Therefore, the distance over which the force acts is 20 meters.
explain about kinetic energy ?The initial kinetic energy of the object is zero since it is at rest. The work done on the object by the applied force is equal to the change in its kinetic energy:
[tex]W = ΔK[/tex]
where W is the work done and [tex]ΔK[/tex] is the change in kinetic energy.
The work done by the force can be found using:
[tex]W = Fd[/tex]
where F is the force applied and d is the distance over which the force acts.
Since the object starts from rest, we can use the equation for the work-energy principle:
[tex]W = Kf - Ki[/tex]
where Kf is the final kinetic energy and Ki is the initial kinetic energy.
Setting these two expressions for W equal to each other, we have:
[tex]Kf - Ki = Fd[/tex]
Substituting the given values, we have:
[tex]Kf - 0 = (25 N) dKf = 25d[/tex]
But we also know that the final kinetic energy is[tex]5.0 x 10^2 J[/tex], so:
[tex]5.0 x 10^2 J = 25d[/tex]
d = 20 meter
Therefore, the distance over which the force acts is 20 meters.
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A woman normally weighs 125 lb. If she is standing on a spring scale in an elevator that is traveling downward, but slowing down, the scale will read.
The reading on the spring scale will depend on the acceleration of the elevator and the direction of that acceleration.
If the elevator is traveling downward but slowing down (i.e., accelerating in the upward direction), the scale will read less than the woman's normal weight of 125 lb. This is because the upward acceleration of the elevator reduces the effective weight of the woman, making her appear lighter on the scale. To determine the reading on the scale, you would need to know the acceleration of the elevator at that particular moment. If the elevator is slowing down at a rate of, say,[tex]2 m/s^2,[/tex]then the scale would read:
Weight = mass x acceleration due to gravity
Weight =[tex]56.7 kg x (9.81 m/s^2 - 2 m/s^2)[/tex]
Weight =[tex]56.7 kg x 7.81 m/s^2[/tex]
Weight = [tex]442.5 N[/tex]
Converting this to pounds, the reading on the scale would be approximately:
Weight = [tex]442.5 N x (1 lb / 4.448 N)[/tex]
Weight[tex]≈ 99.4 lb[/tex]
So, the scale would read approximately 99.4 lb, which is less than the woman's normal weight of 125 lb.
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When you toss a ball straight up, what happens to its velocity while it is traveling upward?
Answer:
Explanation:The object slows down as it moves upward until it reaches a maximum height, at which time the velocity is zero. Then the velocity increases as the object falls toward the ground.
if 120 waves produced per minute find the frequency
The frequency of the wave, given that 120 waves were produced per minutes is 2 Hertz
How do I determine the frequency of the wave?Frequency is defined as the number of complete oscillations made in 1 second.
From the question given above, the following were obtained:
Frequency (in per minute) = 120 waves per minuteFrequency (in per second) =?Thus, to obtain the frequency (in per second), we shall convert 120 waves per minute to per second. Details below:
1 wave per minute = 1/60 wave per second
Therefore,
120 wave per minute = 120 × 1/60
120 wave per minute = 2 waves per second
120 wave per minute = 2 Hertz
Thus, we can conclude from the above calculation that the frequency is 2 Hertz
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Two blocks are connected by a string as shown. The inclination of the ramp is theta = 35 degrees while the masses of the blocks are m1=2.1kg and m2=11kg. Friction is negligible.Part (a): What is the magnitude of the acceleration of each block in m/s^2?Part (b): What is the tension in the rope in newtons?
(a) The acceleration of each block is zero. (b) The tension in the rope is 97.7 N.
(a) The forces acting on each block are,
For m1,
F_net = T - mg*sin(35)
For m2,
F_net = mg*sin(35) - T
Since the two blocks are connected by a rope, they will have the same acceleration.
T - mgsin(35) = mgsin(35) - T
T = mg*sin(35)
Substituting this value of T,
F_net = T - mg*sin(35)
F_net = mgsin(35) - mgsin(35)
F_net = 0
Therefore, the net force acting on each block in the direction of motion is zero.
(b) To find the tension in the rope,
T = mg*sin(35)
T = (2.1 kg + 11 kg)9.81 m/s^2sin(35)
T = 97.7 N
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• Point A - the instant before the figure drops. It is at rest and the spring is not stretched.
• Point B - an instant when the figure is falling. It is lower than its original position, and
moving downwards, but the spring has not yet begun to stretch.
• Point C - the very last instant for which the figure is falling but the spring has not yet
begun to stretch.
• Point D - an instant when the figure is falling and the spring is stretching.
Point E - the instant at which the figure has reached its lowest position and is
momentarily motionless before rebounding.
