The following is required to have a successful collision: ii. A collision of the appropriate orientation must occur, iii. Transfer of energy must occur in a collision such that the molecule has energy equal to or greater than the activation energy, v. Formation of products.
What is collision?Collision is when two objects come in contact with one another and experience a force as a result. This force can be a direct result of the objects hitting each other, or it can be the result of the objects exerting a force on one another in order to move away. In either case, the objects experience a momentary change in their respective velocities.
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A 4.0 kg mass is released from rest at the top of a frictionless ramp 2.0 m above ground. It slides down the ramp to a level, horizontal portion of frictionless track and then collides with a stationary 8.0 kg mass. Immediately after the collision, the larger mass has a velocity v_l = +3.5 m/s (i.e., heading to the right)
The velocity of the smaller mass just after the collision is B) +0.7 m/s.
To calculate the velocity of the smaller mass after the collision:
Use the law of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision: (m1 * v1) + (m2 * v2) = (m1 * v1') + (m2 * v2')
Substitute in the known values: (4.0 kg * 0 m/s) + (8.0 kg * 0 m/s) = (4.0 kg * v4) + (8.0 kg * (vg + 3.5 m/s))
Solve for the velocity of the smaller mass (v4): v4 = (8.0 kg * (vg + 3.5 m/s)) / 4.0 kg
Substitute in the value for the velocity of the larger mass (vg) which is not given in the question: v4 = (8.0 kg * (0 m/s + 3.5 m/s)) / 4.0 kg
Solve for the velocity of the smaller mass (v4): v4 = (8.0 kg * 3.5 m/s) / 4.0 kg
Simplify the calculation: v4 = 2.8 m/s / 4.0 kg
Divide the final value by the mass of the smaller object: v4 = 0.7 m/s
So the velocity of the smaller mass just after the collision is 0.7 m/s.
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The density of a fluid is given by the empirical equation rho = 70.5exp(8.7 times 10^-7P) A. Where p is density (lbm/ft^3) and P is pressure (lbf/in^2). (1 N=0.2250 Ibf; I g=0.002205 Ibm; 1 ft=12in=30.48cm) ? B. What are the units of 70.5 and 8.27 times 10^7? C. Calculate the density in g/cm^3 for a pressure of 9.0 times 10^6 N/m^2. Derive a formula for p (g/cm) as a function of P (N/m^2).
This equation can be used to calculate the density in g/cm^3 for any given pressure in N/m^2.
What is density?Density is a measure of mass per unit of volume, usually expressed in kilograms per cubic meter. It is an important physical property of matter and is used to compare the relative densities of different substances. Density is also used to calculate the buoyancy of objects in a fluid. The density of a substance is affected by temperature and pressure. In general, substances with higher densities tend to be more compact and therefore more dense.
A. The units of 70.5 and 8.7 times 10^7 are lbm/ft^3 and lbf/in^2 respectively.
B. To calculate the density in g/cm^3, we must convert the pressure from N/m^2 to lbf/in^2 by multiplying it by 0.2250. Thus, we have 9.0 times 10^6 N/m^2 * 0.2250 = 2.025 times 10^7 lbf/in^2. Plugging this into the equation, we have rho = 70.5exp(8.7 times 10^-7 * 2.025 times 10^7) = 1176.6 g/cm^3.
To derive a formula for p (g/cm) as a function of P (N/m^2), we can simply rearrange the equation to solve for p. Thus, we have p = 70.5exp(8.7 times 10^-7 * P) / 0.002205. This equation can be used to calculate the density in g/cm^3 for any given pressure in N/m^2.
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which of the following word is the correct option for below question: component, points, parts. when solving conservation of motion problems in two dimensions it is important to break te velocity of each objet into x and y
When solving conservation of motion problems in two dimensions, it is important to break the velocity of each object into x and y component.
What is velocity?Velocity is a vector representation of an object's or particle's displacement with respect to time. The meter per second (m/s) is the standard unit of velocity magnitude (also known as speed). Alternatively, velocity magnitude can be expressed in centimeters per second (cm/s). The direction of movement of the body or item is defined by velocity. Speed is fundamentally a scalar number. Velocity is, in essence, a vector quantity. It is the pace at which distance changes. It is the displacement rate of change. Simply put, velocity is the rate at which something travels in a certain direction. For example, the speed of a car driving north on a highway or the speed of a rocket after launch.
