The electrophorus is a device used to generate static electricity.
When the metal disk of the electrophorus is placed on top of the charged plastic sheet, the charges on the plastic sheet will induce an opposite charge on the bottom of the metal disk and a like charge on the top of the metal disk.
This is due to the fact that opposite charges attract and like charges repel. When the top surface of the metal disk is briefly connected to ground, the like charges on the top of the metal disk will flow to the ground, leaving the metal disk with an opposite charge on the bottom and no charge on the top.
When the metal disk is disconnected from the ground, it will be left with an opposite charge on the bottom and no charge on the top.
This is because the charges on the bottom of the metal disk are attracted to the charges on the plastic sheet and are therefore not free to move to the ground.
If we assume that positive charge is stationary and that negative charge moves, the same process will occur.
The negative charges on the plastic sheet will induce a positive charge on the bottom of the metal disk and a negative charge on the top of the metal disk.
When the top surface of the metal disk is briefly connected to ground, the negative charges on the top of the metal disk will flow to the ground, leaving the metal disk with a positive charge on the bottom and no charge on the top.
When the metal disk is disconnected from the ground, it will be left with a positive charge on the bottom and no charge on the top. This is because the positive charges on the bottom of the metal disk are attracted to the negative charges on the plastic sheet and are therefore not free to move to the ground.
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Object 1 with mass 1=3.25 kg
is held in place on an inclined plane that makes an angle
of 40.0∘
with the horizontal. The coefficient of kinetic friction between the plane and the object is 0.535.
Object 2 with mass 2=4.75 kg
is connected to object 1 with a massless string over a massless, frictionless pulley. The objects are then released.
Calculate the magnitude
of the initial acceleration.
Calculate the magnitude
of the tension in the string once the objects are released.
The magnitude of the initial acceleration of the object is 4.2 m/s².
The tension in the string once the object starts moving is 13.65 N.
What is the magnitude of the initial acceleration?The magnitude of the initial acceleration of the object is calculated by applying Newton's second law of motion as follows;
F(net) = ma
m₂g - μm₁g cosθ = a(m₁ + m₂)
where;
m₁ and m₂ are the masses of the blocksg is acceleration due to gravityμ is coefficient of frictionθ is the angle of inclinationa is the acceleration(4.75 x 9.8) - (0.535 x 3.25 x 9.8 x cos40) = a(3.25 + 4.75)
33.5 = 8a
a = 33.5/8
a = 4.2 m/s²
The tension in the string once the object starts moving is calculated as;
T = m₁a
T = 3.25 x 4.2
T = 13.65 N
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According to the principal of superposition,
Answer:
the resultant wave is the algebraic sum of all the waves reaching that particular point at a given time.
Explanation:
imagine two or three waves reaching a particular particle x at the same time. The particle will vibrate those waves and give out or transmit a resultant wave which is the algebraic sum of the incoming two waves. If both the waves have the same amplitude and phase, the resultant wave will be amplified. However if the waves have the same amplitude and equal but opposite phase then the resultant wave will be a straight line
football or basketball which one is easier to get you offers
Answer:
basketball
Explanation: cause it is
Answer:
It honestly depends on which one you're better at.
Explanation: I mean that's what I think.
A thin piece of semiconducting silicon will be used to fabricate an electrical device. This layer is 0.10 cm thick and cut into a strip 0.50 cm wide by 1.50 cm long. Electrical contacts are placed at opposite ends of its length. The intrinsic carrier concentration of the silicon at room temperature (300K) is 1.0x1010/cm3 and the bandgap energy is 1.12 eV.
Required:
a. If the application of 1.0 volt to the contacts results in a current of 0.019 amps, what is the resistivity in (ohm-cm) of the material?
b. If the material's conductivity is due to doping with aluminum to a level of [Al]= 1x10^17 atoms/cm^3, what is the resulting conductivity "type" and what is the mobility of these "majority" carriers in this material (assuming that the aluminum is fully ionized - i.e. all Al atoms donated electrons).
We have that for the Question "a)what is the resistivity in (ohm-cm) of the material? b) what is the resulting conductivity "type" and what is the mobility of these "majority" carriers in this material"
Answer:
Resistivity = \(1.754 ohm-cm\)Conductivity = \(6.25*10^{25} cm^3/V-s\)
From the question we are told
This layer is 0.10 cm thick and cut into a strip 0.50 cm wide by 1.50 cm long. The intrinsic carrier concentration of the silicon at room temperature (300K) is 1.0x1010/cm3 and the bandgap energy is 1.12 eV.
A) Resistivity is given as,
\(p = \frac{RA}{l}\)
where,
\(R = \frac{V}{I}\)
Therefore,
\(p = \frac{VA}{Il}\\\\p = \frac{1*(0.1*0.5)}{0.019*1.5}\\\\p = 1.754 ohm-cm\)
B) Conductivity is given as,
\(U = \frac{\rho}{pe}\\\\U = \frac{10^{17}}{10^{10}*1.6*10^{-19}}\\\\U = 6.25*10^{25} cm^3/V-s\)
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A pyramid was built with approximately 2.3 million stone blocks, each weighing 2.4 tons (1 ton = 2,000 lbm). Find the mass of the pyramid in kg.