Fill out Table 2 below to show how energy is transferred between forms during the
drop. In each box write either Maximum, Zero, Increasing, or Decreasing.
The magnitude of the GPE depends on the position of the object.
How does the GPE change as the object is falling?Some parts of the question appears to be missing but I will try to answer generally.
As an object falls, its gravitational potential energy (GPE) decreases.
Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. The GPE of an object is directly proportional to its mass, the acceleration due to gravity, and its height above a reference level. The formula for gravitational potential energy is:
GPE = mgh
where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object above the reference level.
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A coil of wire made of 500 circular loops of radius r=25.0cm is in a uniform magnetic field B=0.200T. The surface of the loop is initially perpendicular to the magnetic field when it is moved within 0.250s such that the surface of the loop then makes an angle of 45 degrees with respect to the magnetic field.
(a) What is the change in magnetic flux, in Tesla-square meters, on the coil of wire?
(b)What is the induced emf, in Volts, on the coil of wire?
Answer:
1.3 and 2.5
Explanation:
I did mental math
Answer:
(a) The change in magnetic flux is equal to the product of the magnetic field strength, the area of the coil, and the cosine of the angle between the magnetic field and the surface of the loop. Therefore, the change in magnetic flux is equal to 0.200T x (π x (25.0cm)^2) x cos(45°) = 7.85 x 10^-3 Tesla-square meters.
(b) The induced emf is equal to the change in magnetic flux divided by the time taken for the change to occur. Therefore, the induced emf is equal to 7.85 x 10^-3 Tesla-square meters / 0.250s = 3.14 Volts.
A ball strikes the floor for 0.0105 s and experiences a change in momentum of 1.52 kg·m/s. What is the force experienced by the ball?
Answer:The concept of momemtum will be used to solve this question.A moving body's momemtum, which is generally equal to the product of the body's mass and velocity, is a quality that the body has as a result of its mass and motion.
Explanation:
In which direction will heat naturally flow?
from an object at 40°C to an object at 20°C
from an object at 40°C to an object at 40°C
from an object at 40°C to an object at 80°C
from an object at 0°C to an object at 100°C
Heat will naturally flow from an object at 40°C to an object at 20°C.
What is heat?Heat is described as the energy that is transferred from one body to another as the result of a difference in temperature.
Heat will naturally flow from an object at a higher temperature to an object at a lower temperature. So in the above scenario, heat will naturally flow from an object at 40°C to an object at 20°C.
In conclusion, the basic concept of thermodynamics states that heat will flow spontaneously from a higher-temperature body to a lower-temperature body in order to equalize the temperatures of the two bodies.
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Consider a one-dimensional collision that involves a body of mass m1 originally moving in the positive x direction with the speed v0 colliding with a second body of mass m2 originally at rest. The collision could be completely inelastic, with two bodies sticking together, completely elastic, or somewhere in between. After the collision, m1 moves with velocity v1 while m2 moves with velocity v2. If m1 > m2, then ___________.?
If m1 > m2, then the sign of the velocity of m2, v2, will be positive after the collision.
Why is the velocity positive?
This is because in a one-dimensional collision, the momentum of the system is conserved. Before the collision, only m1 has momentum, so the total momentum is mv0. After the collision, the two masses stick together, so the total momentum is (m1 + m2) * v, where v is the velocity of the combined masses.
Conservation of momentum gives:
mv0 = (m1 + m2) * v
Solving for v gives:
v = mv0 / (m1 + m2)
Since m1 > m2, the denominator is larger than the numerator, so v is smaller than v0. Therefore, after the collision, both masses will be moving in the positive x direction, and m2 will have a positive velocity, v2, while m1 will have a smaller positive velocity, v1. The actual values of v1 and v2 depend on the specific details of the collision (e.g., whether it is elastic or inelastic).
So the velocity of m2, v2, will be positive after the collision.