Here,
When addressing conservation of motion issues in two dimensions, it is necessary to divide each object's velocity into x and y components.
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What effect does increasing the moon’s mass have on the earth?
Answer:
Explanation:
If the moon doubled in mass, that means that the Earth will not experience a total solar eclipse like today also, if it doubled in mass, tide waves would increase in size, as the moon would be bigger and would have a bigger gravitational pull
Calculate the increase in length of a 40 cm brass rod that is heated from 30 ° C to 50 ° C ( linear expansion of Brass is 1.9 x 10³8¹¹ )
a. 0.015 cm b.0.051 cm c.1.9 cm d. 15.20 cm
The solution for the increase in length of a 40 cm brass rod that is heated from 30 ° C to 50 ° C ( linear expansion of Brass is 1.9 x 10³8¹¹ ) is
0.051 cm. In this case Option B is correct.
Linear Expansion Theory: What Is It?
The linear expansion theory, which is used in this question, states that when an object is heated or cooled, its expansion or contraction will be proportional to its original length and the temperature change.
First, determine Brass' linear expansion (1.9 x 108 11).
Step 2: Determine how long the 40 cm brass rod will grow. Increase in length equals (Brass linear expansion) times (Temperature change) times (Rod length).
(1.9 x 108 11) x (20°C) x (40 cm) length increase
Step 3: Determine the lengthening.
lengthening equals 0.051 cm
Response: 0.051 cm
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Tension force has units of ________. Check all that apply.
Answer:
Newton (N)
Explanation:
scallops use muscles to close their shells. opening the shell is another story--muscles can only pull, they can't push. instead of muscles, the shell is opened by a spring, a pad of a very elastic biological material called abductin. when the shell closes, the pad compresses; a restoring force then pushes the shell back open. the energy to open the shell comes from the elastic energy that was stored when the shell was closed. (figure 1) shows smoothed data for the restoring force of an abductin pad versus the compression. when the shell closes, the pad compresses by 0.15 mm. How much elastic potential energy is stored?
10J elastic potential energy is stored.
The mechanical potential energy stored in the configuration of a material or a physical system during elastic deformation as a result of work applied to it is known as elastic energy. When objects are momentarily compressed, stretched, or otherwise distorted, elastic energy is produced. Solid body and material mechanics formalisms are essentially produced via elasticity theory. Calculations of mechanical equilibrium positions using the elastic potential energy equation. The energy is potential because when the object is permitted to return to its original shape (reformation) by its elasticity, it will change into other forms of energy, such as kinetic energy and sound energy.
compression = expansion
force=2.5N
K= [tex]\frac{F}{x}[/tex]=[tex]\frac{2.5N}{0.2\times10^{-3} }=1.25\times10^4 N/m[/tex]
compression=0.15mm
Energy= [tex]\frac{1}{2}Kx^{2}[/tex]
Energy= [tex]\frac{1}{2}1.25\times 10^{-4}( 2.25\times10^{-10})J[/tex]
Energy=[tex]1.40625\times 10^{-4}\\[/tex]joules
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The Kingda Ka roller coaster in New Jersey is the world's tallest ride of its kind. As the passenger cars are launched from rest at the start, they are accelerated uniformly to a speed of 57 m/s (128 mph) in just 3.5 s. (Assume the cars are launched in the positive horizontal direction. Indicate the direction with the sign of your answer where appropriate.)
(a) What is the acceleration experienced by passengers on this ride in m/s2?
m/s2
What is the acceleration experienced by passengers on this ride in g's?
g
(b) If a certain passenger has a mass of 68 kg, what is the force in newtons that acts on him during the launch phase of this ride?
N
What is the force in pounds that acts on him during the launch phase of this ride?
lb
a) The acceleration is 16.3 m/s^2
b) The acceleration is 1.66 g
c) The force that acts is 666.4 N
d) The force in pounds is 149.8 pounds
What is the acceleration?We have to note that when we talk about the acceleration, we mean the change in the velocity of the object with respect to the time that is taken. In the case of the problem that we have here, we are told that the passenger cars are launched from rest at the start, they are accelerated uniformly to a speed of 57 m/s (128 mph) in just 3.5 s.
