Answer:
57.19461 m/s²
-9.20833 m/s²
Explanation:
t = Time taken
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration
Equation of motion
[tex]v=u+at\\\Rightarrow a=\dfrac{v-u}{t}\\\Rightarrow a=\dfrac{\dfrac{663}{3.6}-0}{3.22}\\\Rightarrow a=57.19461\ m/s^2[/tex]
The acceleration during the race is 57.19461 m/s²
[tex]v=u+at\\\Rightarrow a=\dfrac{v-u}{t}\\\Rightarrow a=\dfrac{0-\dfrac{663}{3.6}}{20}\\\Rightarrow a=-9.20833\ m/s^2[/tex]
The acceleration while stopping is -9.20833 m/s²
The assumptions made here are:
The initial velocity of the dragster at the start of the race is zero
The acceleration is constant in both cases of acceleration.
The final velocity when it stops is zero
Motion is in a straight line path
A 2.50-g bullet, traveling at a speed of 425 m/s, strikes the wooden block of a ballistic pendulum, such as that in the picture. The block has a mass of 215 g. (a) Find the speed of the bullet/block combination immediately after the collision. (b) How high does the combination rise above its initial position?
Answer:
4.88505 m/s
1.21629 m
Explanation:
[tex]m_1[/tex] = Mass of bullet = 2.5 g
[tex]m_2[/tex] = Mass of block = 215 g
[tex]v_1[/tex] = Velocity of bullet = 425 m/s
[tex]v_2[/tex] = Velocity of block
Here, the linear momentum is conserved
[tex]m_1v_1+m_2v_2=(m_1+m_2)v\\\Rightarrow v=\dfrac{m_1v_1+m_2v_2}{m_1+m_2}\\\Rightarrow v=\dfrac{2.5\times 10^{-3}\times 425+0.215\times 0}{2.5\times 10^{-3}+0.215}\\\Rightarrow v=4.88505\ m/s[/tex]
The speed of the combination of mass is 4.88505 m/s
The energy in the system is conserved
[tex]\dfrac{1}{2}(m_1+m_2)v^2=(m_1+m_2)gh\\\Rightarrow h=\dfrac{v^2}{2g}\\\Rightarrow h=\dfrac{4.88505^2}{2\times 9.81}\\\Rightarrow h=1.21629\ m[/tex]
The maximum height the combined mass will reach is 1.21629 m
Answer:
Explanation:
mass of bullet, m = 2.5 g
initial velocity of bullet, u = 425 m/s
mass of block, M = 215 g
(a) Let the speed of bullet block system is v
Use the conservation of momentum
m x u + M x 0 = (M + m) x v
2.5 x 425 = ( 215 + 2.5) x v
v = 4.89 m/s
(b) Let it rise upto height h
Use conservation of energy
Kinetic energy after collision = Potential energy
1/2 (M + m) v² = ( M+ m) x gx h
0.5 x 4.89 x 4.89 = 9.8 x h
h = 1.22 m
The names of the seven days of the week are derived from the names of the bodies of the solar system that are visible to the naked eye.
Answer:
Baja naja kanaka kanaka man's kana kana
The magnitude of vector A is 15.0 units and points in the direction 330° counterclockwise from the positive x-axis. Calculate the x- and y-components of this vector.
Answer:
[tex]V_{x}[/tex] = 12.99 , [tex]V_{y}[/tex] = -7.5
Explanation:
v=15units , θ=330°
the magnitude of the horizontal and vertical components are gotten by the formula below
[tex]V_{x}[/tex] = Vcosθ
[tex]V_{y}[/tex] = Vsinθ
[tex]V_{x}[/tex] = 15*cos330
[tex]V_{x}[/tex] = 12.99 (positive implies to the right)
[tex]V_{y}[/tex] =15*sin330
[tex]V_{y}[/tex] = -7.5 (negative implies downwards)
Two balls undergo a perfectly elastic head-on collision, with one ball initially at rest. If the incoming ball has a speed of 200 m/s . Part APart complete What is the final speed of the incoming ball if it is much more massive than the stationary ball?
