fill in the blank. Consider the inverse square law: When light leaves a light bulb, it spreads out over more and more space as it goes. This makes the light thinner, with less and less light present the further from the light bulb we look. If we stand looking at a light bulb and see how bright it is, then move to be four times farther away from the light bulb, the light from the bulb will look ____________ less bright. Group of answer choices
Answer:
Explanation:
Intensity of light is inversely proportional to distance from source
I ∝ 1 /r² where I is intensity and r is distance from source . If I₁ and I₂ be intensity at distance r₁ and r₂ .
I₁ /I₂ = r₂² /r₁²
If r₂ = 4r₁ ( given )
I₁ / I₂ = (4r₁ )² / r₁²
= 16 r₁² / r₁²
I₁ / I₂ = 16
I₂ = I₁ / 16
So intensity will become 16 times less bright .
"16 times " is the answer .
A ball is tossed up into the air with an initial speed of 5.0. How long does it take to return to the person's hand
Answer:
Explanation:
\(y(t) = 5t-5t^2\)
When y(t) = 0, the ball is on the hand.
\(0=5t-5t^2\\0=5t(1-t)\\t=0,1\)
It takes 1 second.
There are several different possibilities.
==> If the 5.0 means 5 miles per hour, that's 2.24 meters per second, up.
The acceleration of gravity is 9.8 m/s down, so the ball stops, turns around, and starts falling in (2.24/9.8) = 0.229 second. Then, after is starts to fall, it takes the same amount of time to the person's hand.
Total time = 0.457 second.
==> If the 5.0 means 5 meters per second, up . . .
The acceleration of gravity is 9.8 m/s down, so the ball stops, turns around, and starts falling in (5.0/9.8) = 0.51 second. Then, after is starts to fall, it takes the same amount of time to the person's hand.
Total time = 1.02 second.
==> If the 5.0 means 5 km/minute, that's about 83.33 meters per second, up.
The acceleration of gravity is 9.8 m/s down, so the ball stops, turns around, and starts falling in (83.33/9.8) = 8.503 seconds. Then, after is starts to fall, it takes the same amount of time to the person's hand.
Total time = 17.01 seconds.
==> If the 5.0 means 5 furlongs per fortnight, that's about 0.00083 meters per second, up.
The acceleration of gravity is 9.8 m/s down, so the ball stops, turns around, and starts falling in (0.00083/9.8) = 0.000085 second. Then, after is starts to fall, it takes the same amount of time to the person's hand.
Total time = 0.00017 second.
This is why all of your numbers always need their units.
The box shown on the rough ramp above is sliding up the ramp. calculate the acceleration of the box
We are given that a block is sliding up an incline. A diagram of the situation is given as follows:
To determine the acceleration we will add the forces parallel to the ramp, we will call this direction the x-direction:
\(\Sigma F_x=-mg_x-F_f\)Where:
\(\begin{gathered} m=\text{ mass} \\ g=\text{ acceleration of gravity} \\ mg_{}=\text{ weight} \\ mg_x=\text{x-component of the} \\ F_f=\text{ force of friction} \end{gathered}\)Now we determine the x-component of the weight by using the trigonometric function sine:
\(\sin 40=\frac{mg_x}{mg}\)Now we multiply both sides by "mg":
\(mg\sin 40=mg_x\)Now we substitute this value in the sum of forces:
\(\Sigma F_x=-mg_{}\sin 40-F_f\)Now, to determine the force of friction we will use the following formula:
\(F_f=\mu N\)Where:
\(N=\text{ normal force}\)To determine the normal force we add the forces in the direction perpendicular to the ramp, we will call this direction the y-direction:
\(\Sigma F_y=N-mg_y\)Where:
\(mg_y=y-\text{component of the weight}\)Now, since there is no movement in the y-direction, the sum of forces is equal to zero:
\(N-mg_y=0\)Now we solve for the normal force:
\(N=mg_y\)Now we calculate the y-component of the weight using the trigonometric function cosine:
\(N=mg\cos 40\)Now we substitute this value in the expression for the friction force:
\(F_f=\mu mg\cos 40\)Now we substitute this value in the sum of forces in the x-direction:
\(\Sigma F_x=-mg_{}\sin 40-\mu mg\cos 40\)Now, since the sum of forces is equivalent to the product of the mass by the acceleration we have:
\(-mg_{}\sin 40-\mu mg\cos 40=ma\)We can take "-mg" as a common factor on the left side:
\(-mg(_{}\sin 40+\mu\cos 40)=ma\)We can cancel out the mass:
\(-g(_{}\sin 40+\mu\cos 40)=a\)Now we substitue the values:
\(-(9.8\frac{m}{s^2})(\sin 40+0.2\cos 40)=a\)Now we solve the operations:
\(-7.8\frac{m}{s^2}=a\)Therefore, the acceleration is -7.8 meters per second squared.
Refer to an imaginary "frictionless" piston. This piston is capable of moving up or down within the container's walls without any resistance (assume there is no friction between the walls of the container and the piston). In addition, there is a complete seal around the piston, which prevents any particles from getting into or out of the container. In figure (a), the piston is at a resting position, with the pressure inside equal to the pressure outside. The temperatures inside and outside are identical. In figure (b), the piston is drawn out so that the volume inside the container is twice as great as in figure (a). Describe what would happen to the pressure inside the containerand explain why this would occur.
ANSWER and EXPLANATION
To explain this, we have to apply Boyle's law which states that:
This implies that as pressure increases, volume decreases, and as volume increases pressure decreases.
It is given mathematically as:
\(\begin{gathered} P\propto\frac{1}{V} \\ \\ P=\frac{k}{V} \\ \\ P_1V_1=P_2V_2 \end{gathered}\)where k = constant of proportionality
P = pressure
V = volume
In the given figures, the piston is drawn out so that the volume inside the container is doubled.
From the equation, if V2 is twice as much as V1, it implies that:
\(P_1V_1=P_2(2V_1)\)Solve for P2 in the equation:
\(\begin{gathered} P_2=\frac{P_1V_1}{2V_1} \\ \\ P_2=\frac{P_1}{2} \end{gathered}\)Therefore, as we see from the solution above, the pressure inside the container will be half of what it originally was.
Hence, if the volume inside the container is twice as great as before, the pressure is halved.