Total weight in tons
\(\\ \sf\longmapsto 2.3\times 10^6\times 2.4\)
\(\\ \sf\longmapsto 5.52\times 10^6\)
\(\\ \sf\longmapsto 5520000ton\)
1ton=1000kg\(\\ \sf\longmapsto 5520000\times 1000\)
\(\\ \sf\longmapsto 5520000000kg\)
\(\\ \sf\longmapsto 5.52\times 10^9Kg\)
.A 7.5 kg bowling ball would require what force to accelerate it down an alleyway at a rate of
3.2 m/s² down the alley
Newton's second law tells us that force is directly proportional to mass and acceleration, such that:
F = m aWhere force is measured in newtons (N).
The three fundamental laws of Newton are:
Law of inertia: every body resists change.Force Law: Force equals mass times acceleration.Law of action/reaction: every action will have a particular reaction.Newton's laws are fundamental to understanding the interaction between bodies. Today they are still valid, although at the atomic level it has some exceptions that quantum mechanics studies.
A 7.5 kg bowling ball would require what force to accelerate it down an alleyway at a rate of 3.2 m/s² down the alley
Data:
m = 7.5 kg
F = ?
a = 3.2 m/s²
The formula to calculate the force is: F = m * a
We clear, but in this case it is not necessary, since we only want to calculate the force.
F = m * a F = 7.5 kg * 3.2 m/s² F = 24 NThe force you need to accelerate down the alley is 24 Newtons.
A circuit is built based on this circuit diagram.
What is the equivalent resistance of the circuit?
0.61 Ω
Ο 1.6 Ω
7.5Ω
Ο 18 Ω
12V
3.0 Ω.
6.0 Ω
9.Ο Ω.
Will mark brainlyest. No “links” I don’t want them
\(\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}\)
Actually Welcome to the concept of resistors,
The equivalent circuit is given as,
1/Rp = 1/3 + 1/6 + 1/9
1/Rp = 6+3+2/18
1/Rp = 11/18
Rp = 18/11 ==> 1.63 ==> 1.6 ohms
hence the equivalent resistance of the circuit is 1.6 ohms
The equivalent resistance of the circuit is 1.6Ω. The correct option is B.
What is Ohm’s law?Ohm’s law state that ” At constant temperature, the current (I) flowing through a conductor is directly proportional to the potential difference(V) across the two endpoints of the given conductor.”
I.e V ∝ I
V=IR
Where V= potential difference across the conductor.
I = current flowing through the conductor.
R= constant pf proportionality i.e resistance which unit is ohm(Ω).
There are two ways we can connect the resistors.
(i) series connection
If a number of resistors are said to be connected in series When the same current (I) flows through them.
Let R1, R2, and R3 be the resistors connected in series.
Then the R equivalent is
Req=R1+R2+R3
(ii) parallel connection
A number of resistors are said to be connected in parallel when the same potential difference(V) exists across each of them.
Let R1, R2, and R3 be the resistors connected in parallel.
Then the R equivalent is
1/Req=1/R1+1/R2+1/R3
In this question,
The three resistance connected in parallel by applying the above formula we get,
1/Req=1/R1+1/R2+1/R3
1/Req = 1/3 + 1/6 + 1/9 ................. (∵R1=3Ω,R2=6Ω AND R3=9Ω)
1/Req =11/18
Req=18/11
Req=1.6363Ω
Req≈1.6Ω
Therefore, The equivalent resistance of the circuit is 1.6Ω.
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A car traveled a distance of 30 km in 20 minutes (1/3 hours). What was the
speed of the car?
A. 90 km/hr
OB. 60 km/hr
O C. 30 km/hr
D. 10 km/hr
Help me pleaseee!!
Would appreciate ^^
**BRAINLIST, thanks and
points***
The battery has an internal resistance of 2.50
4.1 Show that the resistance of the 6.2 V, 4.5 W lamp at its working potential difference
(pd) is about 9.
Look at photo for more info
4.2 The terminal pd across the battery is 6.2 V.
Calculate the emf of the battery.
rope
Pulleys P and M are frictionless so that the tension in the rope attached to A is equal to the weight of A
A weighs 35 N and the weight of moveable pulley M is negligible.
Calculate the tension in the horizontal cable C when the gate is closed.
tension
3.3 Pulley M is pulled to the left as the gate is opened.
10/36
Explain why this increases the tension in the horizontal cable C.
The resistance of working potential difference of the 6.2 V, 4.5 W lamp is 8.54 ohm. When terminal pd across the battery is 6.2 V, the emf of the battery is 8.01 V.
What is resistance?The opposition that a substance provides to the flow of electric current is referred to as resistance. The uppercase letter R represents it. The ohm is the standard unit of resistance, which is sometimes written as a word and sometimes represented by the uppercase Greek letter omega. Resistance is a measure of an electrical circuit's resistance to current flow. Resistance is measured in ohms, which is represented by the Greek letter omega ().