Answer:
Explanation:
Check the attachment for solution
Answer: The final speed of the incoming ball is approximately 200m/s
Explanation:
Using the law of conservation of momentum.
m1(u1) + m2u2 = m1v1 + m2v2
And also law of conservation of kinetic energy for elastic heads on collision we can derive the formula for elastic heads on collision which is given below:
For elastic heads on collision.
v1 = [( m1 - m2)/(m1+m2)] u1 ......1
v2 = [(2m1)/(m1+m2)]u1 ......2
Where,
m1 and m2 are the mass of the incoming and stationary ball respectively.
u1 and u2 are the initial speed of the incoming and stationary ball respectively.
v1 and v2 are the final speed of the incoming and stationary ball respectively.
a) to determine the final speed of the incoming ball using equation 1
v1 = [( m1 - m2)/(m1+m2)]u1
Since m1 >> m2
m1 - m2 ~= m1 and m1 +m2 ~= m1
So, equation 1 becomes
v1 ~= [m1/m1]u1
v1 ~= u1
Since u1 = 200m/s
v1 ~= 200m/s
Additional tips: using equation 2 we can derive the approximate final speed of the stationary ball following the same assumptions. If well solved v2 = 2u1 = 400m/s
Anthony sends a series of pulses of amplitude 43 cm down a string that is attached to a post at one end. Assume the pulses are reflected with no loss of amplitude.(a) What is the amplitude at a point where two pulses are crossing if the string is rigidly attached to the post?cm(b) What is the amplitude at a point where two pulses are crossing if the end at which reflection occurs is free to slide up and down?cm
The amplitude where two pulses cross on a string rigidly attached to a post is momentarily zero due to destructive interference. However, when the end is free to move and two pulses cross, they superimpose constructively, resulting in a combined amplitude of 86 cm.
When Anthony sends a series of pulses of amplitude 43 cm down a string tied to a post:
(a) If the string is rigidly attached to the post, the reflected pulse inverts. Therefore, when two pulses of the same amplitude cross, they interfere destructively at the instant they coincide and the amplitude at the point of crossing is momentarily zero. However, since they're not lasting interactions, the amplitude of each pulse remains 43 cm before and after crossing.
(b) If the end is free to slide up and down, the reflected pulse does not invert and remains in phase with the incident pulse. Now, as two pulses of the same amplitude (43 cm) cross, they temporarily superimpose constructively, resulting in a combined amplitude of 86 cm, which is the sum of their individual amplitudes.
The phenomenon described here is a demonstration of wave interference, specifically in the context of reflected transverse waves on a string. It shows the distinct difference between reflections from fixed end (inverting) and free end (non-inverting) boundaries.
For a rigidly attached end, the amplitude is 0 cm due to destructive interference, while for a free boundary, it is 86 cm due to constructive interference.
When dealing with wave pulses on a string, the amplitude of the resulting wave at a point where two pulses are crossing depends on the boundary conditions at the end of the string.
(a) Rigidly Attached EndWhen the string is rigidly attached, the reflected pulse inverts upon reflection. This means that the original pulse and the reflected pulse will be out of phase by 180 degrees when they meet. If the amplitude of each pulse is 43 cm, the resulting amplitude at the point of crossing will be zero (43 cm - 43 cm = 0 cm) due to destructive interference.
(b) Free to Slide Up and DownWhen the end at which reflection occurs is free to move up and down (a free boundary condition), the reflected pulse remains in phase with the incident pulse. Therefore, the amplitudes add constructively. Hence, at the crossing point, the resulting amplitude will be the sum of the individual amplitudes: 43 cm + 43 cm = 86 cm.
In summary, the conditions at the end of the string determine whether the interference is constructive or destructive, affecting the amplitude at the crossing point of two pulses.
A small glass bead has been charged to 8.0 nC. What is the magnitude of the electric field 2.0 cm from the center of the bead? (k = 1/4ΔΉ0 = 8.99 × 109 N · m2/C2)A) 3.6 × 10-6 N/C B) 1.4 × 10-3 N/C C) 1.8 × 105 N/C D) 3.6 × 103 N/C
Answer:
C) 1.8×10⁵ N/C.
Explanation:
Electric field: This can be defined as the region where electric force is experienced.
Electric Field intensity: This is defined as the force per unit charge which it exert at that point.
The S.I unit of electric field is N/C.
Mathematically, Electric Field intensity can be represented as,
E = kq/r².................... Equation 1
Where E = electric field intensity, q = charge, r = distance. k = proportionality constant.
Given: q = 8.0 nC = 8×10⁻⁹ C, r = 2.0 cm = 0.02 m, k = 8.99×10⁹ Nm²/C²
Substituting into equation 1
E = (8.99×10⁹×8×10⁻⁹)/0.02²
E = 71.92/0.0004
E = 1.798×10⁵ N/C.
E ≈ 1.8×10⁵ N/C.
The right option is C) 1.8×10⁵ N/C.