Note that;
v = u + at
v = final velocity]
u = initial velocity
t = time taken
a = acceleration
Then;
a = v - u/t
a = 57 - 0/3.5
a = 16.3 m/s^2
The acceleration in g's is 16.3 m/s^2/9.8 m/s^2 = 1.66 g
The force that acts on the passenger is; 68 Kg * 9.8 m/s^2 = 666.4 N
The weight in pounds of the passenger is 149.8 Pounds
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problem 1-45: the column is made of concrete having a density of 2.30 mg/m3 . at its top b it is subjected to an axial compressive force of 15 kn. determine the average normal stress in the column as a function of the distance z measured from its base.
The average normal stress in the column as a function of the distance z from its base is (237.68 - 21.43z) kPa or (237,684.54 - 21,431.12z) Pa.
The full question is in the attachment. There is a weight force that works in the concrete column. The formula w = mg
m = mass of the column (kg) g = the acceleration due to gravity (9.8 m/s²) w = the weight (N)The mass of the column is unknown but the density is known. The formula for density ρ = m ÷ V
m = ρV
ρ = the density = 2.30 Mg/m³ = 2,300 kg/m³ V = the volume of the column The volume of the tubular columnThe weight force
w = mg = ρVg = ρg × πr²h
w = 2,300 × 9.8 × 3.14 × 0.18² × (4 - z)
w = 2,293.13 (4 - z)
w = (9,172.52 - 2,293.13z) N
The column is in equilibrium then Newton's first law applies
The axially compressive force = F₁ = 15 kN = 15,000 N∑F = 0
N - F₁ - w = 0
N = F₁ + w
N = 15,000 + (9,172.52 - 2,293.13z)
N = (24,172.52 - 2,293.13z) Newton
The average normal stress can be calculated by the formula
σ = F/A
σ = the stress (Pascal) F = the force (N) A = the area of the baseσ = N ÷ A
σ = (24,172.52 - 2,293.13z) ÷ 0.1017
σ = (237,684.54 - 21,431.12z) Pascal
σ = (237.68 - 21.43z) kPa
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A constant net force, F net is applied to a cart with mass,m, causing an acceleration,a. If the mass of the cart is doubled, but the net force remains the same, what will the acceleration of the car be?
The acceleration of the car will be halved. Option A is the correct answer.
What is acceleration?This refers to the rate of change of velocity. It is the speed that is changing but not at all times. When an object moves in a circular path at a constant speed, it is still accelerating, because the direction of its velocity is changing.
Solving for the acceleration:
The acceleration of the car will be halved. This is because the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. Therefore, if the mass of the cart is doubled and the net force remains the same, the acceleration will be halved:
(a = Fnet/m).
The equation is :
F=ma
If we keep force constant and mass doubles, acceleration will be halved.
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some psychologists believe that eating disorders representative fence against unconscious conflicts related to sexual development. These psychologists have adopted a _____ approach to eating disorders.
Some psychologists believe that eating disorders represent a defense against unconscious conflicts related to sexual development. These psychologists have adopted a Psychoanalytic approach to eating disorders.
What is a Psychoanalytic approach?A psychoanalytic approach is based on the idea that our unconscious thoughts, feelings, and motivations can have a powerful influence on our behavior by focusing on helping individuals to gain insight into their unconscious processes, recognize and resolve conflicts, and modify their behavior.
Therefore, with this data, we can see that a Psychoanalytic approach is based on unconscious mental processes to develop a cure.
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A baseball is hit almost straight up into the air with a speed of 22 m/s. Estimate (a) how high it goes, and (b) how long it is in the air. (c) What factors make this an estimate ?
(a) The ball goes up to the height of 31.89 m. (b) The ball stays for 5.1 s in the air. (c) The acceleration due to gravity and wind resistance can affect the estimation.
What is Acceleration due to gravity?Acceleration owing to gravity is the term used to describe the rate at which a body's velocity changes as a result of the earth's gravitational pull. In general, it is assumed that the acceleration caused by gravity is in the downward direction.
The acceleration caused by gravity has been calculated as, however as it changes from location to location, it may have an impact on the estimation.
You may have thought that the wind has no impact, but it can actually generate drag and even cause the ball to shift course.
Therefore, (a) The ball goes up to the height of 31.89 m. (b) The ball stays for 5.1 s in the air. (c) The acceleration due to gravity and wind resistance can affect the estimation.
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In video 1 for Chapter 17, how does the fringe spacing change when the distance between the slits, d, is increased?
The fringes get farther apart.
The fringe spacing stays the same.
The fringes get closer together.
It depends on how wide the slits are.
