The drawing shows an edge-on view of two planar surfaces that intersect and are mutually perpendicular. Surface (1) has an area of 1.70 m².
What do you know about Surface?Surface is a line of tablet computers developed by Microsoft and sold under their brand. Surface tablets have a 10.6-inch wide touch screen display and come with USB support, dual Wi-Fi antennae, a built-in kickstand to make the tablet stand up by itself and an optional keyboard that doubles as the tablet's cover.
What does Surface mean in tech?A surface computer is a computer which interacts with users through an ordinary object instead of through monitor and keyboard. Commands are input through the use of bare hands by touching or dragging the surface .
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PART ONE
The figure shows a claw hammer as it pulls a
nail out of a horizontal board.
If a force of magnitude 99.9 N is exerted horizontally as shown, find the force exerted by the hammer claws on the nail. (Assume that the force the hammer exerts on the nail is parallel to the nail).
Answer in units of N.
PART TWO
Find the force exerted by the surface on the point of contact with the hammer head. Assume that the force the hammer exerts on the nail is parallel to the nail.
Answer in units of N.
(1) The force exerted by the hammer claws on the nail is 57.3 N.
(2) The force exerted by the surface on the point of contact with the hammer head is 81.83 N.
What is the force exerted by the hammer claws on the nail?The force exerted by the hammer claws on the nail is calculated as follows;
Fy = Fn sinθ
where;
θ is the angle of inclination of the hammerFy = 99.9 N x sin (35)
Fy = 57.3 N
The force exerted by the surface on the point of contact with the hammer head is calculated as follows;
Fx = Fn x cosθ
Fx = 99.9 N x cos (35)
Fx = 81.83 N
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PART ONE
A square plate is produced by welding together four smaller square plates, each of side a. The weight of each of the four plates is shown in the figure.
Find the x-coordinate of the center of gravity (as a multiple of a).
Answer in units of a.
PART TWO
Find the y-coordinate of the center of gravity (as a multiple of a).
Answer in units of a.
(a) The x coordinate of the center of the gravity is 1.48 a
(b) The y coordinate of the center of the gravity is 1.33 a.
What is the direction of the center of the gravity?
The direction of the weights of the four square plates is calculated as follows;
θ = arc tan ( dy / dx )
where;
dy is the displacement in vertical directiondx is the displacement in the horizontal directiondy = 2a
dx = 2a
θ = arc tan ( dy / dx )
θ = arc tan ( 2a / 2a )
θ = arc tan ( 1 )
θ = 45⁰
The x coordinate of the center of the gravity is calculated as follows;
x = ( m₁x₁ + m₂x₂ ) / ( m₁ + m₂ )
x = ( (90 + 50)a + (40 + 90)2a ) / ( 90+50 + 40 + 90 )
x = (140a + 130(2a) ) / ( 140 + 130 )
x = (140a + 260a ) / (270)
x = 1.48 a
The y coordinate of the center of the gravity is calculated as follows;
y = ( m₁y₁ + m₂y₂ ) / ( m₁ + m₂ )
y = ((90 + 90)a + (50 + 40)2a ) / (90+90 + 50+40 )
y = (180a + 90(2a) ) / (180 + 90)
y = (180a + 180a) / (270)
y = (360a) / ( 270)
y = 1.33 a
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conservation of momentum: a small car meshes with a large truck in a head-on collision. which of the following statements concerning the magnitude of the momentum change during the collision is correct? (there could be more than one correct choice.)
The truck and the tiny car both experience the same amount of momentum difference.
What is the definition of momentum in physics?
whenever a person is struck in the face by a ball that was thrown at him. It demonstrates how challenging it might be to change the course of events. A baseball is swooping in the air. A large truck is moving. This kind of firearm discharged a bullet.
In what situations does momentum actually matter?
Momentum is a property of almost all motion-related activities. It is a cornerstone of physics. In sports, the word "momentum" is frequently used. A side that has momentum is therefore moving and will require effort to stop.
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indicate whether the following statements are true or false. In each case give a reason for your answer. If W ⊂ Rn is a subspace and v ∈ Rn, then prW (v) is the least-squares approximation to v by a vector in W except when prW (v) = 0..