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Again, combining the heat equations with the heat flow equation, we find that the difference in the temperature between the sample (or Polly) and the cold bath followed an exponential decay, i.e., Tdir = (constant) - Setting time equal to 0 tells us that the prefactor (constant) out front simply is the initial temperature difference. Knowing the decay constant from the previous question and the temperature difference at some later time, then, we can find the time it takes for the difference between the sample's (Polly's) internal temperature and the bath's temperature to reach some specific value. According to the data you took at the (possible) crime scene and your answer to the previous problem, determine how many hours (to the nearest hour) Polly has been deceased (in hours, to the nearest hour)? Again, Polly's and the water bath's initial temperatures were 37°C and 2°C, respectively, and the final temperatures you measured were 13°C and 7°C. Hence, you could determine if foul play may have been involved (say, someone had been seen leaving Polly's apartment a certain time before her body was discovered). 18.703 As you are assisting in the investigation, you notice that Polly's apartment has maintained a cozy temperature even though her heat had been turned off and it's a cold winter's day. (Could this be another clue?) One explanation is that her apartment has nice double pane windows, consisting of two glass panes that are each 4-mm thick sandwiching a well-sealed air gap 6-mm thick. In "steady state", the rate that heat flows through a glass pane equals the rate that heat flows through the air gap in the double pane window (otherwise there would be a net heat flow into the air or window, changing its temperature -- whatever flows into one of these materials must flow out to maintain a given temperature). Since the thermal conductivity of still air (0.025 W/(mºC)] is much smaller than the thermal conductivity of glass (0.80 W/(m°C)], the temperature difference across the double pane window is almost entirely over the air gap. (Again, in this steady state, the rate of heat flow through the glass and air are the same for the double pane window, so if the conductivity of air is much smaller than that of glass, the temperature difference across the air must be much larger than that across the glass for these windows.) Considering this, what is the ratio of the rate of heat flow through a cheap window with a single pane of glass 4-mm thick compared to a nicer double pane window with an air gap of 6 mm if the temperature difference across them is the same (and they have the same areas)? Neglect heat leaks at the edges of the windows.
the ratio between the rate of heat flow through a cheap window with a single pane of glass that is only 4 mm thick to a nicer double pane window with an air gap of 6 mm is 76.6667.
K[tex]_{glass}[/tex]=0.80 W/m°C
K[tex]_{air}[/tex]=0.025 W/m°C
Q=[tex]\frac{\triangle T}{R_{Th} }[/tex]
(R[tex]_{Th}[/tex])[tex]_{double pane}[/tex]×Q[tex]_{double pane}[/tex]=(R[tex]_{Th}[/tex])[tex]_{single pane}[/tex]×Q[tex]_{single pane}[/tex]
(R[tex]_{Th}[/tex])[tex]_{double pane}[/tex]=∑[tex]\frac{l}{KA}[/tex]
= [tex]\frac{3}{0.8A} +\frac{7}{0.025 A}+\frac{3}{0.8 A}\\[/tex]
=[tex]\frac{287.5}{A}[/tex]
(R[tex]_{Th}[/tex])[tex]_{single pane}[/tex]=[tex]\frac{3}{0.8A}[/tex]=[tex]\frac{3.75}{A}[/tex]
[tex]\frac{Q_{single pane} }{Q_{double pane}} =\frac{R_{Th}_{double pane} }{R_{Th}_{single pane}}[/tex]
= 76.6667
Heat flow, also known as heat transfer, is the movement of thermal energy from a region of higher temperature to a region of lower temperature. This occurs due to the random motion of atoms and molecules within a material. There are three main mechanisms of heat flow: conduction, convection, and radiation. Conduction is the transfer of heat through a material by direct contact, while convection involves the movement of a fluid (such as air or water) due to temperature differences. Radiation is the transfer of heat through electromagnetic waves, such as from the sun or a fire. Heat flow is a fundamental concept in thermodynamics and plays a critical role in many fields, including engineering, physics, chemistry, and biology.
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Calculate the distance between the center of the earth and the center of the moon at which the gravitational force exerted by the earth on an object is equal in magnitude to the force exerted by the moon on the object
( solution)
At the neutral point, the distance between the Earth's center and the Moon's center is about 399,000 kilometers, or 3.989 x 10⁸ meters.
What is the force of gravity?Planets, stars, and galaxies all move because it is one of the fundamental forces of the universe. According to Newton's law of gravitation, the distance between two objects and their masses determine the magnitude of the gravitational force
We can make use of the fact that the gravitational force between two objects is inversely proportional to the square of the distance between their centers and proportional to the product of their masses to calculate this distance. As a result, we can solve for the distance by setting the force of gravity that the Earth exerts on the object to be equal to the force of gravity that the Moon exerts on the object.
The masses of the Earth and the Moon, M_E and M_M, respectively, and the distance between their centers, d. The following factors determine the Earth's gravitational pull on the object:
F_E is equal to G × M_E × m / (d₂), where m is the mass of the object and G is the gravitational constant. The following factors determine the Moon's gravitational pull on the object:
F_M = G × M_M × m / ((R-d)²)
where R is the distance between the centers of the Earth and Moon
Setting F_E equal to F_M, we get:
G × M_E × m / (d²) = G × M_M × m / ((R-d)²)
Simplifying and solving for d, we get:
d = R × (M_E / (3 × M_M))¹/³
Values for the masses and the radius of the Earth-Moon system (R = 3.844 x 10⁸ meters), we get:
d = 3.989 x 10⁸ meters
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What is the gauge pressure in atm at point p , where the needle meets the wider body of the syringe? the pressure at the exit of the needle is 1. 0 atm.