The innermost electron shell of an atom can hold up to _____ electrons. The innermost electron shell of an atom can hold up to _____ electrons. A.18 B. 1 C. 32 D.2 8
Answer:
D. 2
Explanation:
The innermost electron shell of an atom can hold up to 2 electrons.
All the elements in the periodic table have only two electrons in their inner most shell. The only exception is hydrogen because it has only one electron.
If Aristotle and Quintilian had a debate about rhetoric, which would likely argue that it is a means to communicate and persuade, and nothing more?
Answer:
Aristotle.
Explanation:
Aristotle is known as the father of rhetoric and it was actually his concept that the rhetoric is just the means of communications and persuade.
In a machine shop, a hydraulic lift is used to raise heavy equipment for repairs. The system has a small piston with a cross-sectional area of 0.075 m2 and a large piston with a cross-sectional area of 0.237 m2 . An engine weighing 3400 N rests on the large piston. What force must be applied to the small piston in order to lift the engine? Answer in units of N.
Answer:
[tex]F_s=1075.9493\ N[/tex]
Explanation:
Given:
area of piston on the smaller side of hydraulic lift, [tex]a_s=0.075\ m^2[/tex]area of piston on the larger side of hydraulic lift, [tex]a_l=0.237\ m^2[/tex]Weight of the engine on the larger side, [tex]W_l=3400\ N[/tex]Now, using Pascal's law which state that the pressure change in at any point in a confined continuum of an incompressible fluid is transmitted throughout the fluid at its each point.
[tex]P_s=P_l[/tex]
[tex]\frac{F_s}{a_s}=\frac{W_l}{a_l}[/tex]
[tex]\frac{F_s}{0.075} =\frac{3400}{0.237}[/tex]
[tex]F_s=1075.9493\ N[/tex] is the required effort force.
Answer:
F = 1076 N
Explanation:
given,
small piston area, a = 0.075 m²
large piston area, A = 0.237 m²
weight on the large piston, W = 3400 N
force applied on the second piston, F = ?
using pascal law for the force calculation
[tex]\dfrac{F}{W}=\dfrac{a}{A}[/tex]
[tex]\dfrac{F}{3400}=\dfrac{0.075}{0.237}[/tex]
F = 0.3165 x 3400
F = 1076 N
The force applied to the small piston in order to lift the engine is equal to 1076 N.
15. Explain how you can make a prediction for the atomic mass from only the atomic mass of each isotope and the ratios of isotopes that are present.
Answer:
The average atomic mass can be calculated from the exact atomic mass of each isotope by multiplying the mass each isotope by its relative abundance and then finding the sum of the result.
for example carbon has two major isotopes ;carbon 12 ,atomic mass with relative abundance of 98.9% and carbon 13 , atomic mass of with relative abundance 1.1%. The relative atomic mass is calculated below.
[tex]RAM = 12*\frac{98.9}{100}+13.003355 *\frac{1.1}{100}[/tex]
RAM=11.868 + 0.143036905
RAM=12.011036905amu
An element forms an ionic compound with bromine having the formula XBr. If the mass number of the element X is 41 and the ion has 18 electrons, what is the element X and how many neutrons does it have?
Answer:
X is calcium and it has 21 neutrons
Explanation:
Calcium 41 is an isotope of calcium with mass number of 41 and atomic number of 20
Number of neutrons = mass number - number of electrons
The number of electrons is the same as the atomic number of the element (calcium)
Number of neutrons = 41 - 20 = 21
Two points (X and Y) in a fluid are at the same depth in a container. The pressure at X is greater than the pressure at Y. Which of the flowing must be true
Answer:
ρ_ x > ρ_ y
Explanation:
The pressure in a fluid depends on its depth with the equation
P = ρ g h
For two points at the same depth there may be several possibilities,
- the pressure is the same if the density of the fluid is equal in the two points
- The pressure is different if the fluid density is different at each point
In this case, as the point x has greater pressure than the point, the density of the fluid in Des is greater than the density of the fluid in Y
ρ_ x > ρ_ y
Polonium, the Period 6 member of Group 6A(16), is a rare radioactive metal that is the only element with a crystal structure based on the simple cubic unit cell. If its density is 9.232 g/cm3, calculate an approximate atomic radius for polonium―209.
Answer:
Approximate atomic radius for polonium-209 is 167.5 pm .
Explanation:
Number of atom in simple cubic unit cell = Z = 1
Density of platinum = [tex]9.232 g/cm^3[/tex]
Edge length of cubic unit cell= a = ?