A. True
B. False
hanging spring when a 0.30 kg mass is suspended from a massless spring, the spring stretches a distance of 2.0 cm. let 2.0 cm be the rest position for the mass-spring system. the mass is then pulled down an additional distance of 1.5 cm and released. results for question 7. 7 1.5 / 1.5 points calculate the period of resulting oscillation in si units. correct answer: 0.284 results for question 8. 8 0 / 1.5 points calculate the total mechanical energy of the system in si units. incorrect answer: 166
the total mechanical energy of the system is: 0.09187 Joule
What is spring constant?"spring constant" (plural: "spring constants") a property of a spring that is determined by the force acting on the spring to the displacement it produces. The stiffness of the spring is quantified by the spring constant, k. For various materials and springs, it varies. The spring becomes stiffer and more challenging to stretch as the spring constant increases.
Given that,
mass (m) = 0.30 kg
distance (x) = 2.0 cm. = 2 × 10⁻² m
Thus, for balancing condition,
kx = mg
or, k = mg /x
or, k = (0.30 × 10) / (2 × 10⁻²)
or, k = 150 N/m
So, the value of spring constant is 150 N/m
Next, time period (T) = 2π √(m /k)
or, T = 2π √(0.30 / 150)
or, T = 0.2808 sec
Total stretches in spring constant = 2 cm + 1.5 cm = 3.5 cm
Total mechanical energy = 1/2 k x²
Total mechanical energy = 1/2 × (150) × (2 × 10⁻²)²
Total mechanical energy = 0.09187 Joule
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The scalar product of the vectors A=3i+4j-5k and B=-i+j-2k
The scalar product of the vectors A = 3i + 4j - 5k and B = -I + j - 2k is -9.
The scalar product (also known as the dot product) of two vectors is a scalar quantity that can be calculated by multiplying the magnitudes of the two vectors and the cosine of the angle between them. The formula to calculate the scalar product of two vectors A and B is:
A.B = |A| |B| cos(theta)
To find the scalar product of two vectors we can also use the following formula:
A.B = (A.i) (B.i) + (A.j) (B.j) + (A.k) (B.k)
where A.i, A.j, A.k, B.i, B.j, B.k are the projections of vectors A and B on the i, j, and k axis respectively.
So, in this case, we have:
following A = 3i + 4j - 5k and B = -i + j - 2k
A.B = (3)(-1) + (4)(1) + (-5)(-2) = -3 + 4 - 10 = -9
Therefore, the scalar product of the vectors A = 3i + 4j - 5k and B = -I + j - 2k is -9.
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A car accelerates uniformly from rest and reaches a speed of 33.8 m/s in 4.7s the diameter of the tire is 64.6 cm find the number of revolutions the tire makes during this motion
The tire makes approximately 280.57 revolutions during this motion.
What are the revolutions?Generally, To find the number of revolutions the tire makes during this motion, we first need to find the distance traveled by the car.
Distance = Initial velocity x time + (1/2) x acceleration x time^2
Since the car starts at rest, the initial velocity is 0 m/s.
The acceleration is uniform, so we can use the formula:
Final velocity = Initial velocity + acceleration x time
In this case, the final velocity is 33.8 m/s, and the time is 4.7s.
So, acceleration = (33.8 m/s - 0 m/s) / 4.7s
= 7.19 m/s^2
Now we can use this value of acceleration to find the distance traveled:
Distance = 0 m/s x 4.7s + (1/2) x 7.19 m/s^2 x (4.7s)^2
= 570.98 m
To find the number of revolutions of the tire, we divide the distance traveled by the circumference of the tire.
The circumference of the tire is equal to the diameter x pi.
Circumference = 64.6 cm x 3.14
= 203.5 cm
Number of revolutions = Distance / Circumference
= 570.98m / (203.5 cm)
=280.57
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figure 21-42 shows a long, nonconducting, massless rod of length l, pivoted at its center and balanced with a block of weight w at a distance x from the left end. at the left and right ends of the rod are attached small conducting spheres with positive charges q and 2q, respectively. a distance h directly beneath each of these spheres is a fixed sphere with positive charge q. (a) find the distance x when the rod is horizontal and balanced
Let the distance of weight W from the bearing is x3,
Then as we can see weight W is trying to give a clockwise rotation around the bearing similarly the charge +q is also applying the same clockwise torque because of the repulsion from the charged sphere beneath it.