The water gauge pressure at location P is;
P p = 104525 Pa
We have been provided;
L = 4 cm = 0.04 m needle length
Water's viscosity; = 1 10(-3) Pa
r = 1 mm = 0.001 m Radius
v = 10 m/s is the speed.
The flow rate via a cylindrical pipe may be calculated using Poiseuille's equation for viscous liquid flow.
Q = (ΔP•πr⁴)/(8ηL)
Flow rate is now also written as;
Q = πr²v
Thus;
πr²v = (ΔP•πr⁴)/(8ηL)
This boils down to;
v = (ΔP•r²)/(8ηL)
Inserting the necessary values;
10 = (ΔP × 0.001²)/(8 × 10^(-3) × 0.04)
ΔP = (10 × 8 × 10^(-3) × 0.04)/(0.001²)
ΔP = 3200 Pa
This implies that;
P atm - P p = P
Where;
P p is the water gauge pressure at point P.
P atm is atmospheric pressure, which equals 101325 Pa.
Thus;
P p - 101325 = 3200
P p = 101325 + 3200
P p = 104525 Pa
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Kangaroos have been clocked at speeds of 65 km/h
How far can a kangaroo hop in 3.90 minutes at this speed?
(part a)
How long will it take a kangaroo to hop 0.20 km
at this speed?
(part b)
a) 4225m or 4.225km b) 11.1s
For part a; convert 65km/h to km/min, to do so all you do is divide 65/60 as there are 60 minutes per hour. Afterwards, multiply by 3.90 to find the distance travelled in 3.90mins.
For part b; convert km/h to km/s, in this one we divide 65/3600 as there are 3600 seconds in one hour. Then, using the S = D/T, where S = speed, D = distance and T= time, we isolate for T and get T = D/S. So then we sub for T=0.20/0.018 (0.018 is the product of 65/3600) and we get T=11.1s.
In this problem, you will practice applying this formula to several situations involving angular acceleration. In all of these situations, two objects of masses m1 and m2 are attached to a seesaw. The seesaw is made of a bar that has length l and is pivoted so that it is free to rotate in the vertical plane without friction. Assume that the pivot is attached tot he center of the bar. You are to find the angular acceleration of the seesaw when it is set in motion from the horizontal position. In all cases, assume that m1>m2.
Now consider a similar situation, except that now the swing bar itself has mass mbar.(Figure 2)
Find the magnitude of the angular acceleration ? of the seesaw.
Express your answer in terms of some or all of the quantities m1, m2, mbar, l, as well as the acceleration due to gravity g.
The rotational acceleration and speed are shared by all of the points of a rigid body. As a result, the angular acceleration is positive and the rotation is anticlockwise.
A- 2*[(m1 - m2)/(m1 + m2)] *g/L The angular acceleration is positive and the rotation is anticlockwise. (m1 - m2)/(m1+ m2 + mbar/3) B- 2* *g/L The angular acceleration is positive and the rotation is anticlockwise.
(A) The magnitude of angular acceleration of the seesaw in this case is .
2(m₁-m₂)g÷(m₁+m₂)L
(B) The magnitude of angular acceleration of the seesaw in this case is
(m₁ g-m₂ g)÷(m₁+m₂)L
For a massless sea saw bar, with attached masses at each end, the torque produced due to the masses is,
ω=(m₁+m₂)+1/2
And, moment of inertia of the system of two masses is,
I=(m₁+m₂)L/4
The using the expression of torque as,
Angular acceleration is the term used to describe the temporal pace at which angular velocity varies. Radians per second is the accepted unit of measurement. Therefore, = d d t. Angular acceleration is also known as rotational acceleration.
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Please help, I don't know how to draw a force triangle!!! Please help with explanation!
(a) Equilibrium is a state in which sum of all the forces acting on an object in a particular direction is zero.
(b) The triangle vector is in the image uploaded.
(c) The value of tension 1 and tension 2 are 191.4 N and 160.58 N.
What is meant by equilibrium?
Equilibrium is the condition of a system when neither its state of motion nor its internal energy state tends to change with time.