Atomic mass of Po (M) = 209 g/mol
Formula used :
[tex]\rho=\frac{Z\times M}{N_{A}\times a^{3}}[/tex]
where,
ρ = density
Z = number of atom in unit cell
M = atomic mass
[tex](N_{A})[/tex] = Avogadro's number
a = edge length of unit cell
On substituting all the given values , we will get the value of 'a'.
[tex]9.232 g/cm3=\frac{1 \times 209 g/mol}{6.022\times 10^{23} mol^{-1}\times (a)^{3}}[/tex]
[tex]a = 3.35\times 10^{-8} cm[/tex]
Atomic radius of the polonium in unit cell = r
r = 0.5a
[tex]r=0.5\times 3.35\times 10^{-8} cm=1.675\times 10^{-8} cm[/tex]
[tex]1 cm = 10^{10} pm[/tex]
[tex]1.675\times 10^{-8} cm=1.675\times 10^{-8}\times 10^{10}=167.5 pm[/tex]
Approximate atomic radius for polonium-209 is 167.5 pm.
To find the approximate atomic radius of polonium-209, we can use its simple cubic crystal structure and the fact that its coordination number is six. By determining the mass contained within a unit cell and its volume, we can calculate the atomic radius.
Explanation:To approximate the atomic radius of polonium-209, we can use the fact that polonium crystallizes in a simple cubic structure. In this structure, each polonium atom contacts only its four nearest neighbors in its layer, one atom directly above it in the layer above, and one atom directly below it in the layer below. The coordination number for a polonium atom in a simple cubic array is six.
Since the coordination number is six, we can visualize a polonium atom at the center of a simple cubic unit cell, with one atom at each corner of the cube. The distance from the center of the unit cell to its vertices gives an approximation of the atomic radius of polonium-209.
Given that the density of polonium is 9.232 g/cm3, we can use the formula density = mass/volume to find the mass contained within the unit cell. With the knowledge that a unit cell contains one-eighth of a polonium atom at each of its eight corners, we can determine the volume of the unit cell. By dividing the mass contained within the unit cell by its volume, we can calculate the approximate atomic radius of polonium-209.
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a typical flute is about 66 cm long . a piccolo is a very similar instrument ,through it is smaller, with a length of about 32 cm. how does the pitch of a piccolo compare to that of a flute?
Answer:
The Piccolo have higher frequency than Flute.
Explanation:
given,
length of the tube, L = 66 cm
length of the piccolo, L'= 32 cm
speed of sound = 343 m/s
A flute is open open tube with a fundamental frequency of ;
[tex]f = \dfrac{v}{2L}[/tex]
[tex]f = \dfrac{343}{2\times 0.66}[/tex]
f = 260 Hz
A piccolo is also an open open tube so, fundamental frequency is:
[tex]f = \dfrac{v}{2L}[/tex]
[tex]f = \dfrac{343}{2\times 0.32}[/tex]
f = 536 Hz
from the above calculation we can clearly see that the piccolo have much higher frequency than the flute.
now, The Piccolo have higher frequency than Flute.
Lance arrives at the airport (with flowers and balloons in hand) to welcome a friend. Her plane is delayed. While waiting, he notices that it takes 2 minutes 47 seconds to get down the hall on the moving sidewalk. while walking (not on the moving sidewalk) it took him 112 seconds. If he walks while on the sidewalk, how long (s) will it take him?
Answer:
t = 67.04 s
Explanation:
given,
time taken by Lace on the side walk = 2 min 47 s
= 167 s
time taken by the Lace while walking = 112 s.
now, time taken by the Lace when he is walking on the side walk = ?
Assume the distance be equal to 'd'
speed of Lace on side walk
we know, distance = speed x time
[tex]v_{sidewalk}=\dfrac{d}{167}[/tex]
speed of the lace while walking
[tex]v_{walking}=\dfrac{d}{112}[/tex]
time taken by Lace to cover the distance by walking on the side walk
[tex]t = \dfrac{distance}{v_{sidewalk}+v_{walking}}[/tex]
[tex]t = \dfrac{d}{\dfrac{d}{167}+\dfrac{d}{112}}[/tex]
[tex]t = \dfrac{167\times 112}{167+112}[/tex]
t = 67.04 s
time taken by the Lace walking on the side walk is equal to 67.04 s
A particle of charge 3.53×10 −8 C experiences a force of magnitude 6.03×10 −6 N when it is placed in a particular point in an electric field. What is the magnitude of the electric field at that point?
Explanation:
Electric field is the ratio of force and charge.