But +2q charge torque is in a counter-clockwise direction. thus to make the rod balanced torque from weight W and +q charge must be balanced by the torque by +2q charge.
Let F and F1 be the force on +q and +2q respectively because of the fixed +Q charge.
as, F= kq[tex]\frac{Q}{h^2}[/tex] and F1= 2kq[tex]\frac{Q}{h^2}[/tex] =2F
as for the balance of the rod
FL/2+ Wx3 = 2FL/2
Wx3= FL/2
x3 = kqQ[tex]\frac{L}{2Wh^2}[/tex]
x= [tex]\frac{L}{3} +x3[/tex]
x= [tex]\frac{L}{2} * (kq\frac{Q}{Wh^2} +1)[/tex]
so put the weight above x to balance the rod.
Maximum such notions of distance, both physical and metaphorical, are formalized in arithmetic the use of the perception of a metric place.inside the social sciences, distance can test with a qualitative size of separation, along with social distance or psychological distance.
Distance is a numerical or every so often qualitative dimension of how a long way aside gadgets or points are. In physics or regular utilization, the space may seek advice from a physical period or an estimation primarily based on different criteria (e.g. " counties over"). due to the fact spatial cognition is a wealthy source of conceptual metaphors in human thought, the time period is also often used metaphorically to mean a measurement of the quantity of distinction between similar objects (which includes statistical distance between possibility distributions or edit distance among strings of text) or a degree of separation (as exemplified by using the gap between human beings in a social community).
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You are handed an apple that has a mass of 102g. To get a better idea of what different pressures feel like, you rig up several systems where the force of the apple is distributed over objects of different size. a) What is the weight of this apple? (in units of N and lbf) b) You stick a square-ended toothpick into the apple and balance it on your finger. What is the pressure of the apple (in units of Pa, psi, and atm) that you feel on your finger? c) You cut the apple up into slices and place them on your hand. What is the pressure of the apple on your hand (in units of Pa, psi, and atm)? d) You smash the apple into applesauce and spread it over a table. What is the pressure of the applesauce on the table (in units of Pa, psi, and atm)?
a) 9.80 N b) 0.0059 atm c) P = (9.80 N) / (total area of slices) d) P = (9.80 N) / (total area of applesauce)
What is pressure of applesauce?a) The weight of an object is equal to its mass multiplied by the acceleration due to gravity. On Earth, the acceleration due to gravity is approximately 9.81 m/s^2. So the weight of the apple is:Weight = (102 g) * (9.81 m/s^2) = 1004.82 g * 9.81 m/s^2 = 9.80 Nb) To find the pressure on your finger when the apple is balanced on a toothpick, we can use the formula P = F/A, where P is pressure, F is force, and A is area. The force of the apple is its weight (9.80 N) and the area of contact on your finger is the cross-sectional area of the toothpick. So, the pressure on your finger is:P = (9.80 N) / (pi * (0.00625 cm/2)^2) = 9.80 N/ 2.44 x 10^-5 cm^2 = 4.01 x 10^5 Pa or 4.01 x 10^5 N/m^2 = 4.01 x 10^5 Pa = 4.01 x 10^5 N/m^2 = 4.01 x 10^5 Pa = 59 psi = 0.0059 atmc) To find the pressure on your hand when the apple is cut into slices, we can use the same formula P = F/A, where P is pressure, F is force, and A is area. The force of the apple is still its weight (9.80 N) and the area of contact on your hand is the total area of the slices. So, the pressure on your hand is:P = (9.80 N) / (total area of slices)d) To find the pressure of the applesauce on the table, we can use the formula P = F/A, where P is pressure, F is force, and A is area. The force of the applesauce is still its weight (9.80 N) and the area of contact on the table is the area of the applesauce. So, the pressure on the table is:P = (9.80 N) / (total area of applesauce)It should be noted that the above calculations are based on the assumption that the apple is a homogeneous object and that the cross sectional area of toothpick is constant. In reality, the pressure will vary depending on the apple's density and the toothpick's shape and size.To learn more abut pressure refer:
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define, identify, describe and understand various heat sources capable of being a source of ignition.