The value of the tensions, T1 and T2 is calculated as follows;
The sum of the vertical forces is calculated as follows;
T1 sin(50) + T2 sin(40) - 250 sin(90) = 0
0.766T1 + 0.643T2 - 250 = 0
0.643T2 = 250 - 0.766T1
The sum of the horizontal forces is calculated as follows;
-T1 cos(50) + T2 cos(40) + 250 cos(90) = 0
-0.643T1 + 0.766T2 + 0 = 0
0.766T2 = 0.643T1
T2 = (0.643T1) / (0.766)
T2 = 0.839T1
0.643 (0.839T1) = 250 - 0.766T1
0.54T1 + 0.766T1 = 250
1.306T1 = 250
T1 = 250 / 1.306
T1 = 191.4 N
T2 = 0.839T1
T2 = 0.839 x (191.4 N)
T2 = 160.58 N
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At the end of the day, you remember that pulling up on an object will make it easier to slide the object. Using this knowledge you decide to move your 3000 N Grand Piano using a rope. You pull the rope so that it provides an upward force of 900 N and a horizontal force of 1600 N. What is the coefficient of kinetic friction if the piano is being bulled at a constant speed?
The coefficient of kinetic friction is approximately 0.533.
What is the coefficient of kinetic friction?
To find the coefficient of kinetic friction, we can use the equation of the force of friction, which is given by:
f_friction = friction_coefficient x f_norm
where;
f_friction is the force of friction, friction_coefficient is the coefficient of kinetic friction, and f_norm is the normal force.Since the piano is being pulled at a constant speed, the net force on the piano must be zero, which means that the sum of the forces must be equal to zero:
f_net = f_horizontal - f_friction = 0
friction_coefficient = f_friction / f_norm
= (f_horizontal) / (f_norm)
= (1600 N) / (3000 N) = 0.533
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How many g's of force will a nascar driver experience making a 80 m/s turn with a
radius of 200 meters?
3.2 g's
32 g's
2.5 g's
25 g's
3.27 g's of force will be applied to the driver during the turn.
What in science is a force?In science, the term "force" has a particular definition. At this time, it is appropriate to refer to a force as a push or a pull. There is no such thing as a power that something "contains" or "has in it." A force is exerted on one item by another.
We must employ the centripetal acceleration formula to resolve this issue:
a = v² / r
In this case, the velocity is 80 m/s and the radius is 200 meters, so:
a = (80 m/s)² / 200 m = 32 m/s²
To convert this to g's, we divide by the acceleration due to gravity:
32 m/s² / 9.8 m/s²/g = 3.27 g's (rounded to two decimal places)
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During the vietnam war, journalists _____. Select two choices. Called the military's press briefings "five o'clock follies" accepted the u. S. Government's justification for the war could not interview american soldiers while serving did not witness any combat on a firsthand basis.
During the Vietnam War, journalists often referred to the military's press briefings as "five o'clock follies" because they felt that the information provided was often incomplete or misleading.
The two choices that are correct are:
•Called the military's press briefings "five o'clock follies"
•Did not witness any combat on a firsthand basis.
. Additionally, due to the dangers of the conflict, many journalists did not have the opportunity to witness combat on a firsthand basis.
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= 1.2M²₂// then taking a penedy A constant force of 5N ads to 5 sec. on a mass of 5 kg initially at rest. calculate the final momentum!
The final momentum is 25 Kg m/s
What is the momentum?
In physics, momentum is a measure of an object's motion, calculated by multiplying the object's mass by its velocity. Mathematically, momentum is represented by the symbol "p" and can be expressed as:
p = mv
where "p" is momentum, "m" is mass, and "v" is velocity. Momentum is a vector quantity, meaning that it has both a magnitude (the amount of momentum) and a direction (the direction of the motion).
Given that;
Ft = mv - mu
It then follows that;
F = force
m = mass
v and u are the initial and the final velocities
Thus;
5 * 5 = 5v
v = 25/5
= 5 m/s
The final momentum is thus;
5 m/s * 5 Kg
= 25 Kg m/s
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A plane starts from rest and accelerate along the ground before take off.It moves 600 min 12s.Find the distance moved during the 12th seconds
Given,
Initial velocity, u = 0
Distance covered, s = 600m
Time is taken, t = 12s
We know,
[tex]s = ut +[/tex] [tex]1/2 at^{2}[/tex]
[tex]600 = 0*12 + 1/2 (a) (12)^{2}[/tex]
[tex]a = 600 * 2 / (12)^{2} \\a = 100/12\\ = 8.3m/s^{2} \\[/tex]
Uniform acceleration = [tex]8.s m/s^{2}[/tex]
now using,
[tex]v = u + at\\ = 0 + (8.3) (12)\\ = 99.6 m/s[/tex]
Hence, the speed at the end of the 12 sec is 99.6 m/s
The speed at the end of 11 sec = at = (8.3)(11) = 91.3 m/s
Distance covered by the plane in 11 sec =
[tex]2as = v^{2} - u^{2} \\s = v^{2} - u^{2} /\f2a\\= (91.3)^{2} - (0)^{2} / 2(8.3)\\= 425.29m[/tex]
Thus, distance covered during 12th sec = distance covered in 12s - distance covered in 11s = 600 - 425.29 m = 174.71 m
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When light of a certain wavelength is incident on a metal surface no electrons are ejected. Which ONE of the following changes may result in electrons being ejected from the metal surface? A Increase the intensity of the light B
Use light with a much shorter wavelength. C Use metal with a larger work function. D Increase the surface area of the metal.