Force, F = 6 x 10⁻⁶ N
Charge, q = 3.53 x 10⁻⁸ C
We have
[tex]E=\frac{F}{q}\\\\E=\frac{6\times 10^{-6}}{3.53\times 10^{-8}}\\\\E=169.97N/C[/tex]
Electric field at the location of the charge is 169.97 N/C
Now find the components NxNxN_x and NyNyN_y of N⃗ N→N_vec in the tilted coordinate system of Part B. Express your answer in terms of the length of the vector NNN and the angle θθtheta, with the components separated by a comma.
Answer:
[tex]N_{y} =Ncos[/tex]Ф,
[tex]N_{x} =-Nsin[/tex] Ф
Explanation:
Now find the components NxNxN_x and NyNyN_y of N⃗ N→N_vec in the tilted coordinate system of Part B. Express your answer in terms of the length of the vector NNN and the angle θθtheta, with the components separated by a comma.
Vectors are quantities that have both magnitude and direction while scalar quantities have only magnitude but no direction.
This a vector quantity
from the diagram the horizontal component of the length of the vector will be
[tex]N_{y} =Ncos[/tex]Ф
the vertical component will be
[tex]N_{x} =-Nsin[/tex] Ф
this is in the opposite direction because the x can be extrapolated to the negative axis
To solve the problem we must know about vectors and coordinate geometry.
What is a Vector?We know that the vector quantities are those quantities that have magnitude as well as direction.
Each vector quantity can be divided into two parts a horizontal and vertical component, the vertical component is known as the sine component while the horizontal component is known as the cosine component.
Representation of Vector componentA vector component is represented as the product of its length and the component angle.
For example, F Sinθ represents the vertical component of force, with magnitude F, while the F Cosθ represents the horizontal component, and will be in the same line with the axis from which the angle is been measured.
Vector components of the tilted Coordinate,The coordinate in the tilted coordinate will be,
[tex]N_x = N Sin\theta[/tex]
[tex]N_y = N Cos\theta[/tex]
Where N is the vector magnitude and θ is the angle from the axis of measurement.
The sign of the vector will depend upon the coordinate in which it is.
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Suzie Spacewalker hovers in space beside a rotating space station in outer space. Both she and the center of mass of the space station are at relative rest. If the space station is in Earth orbit, then Suzie____________
Answer:
is in the earths orbit
Explanation:
for Suzie to hover in space beside the rotating space station, she and the center of mass of the space station are at relative rest which happens when space station is in Earth orbit, hence she is in the earths orbit.
Two charges, qA and qB, are separated by a distance, d, and exert a force, F, on each other. Analyze Coulomb's law and answer the following questions.
(a) What new force will exist if qA is doubled?
(b) What new force will exist if qA and qB are cut in half?
(c) What new force will exist if d is tripled?
(d) What new force will exist if d is cut in half?
(e) What new force will exist if qA is tripled and d is doubled?
Answer: a. F doubled
b. F reduced by one-quarter i.e
1/4*(F)
c. 1/9*(F)
d. F increased by a factor of 4 i.e 4*F
e. F reduces 3/4*(F)
Explanation: Coulombs law states the force F of attraction/repulsion experience by two charges qA and qB is directly proportional to thier product and inversely proportional to the square of distance d between them. That is
F = k*(qA*qB)/d²
a. If qA is doubled therefore the force is doubled since they are directly proportional.
b. If qA and qB are half, that means thier new product would be qA/2)*qB/2 =qA*qB/4
Which means the product of charge is divided by 4 so the force would be divided by 4 too since they are directly proportional.
c. If d is tripped that is multiplied by 3. From the formula new d would be (3*d)²=9d² but force is inversely proportional to d² so instead of multiplying by 9 the force will be divided by 9
d. If d is cut into half that is divided by 2. The new d would be (d/2)²=d²/4. So d² is divided by 4 so the force would be multiplied by 4
e. If qA is tripled that is multiplied by 3. F would be multiplied by 3 also, if at the same time d is doubled (2*d)²= 4*d² . Force would be divided by 4 at same time. So we have,
3/4*F
Coulomb's Law explains how changes in charge and distance affect the electric force between two charges.