When anything, a process, or an event may ignite or transport energy into a medium to cause combustion, it is said to be a source of ignition. This standard permits the use of open flames as a source of ignition.
Friction, hot surfaces, sparks, and static electricity. bursts of lava and friction-based electricity warmers. Sun Everyone who lives on Earth gets most of their heat from the sun. For plants to prepare their food, they require energy from the sun. The warmth of the sun makes it possible for humans to survive. Fuel ignition results in the release of energy. Heat is the energy that is transmitted when two objects with different surface temperatures touch. system of the sun.
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A swimmer capable of swimming with velocity v relative to water jumps in a flowing river having velocity u. The man swims a distance d downstream and returns back to the original position. Find out the time taken in complete motion.
a. 2dv/v^2 - u^2
b. dv/v^2 - u^2
c. 3dv/v^2 - u^2
d. 4dv/v^2 - u^2
The duration of the motion when a swimmer with a swimming velocity of v in relation to the water jumps into a river with a flowing velocity of u is measured as 2dv/v2 - u2.
What is motion?Motion is the gradual change in an object's position over time. Displacement, distance, velocity, acceleration, time, and speed are all used to describe motion. In physics, motion is a function of a body's position or orientation over time. Translation is defined as movement along a line or a curve. Rotation is a motion that modifies a body's orientation. Motion is the shift in an object's position with respect to time. When an object's position changes over time, it is said to be in motion. By mentioning a reference point, we are able to describe the location of an object. Relative motion exists. An object's distance is defined as the length of its total path.
Here,
t1=d/(u+v)
t2=d/(u-v)
t=t1+t2
=d/(u+v)+d/(u-v)
t=2dv/v²-u²
When a swimmer with a swimming velocity of v jumps into a river with a flowing velocity of u, the length of the motion is calculated as 2dv/v2 - u2.
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which of the answers below best describes the discussion between maria and oliver? maria and oliver are discussing the ranking of buoyant forces on three different objects. maria and oliver are discussing how to correctly determine the pressure at a particular depth in a fluid. maria and oliver are discussing how to correctly determine the number and magnitude of forces on a volume of water. maria and oliver are discussing whether the bouyant force is influenced by the mass of an object. grade summary deductions 0% potential 100% submissions attempts remaining: 3 (33% per attempt) detailed view
Oliver and Maria are debating how to precisely determine the fluid's pressure at a particular depth.
What forces need to be considered in order to understand how a sphere falls in a fluid?
Stokes' law describes how spheres settle in a Newtonian fluid. A particle will sink if the buoyant force acting on a sphere submerged in a Newtonian fluid is not equal to or greater than the gravitational force acting on the sphere. The net downward force on a sphere is what separates the settling force from the buoyant force.
What connection exists between point pressure and depth in a fluid?
Because a liquid's pressure also increases with depth, the pressure of a liquid is inversely proportional to its depth.
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A train is moving along a straight line with a constant acceleration a. A boy standing in the train throws a ball forward with a speed of 10m/s, with respect to the train at an angle of 60 derajat to the horizontal. The boy has to move forward by 1.15m inside the train to catch the ball back at the initial height. The acceleration of the train, in m/s^2 , is:
The acceleration of the train is 5 [tex]m/[/tex] [tex]s^{2}[/tex] .
We can clearly see that the ball will follow a parabolic path so we break it into vertical and horizontal axis
The boy throws the ball and gives it a vertical velocity on which constant acceleration 'g' acts
For the vertical movement
[tex]S = ut - \frac{1}{2} g t^{2}[/tex]
[tex]0 = 10 sin 60[/tex]° - [tex]\frac{1}{2} 10 t^{2}[/tex]
[tex]t = \sqrt{3} s[/tex]
We know that the ball already has a horizontal velocity equal to the moving train's velocity.