A wheel is formed from a hoop of mass 2.6 kg
and seven equally spaced spokes, each of mass
0.11 kg. The hoop’s radius is the length
0.73 m of each spoke.
0.11 kg
2.6 kg
0.73 m
Find the moment of inertia of the wheel
about an axis through its center and perpendicular to the plane of the wheel.
Answer in units of kg · m2
. Answer in units
of kg · m2
.
The moment of inertia of the wheel about an axis through its center and perpendicular to the plane of the wheel is 2.09 kg·m^2.
What is the parallel axis theorem?The moment of inertia of the wheel about an axis through its center and perpendicular to the plane of the wheel can be calculated by using the parallel axis theorem, which states that the moment of inertia of a rigid body about any axis is equal to the moment of inertia about a parallel axis through the center of mass plus the product of the mass and the square of the distance between the two axes.
Here in the Question,
First, we need to find the moment of inertia of the hoop about an axis through its center and perpendicular to the plane of the hoop. This is a well-known result from basic mechanics and is given by:
I_hoop = 1/2 * m_hoop * r^2
where m_hoop is the mass of the hoop and r is its radius. Substituting the given values, we get:
I_hoop = 1/2 * 2.6 kg * (0.73 m)^2 = 1.26 kg·m^2
Next, we need to find the moment of inertia of a single spoke about an axis through its center and perpendicular to its length. This is also a well-known result from basic mechanics and is given by:
I_spoke = 1/12 * m_spoke * L^2
where m_spoke is the mass of the spoke and L is its length. Since the spokes are equally spaced around the hoop, we can consider a single spoke and multiply its moment of inertia by 7 to account for all the spokes. Substituting the given values, we get:
I_spoke = 1/12 * 0.11 kg * (0.73 m)^2 = 0.005 kg·m^2
Therefore, the moment of inertia of all the spokes combined is:
I_spokes = 7 * I_spoke = 0.035 kg·m^2
Finally, we can use the parallel axis theorem to find the moment of inertia of the entire wheel about an axis through its center and perpendicular to the plane of the wheel:
I_wheel = I_hoop + I_spokes + 7 * m_spoke * r^2
Substituting the given values, we get:
I_wheel = 1.26 kg·m^2 + 0.035 kg·m^2 + 7 * 0.11 kg * (0.73 m)^2 = 2.09 kg·m^2
Therefore, The wheel's moment of inertia about an axis passing through its center and perpendicular to its plane is 2.09 kg·m^2.
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(iii) The area of the piston is 5.0 x 10-³m². Calculate the weight that is added to the piston.(the initial pressure is 105000 and the final is 140000, the air decreases from 860 cm3 to 645cm3)
The weight added to the piston is 175 N.
What is the weight that is needed?
The weight that is added to the piston can be calculated using the Ideal Gas Law, which states that PV = nRT
where;
P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is temperature.Since the initial pressure, volume, and temperature are known, we can use the Ideal Gas Law to find the number of moles of gas, n.
Then, we can use the equation for pressure force, to find the weight added to the piston.
F = PA
where;
A is the area of the piston, .First, we'll find the initial number of moles of gas:
P1V1 = nRT
n = P1V1 / RT
T = 298 K is the temperature (room temperature)
n = (105000 Pa x 860 cm^3) / (8.31 J/mol.K x 298 K)
Next, we'll find the final number of moles of gas:
P2V2 = nRT
n = P2V2 / RT
n = (140000 Pa x 645 cm^3) / (8.31 J/mol.K x 298 K)
Now, we have the number of moles of gas for both the initial and final conditions, and we can calculate the change in number of moles of gas, ∆n:
∆n = n2 - n1
Finally, we can use the equation for pressure force to find the weight added to the piston:
F = PA
∆F = P2A - P1A
∆F = (140000 Pa - 105000 Pa) x 5.0 x 10^-3 m^2
∆F = 35000 Pa x 5.0 x 10^-3 m^2
∆F = 175 N
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There are various stages in the formation of coal as heat and pressure are increased and moisture content is decreased. These stages, in order, are
bituminous, peat, lignite, anthracite
bituminous, peat, lignite, anthracite
A
peat, lignite, bituminous, anthracite
peat, lignite, bituminous, anthracite
B
peat, lignite, anthracite, bituminous
peat, lignite, anthracite, bituminous
C
lignite, bituminous, anthracite, peat
lignite, bituminous, anthracite, peat
D
anthracite, bituminous, peat, lignite
Correct order in formation of coal as heat and pressure are increased and moisture content is decreased is (B) peat, lignite, bituminous, anthracite.