Explanation:Coulomb's Law states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Let's analyze the given scenarios:
If qA is doubled, the new force will also be doubled because the force is directly proportional to the charges.If both qA and qB are halved, the new force will be 1/4th of the original force because the force is directly proportional to the product of the charges.If d is tripled, the new force will be 1/9th of the original force because the force is inversely proportional to the square of the distance between the charges.If d is halved, the new force will be 4 times the original force because the force is inversely proportional to the square of the distance between the charges.If qA is tripled and d is doubled, the new force can be calculated by multiplying the individual effects of the changes. The new force will be 6 times the original force because the force is directly proportional to the product of the charges and inversely proportional to the square of the distance.Learn more about Electric Force here:https://brainly.com/question/20935307
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According to Prof. Bill Baker, the freedom of practicing professionals to make ethical decisions may not be worth much.unless they use a patterned approach
a. True.
b. False.
According to Prof. Bill Baker, the freedom of practicing professionals to make ethical decisions may not be worth unless they use a patterned approach for the sake of people and society and their welfare. This is true statement.
Answer: Option A
Explanation:
Ethical Decisions and their impact on society
When we talk about the professional fields; Engineers and Doctors comes first in our minds. The professional fields and persons make the roots of an ideal society for which they must take ethical decisions surely worth for the society.
The society has a right to expect ethical conduct from professionals. The conduct of taking ethical decisions must involve reasoning, planning and well execution. According to the Association for Practical and Professional Ethics, there are certain moral values that one must apply while practicing ethical decisions.
Two pieces of plas- tic, a full ring and a half ring, have the same radius and charge density. Which electric field at the center has the greater magnitude? Discuss and defend your answer.
Answer: The magnitude of the Electric Field at the centre of both plastic would be equal to Zero {i.e E =0}
Explanation: A plastic either full circle or half is an insulator, and the charges in an insulator cannot move around.
Therefore, thier electric potential p(r) = 0.
Recall that,
Electric field intensity E = first derivative of p(r) with respect to r ( radius).since p(r) = 0, E = 0 inside both plastic.
Final answer:
The electric field at the center of the half ring has a greater magnitude than that of the full ring because the full ring's symmetric charge distribution cancels the field out, while the half ring's electric field remains unopposed.
Explanation:
To determine which electric field at the center has the greater magnitude between a full ring and a half ring with the same radius and charge density, we must analyze the symmetrical distribution of charges. In the case of a full ring, the charges are evenly distributed around the ring, resulting in a net electric field at the center that cancels out due to symmetry. However, for a half ring, the symmetry is broken, and there is a net electric field at the center directed away from the flat side of the half ring, because there are no opposing charges to cancel the field out. Therefore, the electric field at the center of the half ring has a greater magnitude than that at the center of the full ring, which is effectively zero.
Q6) A speed skater moving to the left across frictionless ice at 8.0 m/s hits a 5.0-m-wide patch of rough ice. She slows steadily, then continues on at 6.0 m/s. What is the magnitude of her acceleration on the rough ice?
Final answer:
The magnitude of the acceleration of the speed skater on the rough ice is 2.8 m/s², calculated using the equation of motion.
Explanation:
To find the magnitude of the acceleration of the speed skater on the rough ice, we can use the equation of motion: v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement (width of rough ice).
Given that the skater's initial velocity (u) is 8.0 m/s, her final velocity (v) is 6.0 m/s, and the width of the rough ice (s) is 5.0 m.
Rearranging the equation for acceleration, we get a = (v^2 - u^2) / (2s). Substituting the given values, a = (6.0^2 - 8.0^2) / (2 * 5.0) = (-28) / 10 = -2.8 m/s2. The negative sign indicates deceleration, but since the question asks for the magnitude, the acceleration is 2.8 m/s2.
A clam dropped by a seagull takes 3.0 seconds to hit the ground. What is the seagull's approximate height above the ground at the time the clam was dropped?
The seagull dropped the clam from an approximate height of 44.1 meters above the ground. This was calculated using the physics formula for the height of a dropped object, considering the acceleration due to gravity.
Explanation:The subject of the question falls under Physics and it's related to the concept of gravitational acceleration. To calculate the height from which the seagull dropped the clam, we can use the physics formula for the height of a dropped object which is h = 0.5 * g * t^2.
Here, 'g' represents the acceleration due to gravity and has an approximate value of 9.8 m/s2, and 't' represents the time in seconds which is given as 3.0 seconds. So, inserting these values into the equation, we getThe seagull dropped the clam from an approximate height of 44.1 meters above the ground. This was calculated using the physics formula for the height of a dropped object, considering the acceleration due to gravity.
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What is the maximum number of lines per centimeter a diffraction grating can have and produce a complete first-order spectrum for visible light? (Assume that the range of visible wavelengths of light in air is 380 - 760 nm.)