For the vertical movement
[tex]S = ut + \frac{1}{2} a t^{2}[/tex]
[tex]1.15 = 10 cos 60[/tex]° [tex]\sqrt{3} \ \frac{1}{2} \ a \ 3[/tex]
[tex]a = 5 m/ s^{2}[/tex]
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the electric field lines on the left have twice the separation of those on the right. (a) If the magnitude of the field at A is 40 N/C, what is the magnitude of the force on a proton at A? (b) What is the magnitude of the field at B?
This means that if the field lines are near together (i.e., the field line density is greater), it means that the magnitude of the field is large at that location. The cross-sectional field lines should be close together if the field is of small magnitude.
The intersection of two electric field lines: what does it mean?Lines in an electric field cannot intersect. If they did, they would be telling you that a charge at that place would have a force that points in two distinct directions, which is completely illogical. Equipotential lines cannot cross at different potentials either.This means that if the field lines are near together (i.e., the field line density is greater), it means that the magnitude of the field is large at that location. The cross-sectional field lines should be close together if the field is of small magnitude.The cross-sectional field lines should be close together if the field is of small magnitude.To learn more about magnitude refer to:
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the chart shows different speeds at which theoretical spacecraft are traveling horizontally. the speeds are represented as percentages of the speed of light the spacecrafts are traveling, where 0.20c
The figure below displays various horizontal spaceship travel speed, with y being the farthest away from zero. Y is the solution
A spacecraft has never traveled faster than 163 km/s (586,800 km/h; 364,660 mph), which was accomplished by the Parker Solar Probe on November 20, 2021, at 21:25:24 UTC. The probe received a gravity boost from a fly-by of Venus on October 16 that tightened its orbit, allowing it to achieve this speed at perihelion (the closest point in its elliptical orbit around the Sun). It came within 5,307,594 miles (8,541,744 km) of the surface of the Sun. Until the Parker Solar Probe's 17th perihelion on September 27, 2023, this record will hold.
For instance, a spacecraft leaving the surface of the Earth has to be traveling at a speed of about 40,000 kilometers per hour (25,000 miles per hour), or approximately 11 kilometers per second (7 miles per second), in order to enter orbit.
The correct question is:
The chart shows different speeds at which theoretical spacecraft are traveling horizontally. The speeds are represented as percentages of the speed of light the spacecraft are traveling, where 0.20c = 6 × 107 m/s.
Which spacecraft appears the longest to an outside observer?
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A bicycle tire is spinning clockwise at 2.30 rad/s. During a time period =1.95 s, the tire is stopped and spun in the opposite direction, also at 2.30 rad/s. Calculate the change in the tire’s angular velocity and the tire’s average angular acceleration
If a bicycle tire is spinning clockwise at 2.30 rad/s. the change in the tire’s angular velocity and the tire’s average angular acceleration is: 2.63 rad/s².
How to find the average angular acceleration?Change in angular velocity
Δw = wf -wi
Δw = (2.30 rad/s) - (-2.30 rad/s)
= 4.60 rad/s
w_ is negative because it is in the clockwise direction.
Average angular acceleration:
Average angular acceleration = 4.60 rad/s/ 1.75s
Average angular acceleration = 2.63 rad/s²
Therefore the average angular acceleration is 2.63 rad/s².
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if a wave is traveling at a velocity of 120 m/s and has a frequency of 5 hz, which of the following can be determined? A.The mass of the wave. B. The speed of the wave. C.The wavelength of the wave. D. The direction of the wave.
If a wave has a frequency of 5 Hz and is moving at a speed of 120 m/s, its wavelength is 24 m.
Given,
Velocity =120m/s
Frequency=5Hz
So the Wavelength of the wave is,
[tex]\lambda =\frac{v}{f}[/tex]
[tex]\lambda =\frac{120}{5}=24m[/tex]
[tex]\lambda =24m[/tex]
So the Wavelength of the wave is 24m
The number of waves that pass through a fixed point in a given amount of time is defined as the frequency. If a wave takes 1/2 second to pass, the frequency is 2 per second. If it takes one-hundredth of an hour, the frequency is one hundred per hour.
After passing through a series of events or positions and returning to its original state, a body in periodic motion is said to have gone through one cycle or one vibration. Additionally, see angular velocity and simple harmonic motion.
The frequency is 2 per second if the period or time interval, required to complete one cycle or vibration is 1/2 second; 100 per hour if the period is 1/100 of an hour.