Peat is the first stage in the formation of coal, and is made up of partially decomposed plant material with a high moisture content. As heat and pressure are increased, the moisture content decreases and the plant material becomes more compressed, leading to the formation of lignite. Lignite is a low-grade coal with a relatively low carbon content, and is often referred to as brown coal.
With further increases in heat and pressure, lignite is transformed into bituminous coal, which has a higher carbon content and is often used for electricity generation. Finally, with even greater heat and pressure, bituminous coal is transformed into anthracite, which is the highest grade of coal and has the highest carbon content.
The stages of coal formation are important to understand because different types of coal have different uses and properties. For example, anthracite is often used for heating because it burns very cleanly and efficiently, while bituminous coal is often used for electricity generation because it has a higher energy content.
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. You are standing on a bathroom scale inside an elevator. Your weight is 140 lb, but the reading of
the scale is 120 lb. The scale reads the magnitude of the normal force. Note: 1 lb = 4.448 N.
a) What is the magnitude and direction of the acceleration of the elevator? {1.40 m/s²}
b) Can you tell whether the elevator is speeding up or slowing down? EXPLAIN.
The magnitude of the acceleration of the elevator is approximately 1.40 m/s², and it is directed downwards.
What is acceleration?Every procedure where the velocity varies is referred to as acceleration. There are only two methods to accelerate because velocity is a function of both speed and direction: changing your speed, changing your direction, or changing both.
Since the scale reads the magnitude of the normal force, we can equate the normal force with the weight of the person:
N = mg
N = (140 lb) * (4.448 N/lb) = 622.72 N
The scale reads 120 lb, which is equivalent to:
N' = (120 lb) * (4.448 N/lb) = 533.28 N
The magnitude of the acceleration can be calculated as:
ma = mg - N'
a = (g * m) - (N' / m) = [(9.81 [tex]m/s^2[/tex]) * (63.5 kg)] - (533.28 N / 63.5 kg) ≈ 1.40 [tex]m/s^2[/tex]
The elevator could be moving downwards at a constant velocity or accelerating downwards at a rate that is less than the acceleration due to gravity.
Thus, 1.40 [tex]m/s^2[/tex] is the magnitude and direction of the acceleration and
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Find the equivalent resistance between points A and B of the resistor combination shown in this figure for the following values: R1=1.1Ω,R2=2.1Ω,R3=3.1Ω,R4=4.1Ω,R5 =4.9Ω. (b) If a potential difference of 11.6V is applied between points A and B, find the potential difference across resistor R4.
(a) The equivalent resistance between points A and B is 16 Ω.
(b) The potential difference across resistor R4 is 3 V.
What is the equivalent resistance between points A and B?
To find the equivalent resistance between points A and B, we can use the formula for the equivalent resistance of a series circuit:
R_eq = R1 + R2 + R3 + R4 + R5
Substituting the given values:
R_eq = 1.1 Ω + 2.1 Ω + 3.1 Ω + 4.1 Ω + 4.9 Ω = 16 Ω
To find the potential difference across resistor R4, we can use Ohm's law.
V = IR
I = V / R_eq
I = 11.6 V / 16 Ω = 0.725 A
Since R4 is in series with the other resistors, the same current flows through R4 as through the rest of the circuit. So we can use Ohm's law to find the voltage across R4:
V_R4 = I x R4
= 0.725 A x 4.1 Ω
= 3 V
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A frictionless ramp forms a 20.0° angle with the horizontal. A 5.00 kg
load rests on the ramp. Calculate the magnitude of the force that will hold
the load stationary on the ramp, and then determine the ideal mechanical
advantage of the ramp using this information.
The force of approximately 16.9 N is needed to hold the load stationary on the ramp.
What is friction?Friction is the force that prevents two solid objects from rolling or sliding over one another.
Although frictional forces, such the traction required to walk without slipping, may be advantageous, they can provide a significant amount of resistance to motion.
Since the ramp is frictionless, the only forces acting on the load are its weight (mg) and the normal force (N) exerted by the ramp perpendicular to the surface.
We can break the weight into two components: one parallel to the ramp (mg sin θ) and one perpendicular to the ramp (mg cos θ).