As the gap between the slits, d, is widened, the fringe spacing changes, becoming more pronounced.
How would you define distance in plain English?Distance is an object's overall motion in a directionless fashion. Depending of the starting or terminating point, distance can be referred to as the amount of territory an element has travelled.
The purpose of distance calculationWe can find out an object's actual size by knowing how far away it is. The area an object occupies in space above us can be measured. Once we know how far away it is, we can calculate its true size. An thing appears smaller the further away it is.
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sort these stellar objects by their peak wavelength. not all the objects are on the interactive, so determine the trend first, then sort the objects. stellar objects (4 items) (drag and drop into the appropriate area) the sun, a g star with t
The stellar objects the sun a g star is with T= 5500k
Distance between the equivalent positions of two successive waves is known as the wavelength. Two points or particles that are in the same phase and have completed identical percentages of their periodic motion are referred to as "corresponding points." Wavelength is typically measured from crest to crest or from trough to trough in transverse waves (waves with points vibrating at right angles to the direction of their advance); from compression to compression or from rarefaction to rarefaction in longitudinal waves (waves with points vibrating in the same direction as their advance). The Greek symbol lambda (λ) is typically used to represent a wave's length. Wavelength is defined as the product of a wave train's frequency (f) and speed (v) in a medium.
The wavelength of the temperature inversely related to each other. Higher the temperature, lower will be its wavelength.
1. Highest (reddest) a brown dwarf with T=100k
___________________________________________
2. a K star with T=4400k
___________________________________________
3. the sun, a G star with T=5500k
___________________________________________
4.(lowest/bluest) an F star with T=7000k
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Some crosswalks timers are set in consideration that persons older than 65 walk at an average pace of 2.9 ft/sec. Describe how you determined your pace, or average walking speed, in feet per second, by a method of your choice. How does your pace compare to the average pace of persons older than 65?
You can determine the average walking speed by registering the distance covered by different people in the same group. My pace is higher than people older than 65.
How to determine the walking pace?You can determine your average walking pace by recording information about the distance you cover in feet and the second it takes you to cover that distance. Here is an example:
450 feet / 100 seconds = 4.5 feet per second
How does my pace compare to the average of persons older than 65?My pace is faster than the walking pace of someone who is 65.
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The speed of a pendulum is greatest (a) when the pendu- kinetic energy is a minimumb) when the pendu lum's acceleration is a maximum, (c) when the pendulum's potential energy is a minimumof the preceding
Answer:
Explanation:
b. when the pendulum's acceleration is a maximum.
The speed of a pendulum is greatest when the acceleration of the pendulum is at a maximum. This occurs when the pendulum is at the bottom of its swing, where the force of gravity is causing the greatest acceleration. At this point, the pendulum's kinetic energy is at a maximum and potential energy is at a minimum.
Two large parallel copper plates are 5.0 cm apart and have auniform electric field between them as depicted in Fig 22-48. Anelectron is released from the negative plate at the same time thata proton is released from the positive plate. Neglect the force ofthe particles on each other and find their distance from thepositive plate when they pass each other.
I made five attempts to include the digaram but to no avail.
The positive plate is on the left.
The negative plate is on the right.
The proton is released at the positive plate.
The electron is released at the negative plate.
The direction of the electric field is from the positive plate tothe negative plate.
Since the electric field is uniform, the proton and the electron will experience the same acceleration.
What is electric field?An electric field is a physical field generated by electric charges, such as the electrons in a conductor. It is an invisible force that can attract or repel other charged objects in its vicinity.
This means that their velocities will increase at the same rate. Therefore, when they pass each other, their distances from the positive plate will be the same.
The distance from the positive plate to the proton and electron when they pass each other is 5.0 cm. This is the same distance as the distance between the two plates.
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assuming that each cubic centimeter of water has a mass of exactly 1 g, find the mass of 1.87 cubic meter of water.
Assuming that each cubic centimeter of water has mass of exactly 1 g , then mass of 1.87 cubic meter of water is 1.87 kg.
What is mass?We define mass as measure of the amount of matter in a body. And SI unit of mass is Kilogram (kg) and the mass of a body does not change at any time.
As we know, mass = volume x density
where volume is given in cubic meter and density is given in g/cm^3
As water has a density of 1 g/cm^3 at 4 degree Celsius, this means that 1 cm^3 of water has a mass of 1 g.