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a car changes its velocity from 45 km/h to 65 km/h in 3 s. Find the magnitude of its acceleration
The magnitude of the acceleration of the car when its velocity changes from 45km/h to 65km/h in 3 s is 1.9 m/s^2
Let u be the initial velocity of the car.
u=45 km/h (given)
By converting it into m/s , we get:
u=12.5 m/s
Let v be the final velocity of the car, then :
v=65 km/h
v=18.1 m/s ( By converting them into m/s)
Now, let the acceleration of the car while moving to be a, then :
Using the formula, we get:
⇒v = u + at
⇒ 18.1 = 12.5 + a×3 ( Putting all the values)
⇒3a = 18.1 - 12.5
⇒a = 5.6/3
⇒ a = 1.9 m/s^2
Therefore, The magnitude of the acceleration of the car when its velocity changes from 45km/h to 65km/h in 3 s is 1.9 m/s^2
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Suppose' a tree branch falls down to the ground with constant acceleration and takes 2 seconds to hit the ground. Which of the following statements regarding the path of the branch is true? A. Its acceleration is increasing during the time it falls B. It covers the same distance during the first second as it does during the last second. C. It covers more distance during the last second. D. It covers less distance during the last second.
The correct statements is it covers more distance during the last second.
What is mean by acceleration? The rate at which an object's velocity alters over time is called its acceleration. It has both magnitude and direction because it is a vector quantity. The difference between the change in velocity and the change in time is known as acceleration. In physics, acceleration is the rate of change of velocity with respect to time. It is measured in meters per second squared (m/s2). Acceleration is a vector quantity and is therefore described by both the magnitude and direction of the change in velocity. In everyday terms, acceleration is the rate at which an object speeds up, slows down or changes direction. Acceleration can be caused by a number of things, including a push, a pull, gravity, or a change in the net force acting on an object. Acceleration can also be caused by a change in the mass or shape of an object. In some cases, acceleration can be caused by a change in the direction of velocity.To learn more about acceleration refer to:
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The level of magnification that produces the best images using an electron microscope is _____.
A. 2,500 times
B. 100,000 times
C. 250,000 times
D. 1,000,000 times
The level of magnification that produces the best images using an electron microscope is 250,000 times.
What is electron microscope?In order to "image" the specimen and learn more about its structure and composition, electron microscopes (EMs) work similarly to their optical equivalents but employ a focussed beam of electrons rather than photons. There are several kinds of electron microscopes, such as the scanning electron microscope (SEM), the transmission electron microscope (TEM), and the reflection electron microscope (REM.)
Universities, research facilities, and institutes for nanotechnology frequently employ electronic microscopes. These facilities allow for a close examination of the specimen's structure, which can reveal details about its intended use.
correct option: C
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a block of known mass mm is on a disk that rotates about its center, as shown above. the block does not slip on the disk, and travels at a constant tangential speed vv when at a distance rr from the center with a centripetal force of magnitude ff exerted on it. which of the following statements about other quantities that might be determined is correct?
When the block's radius and tangential speed are known, the centripetal acceleration of the block may be determined because ac=v2rac=v2r.
What exactly is a force in science?
Physics appears to have a clear definition for the word "force." A force of this magnitude can be described as either a push or a pull. A force does not "be in it" or "be inside it." A force from another object can affect something else.
What do the terms force and motion mean?
Basically, a push or pull that impacts anything or energy as a property of physical motion or movement is referred to as force. It happens when two things come together. A body is also considered to be in motion when it is moving.
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A charged rod is brought near a negatively charged pith ball electroscope. What conclusion would you draw about the charge on the rod if pith ball moves away from the rod ?O PositiveO NegativeO No chargeO Cant say
The negatively charged rod attracts positive charges and repels negative charges when it is located closer to the electroscope.
What happens when a neutral pith ball is in close proximity to a negatively charged rod?The pith balls' charges polarize when ever an electrified rod is introduced in close proximity to them. They may pick up this very same sign charge if they come into contact the with charged rod. The pith balls act like siblings and avoid touching one another because like charges repel one another.