To keep the load stationary on the ramp, the force applied parallel to the ramp (call it F) must balance the component of the weight parallel to the ramp:
F = mg sin θ
Substituting the given values, we get:
F = (5.00 kg) * (9.81 [tex]m/s^2[/tex]) * sin 20.0° ≈ 16.9 N
Therefore, a force of approximately 16.9 N is needed to hold the load stationary on the ramp.
The ideal mechanical advantage (IMA) of the ramp is the ratio of the length of the ramp (L) to its height (h):
IMA = L/h
Let's say the ramp has a height of h and a base of b. Then:
h = b sin θ
L = b cos θ
Substituting the given angle, we get:
h = b sin 20.0°
L = b cos 20.0°
Dividing L by h, we get:
IMA = L/h = (b cos 20.0°) / (b sin 20.0°) = cos 20.0° / sin 20.0° ≈ 1.16
Thus, the ideal mechanical advantage of the ramp is approximately 1.16.
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A transformer has a primary coil with 175 turns of wire and a secondary coil with 700 turns. An AC voltage source connected across the primary coil has a voltage given by the function
Δv = (200 V)sin(t).
What rms voltage (in V) is measured across the secondary coil?
The rms voltage measured across the secondary coil is 565.68 V.
What does rms value mean?The root mean square (RMS) value of an alternating current (AC) or voltage is the equivalent steady direct current (DC) value that produces the same heating effect or power dissipation in a resistor. In other words, it is the DC voltage or current that would produce the same amount of heat as the AC voltage or current over a given time period.
The rms voltage (V_rms) across the secondary coil can be calculated using the formula:
V_rms,secondary = (N_secondary/N_primary) * V_rms,primary
where N_secondary is the number of turns in the secondary coil, N_primary is the number of turns in the primary coil, and V_rms,primary is the rms voltage across the primary coil.
The rms voltage across the primary coil can be found from the given voltage function:
V_rms,primary = (1/√2) * V_peak,primary
where V_peak,primary = 200 V is the peak voltage across the primary coil.
Substituting the values, we get:
V_rms,primary = (1/√2) * 200 V = 141.42 V
Now, using the formula above, we can calculate the rms voltage across the secondary coil:
V_rms,secondary = (700/175) * 141.42 V = 565.68 V
Therefore, the rms voltage measured across the secondary coil is 565.68 V.
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A jogger runs on the track shown in the figure.
Neglecting the curvature of the corners, what is the distance traveled and the displacement in running from point A to point B?
(part a)
Find the distance and displacement for a complete circuit of the track.
(part b)
A) 130m for distance, 100m for displacement
B)260m for distance, 0m for displacement
Distance is the sum of all movement taken from start to finish, regardless of position or direction. Since we are going from point A, which is halfway through the 30m side, to point B, which is also halfway through another 30m side, we divide both by 2 and add them together to get 30m once more. Then we take into account the long side of the track, measuring 100m, and can decide that the total distance is 130m.
The displacement, however, doesnt take into account the extra 15m travelled on either of the short sides of the track. When talking about displacement, we are only looking at the distance BETWEEN point A and point B, not the real distance travelled to get to them. Think of it as if youve drawn a line between both points and are mesuring that line and that line only. Because that line would have the exact length as the long side of the track, we can decide that the displacement is 100m.
For part B, the distance is easy to find as we just add up all sides of the track. The tricky part is understanding why displacement is zero. Like I said earlier, it's easiest to imagine a line drawn between both points of mesurment when talking about displacement. In this case, we are talking about the jogger leaving from point A and returning to point A. As I'm sure youve guessed, we cannot possibly draw a line between point A to point A, therefore making the displacement 0.
I'm sorry this is a lot of writing, but I, myself, had a lot of difficulty wrapping my head around the concept of displacement and wanted to make sure it was easy to understand. Hope this helps
If the actual mass of the products from the reaction was 120 g , what was the percent yield of the reaction?.
According to the question This gives us a percent yield of 150%.
What is percent yield?Percent yield is a measure used in chemistry to calculate the efficiency of a chemical reaction. It is expressed as a percentage and is calculated by comparing the actual yield of a product obtained in a reaction to the theoretical yield, which is the maximum amount of product that could have been produced.
The percent yield of a reaction is the ratio of the actual yield of the reaction to the theoretical yield of the reaction multiplied by 100.
Therefore, to calculate the percent yield, we need to first calculate the theoretical yield of the reaction. We can do this by multiplying the given mass of reactants, in this case 80 g, by the stoichiometric coefficient of the desired product, which is 1.
This gives us a theoretical yield of 80 g.
Now, to calculate the percent yield, we divide the actual yield, which is 120 g, by the theoretical yield, which is 80 g, and multiply by 100.
This gives us a percent yield of 150%.
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