Answer:
1315789.47368 lines/m
Explanation:
m = Order = 1
[tex]sin\theta[/tex] = 1 For maximum condition
[tex]\lambda[/tex] = Wavelength = 760 nm maximum
From Rayleigh criteria we have the expression for the gap
[tex]d=\dfrac{m\lambda}{sin\theta}\\\Rightarrow d=\dfrac{1\times 760}{1}\\\Rightarrow d=760\ nm[/tex]
The number of lines is the reciprocal of the slit distance
[tex]n=\dfrac{1}{d}\\\Rightarrow n=\dfrac{1}{760\times 10^{-9}}\\\Rightarrow n=1315789.47368\ /m[/tex]
The number of lines is 1315789.47368 per meter
A water molecule can bond to up to _____ other water molecules by ____ bonds.
Answer:
A water molecule can bond to up to four other water molecules by hydrogen bonds.
Explanation:
A water molecule has angular structure about the oxygen atom which has 2 lone pair of electrons in a water molecule. Due to the repulsion of lone pairs we get the angle between the H---O bond as 109.47°.
Each of the hydrogen atom of water attracts one water molecule and the partial negative on the oxygen atom attracts two more water molecules form the electron deficit side to form a pentamer of tetrahedral structure placing itself at the center of the geometry and the bonded molecules at the vertices.
A hydrogen bond is an intermolecular bond. A water molecule bonds up to 4 water molecules by the hydrogen bond.
Hydrogen bond:It is an intermolecular bond that is formed between molecules that have a high difference in electronegativity. A water molecule has two hydrogens. These hydrogens, bond with the oxygen of another water molecule. The oxygen can bond the 2 hydrogens.Therefore, a water molecule bonds up to 4 water molecules by the hydrogen bond.
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A pendulum and a block hanging at the end of a spring are both carefully adjusted to make one vibration per second while on the Earth's surface. Will the period of vibration of the pendulum or of the block on a spring be affected if they are moved to the Moon?
Answer:
For the pendulum , yes and for the spring ,No
Explanation:
We will examine the two cases,
For pendulum;
[tex]T =2\pi \sqrt{\frac{l}{g} }[/tex]
we see that for a pendulum, the period depends on the gravitational acceleration of the region it is. so the period for earth will differ compared to that of the moon.
For a spring;
[tex]T=2\pi \sqrt{\frac{m}{k} }[/tex]
form the equation above is obvious that the period of a spring in vibration is independent of gravitational acceleration of the region it is.
The mass of the bob has no effect on the motion of a pendulum; the period of vibration is determined by the pendulum's length and the acceleration due to gravity.
The movement of the pendula will not differ at all because the mass of the bob has no effect on the motion of a simple pendulum. The pendula are only affected by the period (which is related to the pendulum's length) and by the acceleration due to gravity.
When we look into the night sky, we notice that there are stars dotted across the landscape. We also notice that there are regions of darkness. Knowing that there are more stars in the universe than there are grains of sand on Earth, which of the following statements best explains the regions of darkness in our night sky?
Answer: these regions of darkness are due to no stars being in these regions of the night sky
Suppose you want to determine the electric field in a certain region of space. You have a small object of known charge and an instrument that measures the magnitude and direction of the force exerted on the object by the electric field. How would you determine the magnitude and direction of the electric field if the object were (a) positively charged and (b) negatively charged? (a) The object has a charge of +20.0μC and the instrument indicates that the electric force exerted on it is
40.0μN due east. What are the magnitude and direction of the electric field? (b) What are the magnitude and direction of the electric field if the object has a charge of −10.0μC and the instrument indicates that the force is 20.0μN due west?
Answer:
2 N/C direction of the force
-2N/C opposite to the direction of the force
Explanation:
E = Electric field
q = Charge
Electrical force is given by
[tex]F=Eq\\\Rightarrow E=\dfrac{F}{q}\\\Rightarrow E=\dfrac{40}{20}\\\Rightarrow E=2\ N/C[/tex]
The magnitude of the force is 2 N/C
The force acting on the charge is positive so the direction of the electric field is positive.
[tex]F=Eq\\\Rightarrow E=\dfrac{F}{q}\\\Rightarrow E=\dfrac{20}{-10}\\\Rightarrow E=-2\ N/C[/tex]
The magnitude of the force is 2 N/C
The direction of the electric field is negative and opposite to the direction of the force as the charge is negative.
To determine the magnitude and direction of an electric field, use the formula E = F/Q. For a positively charged object, the electric field has the same direction as the force. For a negatively charged object, the electric field has the opposite direction of the force.