So, mass = 1.87 m^3 x 1 g/cm^3 = 1.87 kg
Therefore, the mass of 1.87 cubic meter of water is 1.87 kg.
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A 21 g ball of clay traveling east at 3.2 m/s collides with a 32 g ball of clay traveling north at 2.1 m/s. What are the speed and the direction of the resulting 53 g ball of clay?
The resulting ball of clay after the collision is moving with a speed of 2.53 m/s in a direction between east and north.
To determine the speed and direction of the resulting 53 g ball of clay after the collision, we need to use the conservation of momentum principle.
Let us call the initial momentum of the first clay ball (21 g) "p1", and the initial momentum of the second clay ball (32 g) "p2". The final momentum of the resulting clay ball (53 g) will be "p3".
The initial momentum of the first clay ball can be calculated as p1 = m1 * v1 = 21 g * 3.2 m/s = 67.2 gm/s (going east)
The initial momentum of the second clay ball can be calculated as
p2 = m2 * v2 = 32 g * 2.1 m/s = 67.2 gm/s (going north)
So, the total initial momentum is p1 + p2 = 67.2 gm/s + 67.2 gm/s = 134.4 g*m/s
After the collision, the total momentum of the resulting clay ball is 134.4 gm/s, and its mass is 53 g. So, we can use the following equation to find its final velocity: p3 = m3 * v3 = 134.4 gm/s = 53 g * v3
So, the final velocity of the resulting clay ball is v3 = 134.4 g*m/s / 53 g = 2.53 m/s.
To find the direction of the resulting clay ball, we can use the vector addition of the initial velocities of both clay balls. The direction of the final velocity vector would be the angle formed between the sum of the vectors and the x-axis.
So, the final velocity vector of resulting clay ball is a vector sum of the initial velocities of both clay balls, and its direction would be somewhere between the east and north direction.
Therefore, the resulting ball of clay after the collision is moving with a speed of 2.53 m/s in a direction between east and north.
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which of the following forces is an example of a contact force
a) gravitational force
b) magnetic force
c) electric force
d) frictional force
Answer:
d) frictional force
Explanation:
What Is a Contact Force?
Contact force is the phrase used to describe a push/pull interaction that occurs when an object comes into contact with another object.
The only force where there is contact between two bodies in the answer choices is frictional force
Answer
d) frictional force
A bottle with a volume of 195 U. S. fluid gallons is filled at the rate of 1.7 g/min. (Water has a density of 1000 kg/m3, and 1 U.S. fluid gallon = 231 in.3.) How long does the filling take?
The time that have been taken by the liquid is 4.4 * 10^5 min.
How long does it take to be filled?The question that we have been asked here is about the rate of the filling of the bottle. We can see that we have been given the volume of the bottle clearly.
We know that the volume of the solution that we have is 195 U. S. fluid gallons or 0.74 m^3. Then we have that;
Density = mass/volume
mass = Density * volume
= 0.74 m^3 * 1000 Kg/m^3
= 740 Kg or 740000 g
Rate = mass/time
Time = mass/rate
Time = 740000 g/1.7 g/min.
= 4.4 * 10^5 min
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find the time-domain voltage over the capacitor using phasor domain techniques. the voltage and current source are both ac (cos) sources with frequency of 1mhz and with the amplitudes of 12 v and 20ma, respectively. assume that, r1
To find the time-domain voltage over the capacitor using phasor domain techniques, we need to first convert the circuit to the phasor domain by replacing the time-varying voltage and current sources with their phasor equivalents. The phasor equivalents of the voltage and current sources are:
V_s = 12 V * e^(j2pift)
I_s = 20mA * e^(j2pift)
where f is the frequency of the sources (1 MHz) and t is time.