What is the electroscope's conclusion?We can infer from all of these statistics that charge induction, underlying atomic and molecular structure of something like the metal components, and the idea that an electroscope operates.
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find the mass of a bullet moving at 45m/s and has kinetic energy of 51 j
The mass of a bullet moving at 45m/s and has kinetic energy of 51 j is 0.050 gram.
What is kinetic energy ?The term kinetic energy is defined as the energy of motion, observable as the movement of an object or subatomic particle.
There are five different types of kinetic energy: radiant, thermal, sound, electrical, and mechanical.
It is represented by formula
K.E = 1/2 mv²
Kinetic energy = 51 j
Mass = ?
Velocity = 45m/s
Then,
Mass = 2 K.E / v²
= 2 × 51 / 45²
= 102 / 2025
= 0.050 gram
Thus, The mass of a bullet moving at 45m/s and has kinetic energy of 51 j is 0.050 gram.
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let the samples of the noise voltage, v (nt) be jointly gaussian random variables. show that x(t) is a gaussian process.
Since x(t) is a linear function of v(nt) which is jointly Gaussian, and the mean of x(t) is a linear function of t, x(t) is also a Gaussian process.
What is Gaussian process?A Gaussian process is a stochastic process whose realizations are Gaussian random variables. To show that x(t) is a Gaussian process, we need to show that:The mean of x(t) is a linear function of t.The covariance function of x(t) is a valid covariance function.The mean of x(t) is defined as E[x(t)], where E[] denotes the expectation operator. Since the noise voltage v(nt) is jointly Gaussian, it follows that x(t) = v(nt) is also Gaussian, and thus its mean is a linear function of t.The covariance function of x(t) is defined as C(s,t) = E[(x(s) - E[x(s)]) (x(t) - E[x(t)])].Since v(nt) is jointly Gaussian, the covariance function of x(t) is also a valid covariance function.Therefore, x(t) is a Gaussian processx(t) = v(nt) is jointly GaussianSince x(t) is a linear function of v(nt) which is jointly Gaussian, and the mean of x(t) is a linear function of t, x(t) is also a Gaussian process.The covariance function of x(t) is a valid covariance function, as it is derived from jointly Gaussian variables.To learn more about Gaussian process refer:
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transitions between solid, liquid, and gaseous states of a substance occur when conditions of temperature or pressure favor the associated changes in phase. when the temperature of a gas is
A substance will switch between its solid, liquid, and gaseous forms when temperature, pressure circumstances encourage corresponding transitions. When a gas's temperature increases, pressure falls.
A state of matter that is gaseous has a distinct mass but no distinguishable shape or volume. Pressure, volume, temperature, material quantity, specific heat, and other quantifiable characteristics of gases include these. The most important characteristics are the four independent variables quantity, volume, pressure, and temperature, which describe the gas's state. When describing how hot or cold something is, the idea of temperature is used. One can measure temperature by using a thermometer. The calibration of thermometers involves the use of various temperature scales.
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hardening parameter is assumed to be related to some measure of the plastic strains via the equation ___
Hardening parameter is assumed to be related to some measure of the plastic strains via the equation [tex]$\sigma_{y0} = K \varepsilon_p^m$[/tex].
What is parameter?Parameter is a special kind of variable used in a function or subroutine to refer to one of the pieces of data provided as input to the function. It is a value that controls the behaviour of a function. It can be used to provide a certain type of flexibility in the function, allowing it to act differently in different situations.
where [tex]$\sigma_{y0}$[/tex] is the hardening parameter, [tex]$K$[/tex] is a material constant, and [tex]$m$[/tex] is the hardening exponent. This equation is used to determine the relationship between the yield stress and the plastic strain, providing a useful tool for predicting the behavior of a material under cyclic loading.
The strain hardening increases the yield strength of the material.
and
Modulus of toughness = [tex]\dfrac{\text{Yieldstress}^2}{2(\text{{Youngs Modulus)}}}[/tex]
Hence, if the yield stress increases, the modulus of toughness increases too.
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Macmillan Learning
A black mamba snake has a length of 2.60 m and a top speed of 4.50 m/s. Suppose a mongoose and a black mamba find
themselves nose to nose. In an effort to escape, the snake accelerates past the mongoose at 8.37 m/s² from rest.