Explanation:To determine the magnitude and direction of an electric field given the charge of an object and the force exerted on it, you can use the formula: E = F/Q, where E is the electric field, F is the force, and Q is the charge.
For a positively charged object (+20.0μC) with a force of 40.0μN due east: The electric field E = F/Q = (40.0μN)/(20.0μC) = 2.0 N/C. The direction of the electric field is in the same direction as the force, due east.
For a negatively charged object (-10.0μC) with a force of 20.0μN due west: The electric field E = F/Q = (20.0μN)/(-10.0μC) = -2.0 N/C. The direction of the electric field is in the opposite direction of the force, due east, as per the convention that electric fields are directed away from positive charges or towards negative charges.
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An out-of-control train is racing toward the Metropolis terminal train station - only Superman can help. The train has a mass of 75000 kg, and Superman has a mass of 115 kg. If the train has a velocity of 35 m/s, how fast does Superman have to fly in the opposite direction to stop it in a totally inelastic steel-Man-of-Steel collision?
Answer:
22826.09 m/s
Explanation:
From the law of conservation of momentum,
Sum of momentum before collision = sum of momentum after collision.
For an inelastic collision, the train and the superman have a common velocity
Note: For the superman to stop the train in an opposite direction, the common velocity after collision is zero, and such the total momentum after collision is zero
Therefore,
MU + mv = 0
MU = - mu............................................ Equation 1
Making u the subject of the equation
u = -MU/m......................................... Equation 2
Where M = mass of the train, U = initial velocity of the train, m = mass of the super man, u = initial velocity of the superman.
Given: M = 75000 kg, U = 35 m/s, m = 115 kg.
u = -(75000×35/115)
u = -22826.09 m/s
Note: The velocity is negative because the direction of the superman is opposite the direction of the train.
Hence the superman have to fly 22826.09 m/s in the opposite direction
Using the principle of conservation of momentum, Superman needs to fly approximately at a velocity of 22826 m/s in the opposite direction to stop the train.
Explanation:To stop the train, Superman needs to exert a force equal to the force being exerted by the train in the opposite direction. Using Newton's second law (F=ma), we can calculate the force needed to stop the train. The force needed can be found by multiplying the mass of the train by its acceleration, which is the change in velocity divided by the time taken to stop. In this case, the initial velocity of the train is given as 35 m/s and it needs to come to a stop, so the change in velocity is 35 m/s.
The question is asking how fast Superman must fly in the opposite direction to stop a moving train using the physics principle of conservation of momentum. In Physics, momentum is calculated using the equation momentum = mass * velocity. Since the train and Superman will collide and stop (an inelastic collision) total momentum before the collision should equal total momentum after the collision. Thus, the velocity of Superman equals (mass of train * velocity of train)/ mass of Superman, i.e., (75000 kg * 35 m/s) / 115 kg which is approximately 22826 m/s in the opposite direction.
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Two blocks of masses M and 3M are placed on a horizontal, frictionless surface. A light spring is attached to one of them, and the blocks are pushed together with the spring between them. A cord holding them together is burned, after which the block of mass 3M moves to the right with a speed of 2.4 m/s. What is the speed of the block of mass M?
Answer:
The speed of the mass M is 7.2 meters per second
Explanation:
In this case because there aren't external forces on the system blocks-spring and the spring is light we should apply the conservation of linear momentum (P) that states:
[tex]\overrightarrow{p}_{f}+\overrightarrow{p}_{i}=0 [/tex] (1)
Momentum is mass (m) times velocity (v) ([tex] \overrightarrow{p}=m\overrightarrow{v}[/tex] (2)) and Initial momentum [tex] \overrightarrow{p}_{i} [/tex] is zero because the blocks are released form rest, so (1) is:
Using (2) on (1):
[tex]\overrightarrow{p}_{f}=M\overrightarrow{v_{M}}+3M\overrightarrow{v_{3M}}=0 [/tex] (3)
It's important to note that momentum and velocity are vector quantities so we should take care of directions, assuming right direction as positive, velocity of 3M mass is positive, and velocity of M mass is negative, (3) is:
[tex]M(-v_{M})+3M(v_{3M})=0 [/tex]
solving for [tex]v_{M}[/tex]
[tex] M(v_{M})=3M(v_{3M})[/tex]
[tex] v_{M}=\frac{3M(v_{3M})}{M}=\frac{3(2.4)}{1}[/tex]
[tex]v_{M}=7.2\frac{m}{s} [/tex]