The phasor voltage across the capacitor can be found using the following equation:
V_C = V_s - I_s * (R_1 + R_2 + j2pifL) - I_s * (1/(j2pifC))
Substituting in the values for the resistance and reactance of the circuit, we get:
V_C = 12 V * e^(j2pift) - 20mA * e^(j2pift) * (1000 Ohm + 2000 Ohm + j2pi10^620e-6 H) - 20mA * e^(j2pift) * (1/(j2pi10^6200e-12 F))
Simplifying, we get:
V_C = 12 V * e^(j2pift) - 20mA * e^(j2pift) * (3000 Ohm + j40pi) - 20mA * e^(j2pift) * (5e5 Ohm)
So, the phasor voltage across the capacitor is V_C = 12 V * e^(j2pift) - 0.02 A * e^(j2pift) * (3000 Ohm + j40pi) - 0.02 A * e^(j2pift) * (5e5 Ohm)
Finally, to find the time-domain voltage over the capacitor, we need to take the inverse Fourier transform of the phasor voltage. This can be done using the following equation:
v_c(t) = real (V_C * e^(-j2pift))
Substituting in the value for V_C, we get:
v_c(t) = real (12 V * e^(j2pift) - 0.02 A * e^(j2pift) * (3000 Ohm + j40pi) - 0.02 A * e^(j2pift) * (5e5 Ohm)
Complete question:
Find the time-domain voltage over the capacitor using phasor domain techniques. The voltage and current source are both AC (sine) sources with frequency of 1MHz and with the amplitudes of 12 V and 20mA, respectively. Assume that, R_1 = 1 k Ohm, R_2 = 2k Ohm, C = 200pF, and L = 20mu H.
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An object is thrown straight up. Which of the following is true about
the sign of work
done by the gravitational force while the object moves up and then
down?
A.Work is positive on the way up, work is positive on the way down
B. Work is negative on the way up, work is negative on the way down
C.Work is negative on the way up, work is positive on the way down
D.Work is positive on the way up, work is negative on the way down E.
Work is zero the way up, work is zero on tâ
The correct option is C. Sign of Work is negative on way up and negative on way down due to gravitational force.
The definition of work is the energy that is either added to or subtracted from something by applying force along a displacement. For a constant force acting in the same direction as the motion, the work is simply equal to the product of the force's magnitude and the distance travelled.
A thrown object's acceleration due to gravity will cause negatively deaccelerate when we throw it vertically upwards.
We represented deacceleration by a (-) sign.
Thus, we may conclude that any work completed when an object is thrown upwards is negative since it defies gravity.
Now, g is accelerating force as it movies in direction of gravity when object comes downwards to earth. Work done when object moves down is positive.
Consequently, the best option will be option (C)
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from the following statements about mechanical waves, identify those that are true for transverse mechanical waves only, those that are true for longitudinal mechanical waves only, and those that are true for both types of waves.
The particles in a medium vibrate perpendicular to the wave's path when it passes through it, indicating that the wave is just a transverse mechanical wave.
The only type of wave that can pass through a medium is a longitudinal mechanical wave, which causes the particles within the medium to vibrate in a direction parallel to the wave's path.
The speed at which a wave moves across a medium depends on an inertial characteristic of that medium. This is true for both transverse and longitudinal mechanical waves.
A transverse wave is a form of wave in which the wave's velocity is always perpendicular to the particle positions in the medium. To see an example, move one end of a Slinky (whose other end is fixed) to the left and right of the Slinky as opposed to back and forth. Waves on the water's surface, for instance.
In physics, a mechanical wave is a wave that incorporates matter oscillation and transmits energy across a medium. Despite the fact that waves can travel long distances, the transmission medium, or the substance, has a limited range. Example - Sound waves
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A marathoner is trying to improve her skill at pacing herself during her races Select the best technology tool available to help provide feedback to the runner so that
she doesn't "burnout" too fast at the beginning of this grueling competition
O Pedometer
O Spreadsheet checklist
O Stopwatch
O Digital pictures
Answer: Stopwatch
Explanation: A stopwatch would be the best technology tool available to help provide feedback to the runner so that she doesn't "burn out" too fast at the beginning of a gruelling competition. A stopwatch can help the runner measure her pace and ensure that she runs at a steady, consistent pace throughout the race. Additionally, a stopwatch can be used to track the runner's split times and provide her with detailed feedback on her performance.
A space probe is launched from Earth headed for deep space. At a distance of 10,000 miles from Earth's center, the gravitational force on it is 264 lb. What is the size of the force when it is at each of the following distances from Earth's center?
(a) 20,000 miles
lb
(b) 30,000 miles
lb
(c) 100,000 miles
lb
The size of the force when it is at 20,000 miles distances from Earth's center is 66 lb.
The size of the force when it is at 30,000 miles distances from Earth's center is 29.33 lb.
The size of the force when it is at 100,000 miles distances from Earth's center is 2.64 lb.
What is gravitational force?
The force of attraction between any two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them, according to Newton's universal law of gravitation.
(a) the size of the force when it is at 20,000 miles distances from Earth's center = (264)/(2²) lb = 66 lb.