How much time ftop does it take the snake to reach its top
speed?
How far dsnake does the snake travel in that time?
How much time freact does the mongoose have to react before
the black mamba's tail passes the mongoose's nose?
ftop
dsnake =
freact=
S
m
S
The black mamba travels a distance of 2.0828 m, which is less than its length of 4.50 m.
How far dsnake does the snake travel in that time?The first equation of motion states:
vf = at + vi
A top speed is _f.
Initial or lowest speed is v i, and acceleration is a.
2.60 = 4.50 t
t +0 = 1.28571sec
The snake needs 1.28571 seconds to attain its peak speed.
Part B:
The second equation of motion states:
S=0.5(4.50) S=vit+at2 w i=0 (1.28571)
2 S = 2.0828m
In that period, the snake moves 2.0828 metres.
Part C:
The black mamba travels a distance of 2.0828 m, which is less than its length of 3.12 m.
2.0828 m<3.12 m
A potential exists for monkeys to capture a black mamba.
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Star A has a magnitude of 9.5; Star B, 5.5; and Star C, 2.5. Which is brightest? Which are visible to the unaided eye? Which pair of stars has a flux ratio of about 16?
Star A has a magnitude of 9.5, star B has a magnitude of 5.5, and star C has a magnitude of 2.5, so star C is the brightest, while star B is visible but star A is not, and the flux of the star is 16, which is the ratio of star A to star B ( [tex]{2}^{9.5-5.5}=16[/tex])
What is the significance of the flux of the star?The star's flux is significant because it explains the amount of light emitted by the star, is useful for studying the star's brightness, and can be used to infer the star's distance from Earth, give the idea of a collision with Earth, and so on.
As a result, star A has a magnitude of 9.5, star B has a magnitude of 5.5, and star C has a magnitude of 2.5, so star C is the brightest, while star B is visible but star A is not, and the flux of the star is 16, which is the ratio of star A to star B.
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What happens
to the energy
level of particles
when melting
occurs?
A. it decreases
B. it increases and
decreases rapidly
C. it increases
D. it stays the same
It decreases happens to the energy level of particles when melting occurs. So, option (a) is correct.
What is energy level?
The fixed distances between the atom's nucleus and the location of electrons are known as energy levels, sometimes known as electron shells. A tiny, positively charged nucleus at the center of an atom is surrounded by electrons, which are tiny, negatively charged particles. A staircase's steps can be compared to energy levels.
What is melting?
Melting is the transformation of a solid into a liquid under the influence of heat. When a solid is impure, it often melts over a wide range of temperatures below the melting point of the main component. In a pure crystalline solid, this process takes place at a specific temperature known as the melting point.
Therefore, decreases happens to the energy level of particles when melting occurs. So, option (a) is correct.
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In Fig. 22−35 the four particles form a square of edge length a=5.00 cm and have charges q 1 =+10.0 nC,q 2 =−20.0 nC,q 3 =+20.0 nC, and q 4 =−10.0 nC, In unit vector notation, what net electric field do not particles produce at the square's center?
Net electric field produced by the four particles at the square's center is zero.
What is electric field?The physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them is called an electric field.
Electric field produced by each particle at the center of the square can be calculated as:
E1 = k * q1 / (5/sqrt(2))^2 = 810^9 N/C * (1010^-9 C) / (5/sqrt(2))^2 = 410^9 N/C
E2 = k * q2 / (5/sqrt(2))^2 = 810^9 N/C * (-2010^-9 C) / (5/sqrt(2))^2 = -810^9 N/C
E3 = k * q3 / (5/sqrt(2))^2 = 810^9 N/C * (2010^-9 C) / (5/sqrt(2))^2 = 810^9 N/C
E4 = k * q4 / (5/sqrt(2))^2 = 810^9 N/C * (-1010^-9 C) / (5/sqrt(2))^2 = -410^9 N/C
So, E net = E1 + E2 + E3 + E4 = 410^9 N/C + (-810^9 N/C) + 810^9 N/C + (-410^9 N/C) = 0 N/C
Therefore, net electric field produced by the four particles at the square's center is zero.
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