(b) the size of the force when it is at 20,000 miles distances from Earth's center = (264)/(3²) lb = 29.33 lb.
(c) the size of the force when it is at 100,000 miles distances from Earth's center = (264)/(10²) lb = 2.64 lb.
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Landon and Jocelyn are partners in pair figure skating. Last weekend, they perfected the death spiral element for inclusion in their upcoming competition. During this maneuver, Landon holds Jocelyn by the hand and swings her in a circle while she maintains her blades on the ice, stretched out in a nearly horizontal orientation. Determine the net force that must be applied to Jocelyn (m = 47.3 kg) if her center of mass rotates in a circle with a radius of 0.915 m once every 1.13 seconds.
The net force that must be applied to Jocelyn is 139 Newton.
How to calculate the net force?The net force acting on Jocelyn during the death spiral can be determined using the equation:
F = m * a
where F is the net force, m is her mass (47.3 kg), and a is her centripetal acceleration.
To find the centripetal acceleration, we can use the equation:
a = v^2 / r
where v is her velocity and r is the radius of rotation.
We know that Jocelyn completes one rotation every 1.13 seconds, so we can calculate her velocity:
v = 2 * pi * r / T
where T is the time for one rotation
Plugging in the known values:
v = 2 * pi * 0.915 m / 1.13 s
v = 5.09
Now we can substitute the value of v into the centripetal acceleration equation:
a = v^2 / r
a = 5.09² / 0.915
a = 28.3
F = ma
F = 47.3 × 28.3
F = 1339 Newton
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a bullet is accelerated down the barrel of a gun. the average force exerted on a 0.020 kg bullet to accelerate it to a speed of 500.0 m/s in a time of 2.00 ms (milliseconds) is
The average force is then F = ma is 5,000 kg m/s2 = 5,000 N.
What is average force?Average force is the mean force of a set of forces. It is used to measure the average magnitude of a force over a period of time or over multiple forces. It is calculated by dividing the sum of all forces by the number of forces.
The average force exerted on the bullet is calculated using Newton's second law, F = ma. The acceleration of the bullet can be calculated by dividing the change in velocity (500.0 m/s) by the time interval (2.00 ms).
a = Δv/Δt
a = 500.0 m/s / 2.00 ms = 250,000 m/s2
The average force is then F = ma = (0.020 kg)(250,000 m/s2) = 5,000 kg m/s2 = 5,000 N.
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the fraction of ice which is submerged in water only depends on the density of the ice and the water. for this problem, assume the density of ice is 928.5 kg/m3.
0.917 fraction of ice which is submerged in water only depends on the density of the ice and the water.
What is density?The density of a material is its mass per unit volume. The most common sign for density is, however the Latin letter D can also be used. The density of a substance is the measure of how densely it is packed together. It is expressed as mass per unit volume. Symbol for density: D or Formula for Density: = m/V, where is the density, m is the object's mass, and V is the object's volume. The density of something describes how compact or dense it is. Let's say you have two boxes, one huge and one tiny. They both, however, weigh the same. That means the small box has a higher density than the large box. Density also tells how concentrated or crowded something is.
Here,
The density of the ice and the water have no effect on the 0.917 proportion of ice that is submerged in water.
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An object attached to a spring vibrates with simple harmonic motion as described by the figure below.
For this motion, find the following.
(a) the amplitude
(b) the period
(c) the angular frequency
(d) the maximum speed
(e) the maximum acceleration
(f) an equation for its position x in terms of a sine function (Do this on paper. Your instructor may ask you to turn in this work.)
The graph provided is a displacement-time graph. The object's displacement is shown on the x-axis, while its travel time is shown on the y-axis.
The largest displacement that an object may make is known as its amplitude. The maximum displacement made by the object is 2 cm.
As a result, the object has an amplitude of 2 cm according to the definition of amplitude.
The amplitude of the object depends on the displacement made by the object. The maximum displacement is made when the object moves to an extreme position in an oscillation.
An object moves from a mean position to an extreme position in a straightforward harmonic motion. One oscillation or cycle is said to be complete when the object travels from the mean position to the extreme position and returns to the mean position.
The displacements are shown on the graph as positive when it moves to the extreme position and negative when it moves back from the extreme position.
According to the presented graph, it takes 4 seconds to complete one oscillation or cycle.
As a result, the time period is 4 seconds according to the definition of time period. Therefore, the time period as ω = 2π/T.
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