Here,
r=2.5 ohm
V= 6.2 volts
P=4.5 watt
P=V²/R
R=V²/P
R=6.2*6.2/4.5
R=8.54 ohm that is about 9 ohm.
I=V/R
I=0.726 A
EMF=V+Ir
=6.2+0.726*2.5
=6.20+1.81
=8.01 volts
The resistance of the 6.2 V, 4.5 W lamp at its working potential difference is 8.54 ohm. The emf of the battery when terminal pd across the battery is 6.2 V is 8.01 V.
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At a sports car rally, a car starting from rest accelerates uniformly at a rate of 9.0m/s² over a straight-line distance of 100m. The time to beat is 4.5s.
a Does the driver do it?
b. If not, what must the acceleration be to do so?
Answer:
The driver does not do it. The acceleration must be greater than 9.0m/s² in order to beat the time of 4.5s. The acceleration must be calculated using the equation a = (d/t)², where a is the acceleration, d is the distance, and t is the time. In this case, a = (100/4.5)², which is equal to approximately 27.78m/s². Therefore, the acceleration must be greater than 27.78m/s² in order to beat the time of 4.5s.
Explanation:
An electric bulb is rated 220 V and 100 W. When it is operated on 110 V, the
power consumed will be-
(a) 100 W
(b) 75 W
(c) 50 W
(d) 25 W
Answer:
50 W
Explanation:
Case 1
Power = V * I
100 = 220 * I
I = \(\frac{100}{220}\) A
Case 2
P = V * I
P = 110 * \(\frac{100}{220}\)
P = 50 W
I think the answer is 50 W
Hope it helps
Two identical billiard balls are rolling toward each other at the same speed. What will be true after they collide head–on?
They will both stop rolling immediately after the collision.
One ball will stop rolling as the other bounces backward at a slower speed.
They will both bounce back at a faster speed after the collision.
They will both bounce back at the same speed they had before the collision.
Answer:
After the head-on collision, both identical billiard balls will bounce back at the same speed they had before the collision. This is because of the conservation of momentum, which states that the total momentum of a closed system remains constant if no external forces act on it. In this case, the two billiard balls are a closed system, and their total momentum before the collision is equal and opposite to their total momentum after the collision. Therefore, they will both bounce back with the same speed they had before the collision.
Explanation:
what metric unit would you use to measure the weight of an elephant
Answer:
kilograms
Explanation:
Which part of a road vehicle must be tested to ensure that there is sufficient friction to stop the vehicle in an emergency?
The part of a road vehicle which must be tested to ensure that there is sufficient friction to stop the vehicle in an emergency is the tyre.
What is Friction?This is referred to as a force that resists the motion of one object against another when they roll or slide against each other.
When dealing with braking, the main factor is to have sufficient friction between the road surface and tyre to bring the vehicle to a standstill. If the tyres are wornout there won't be enough friction to make the vehicle stop during emergencies which is therefore the reason why it was chosen as the correct choice.
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A Ping-Pong ball is shot into a circular tube that is lying flat (horizontal) on a table-top.
Figure attached.
When the Ping-Pong ball exits the tube, which path will it follow in the figure?
d
a
c
b
e
Answer:
e
Explanation:
At the instant shown in Figure 3, the blocks are moving toward each other with the same speed of 0.35 m/s. The blocks collide 0.50 seconds later. What is the speed of the two=block system's center of mass just before the blocks collide?
Answer:
The blocks c
Explanation:
A swimmer bounces straight up from a diving board and falls feet first into a pool. She starts with a velocity of 4.00 m/s, and her takeoff point is 1.90 m above the pool.
Required:
a. What is her highest point above the board?
b. How long a time are her feet in the air?
c. What is her velocity when her feet hit the water?
Answer:
a = 1.152s
b = 0.817 m
c = 7.29m/s
Explanation: let the following
From the first equation of linear motion
V = u+at..........1
parameters be represented as :
t = Time taken
v = Final velocity
a = Acceleration due to gravity = 9.8m/s²
u = Initial velocity = 4 m/s
s = Displacement
V = 0
Substitute the values into equation 1
0 = 4-9.8(t)
-4 = -9.8t
t = 4/9.8
t = 0.408s
From : s = ut+1/2at^2.........2
S = 4×0.408+0.5(-9.8)×0.408^2
S= 1.632-4.9(0.166)
S = 1.632-0.815
S = 0.817m
Her highest height above the board is 0.817 m
Total height she would fall is 0.817+1.90 = 2.717 m
From equation 2
s = ut+1/2at^2
2.717 m = 0t+0.5(9.8)t^2
2.717 m = 0+4.9t^2
2.717 m = 4.9t^2
2.717/4.9 = t^2
0.554 =t^2
t =√0.554
t = 0.744s
Hence, her feet were in the air for 0.744+0.408seconds
= 1.152s
Also recall from equation 1
V= u+at
V = 0+9.8(0.744)
V = 7.29m/s
Hence, the velocity when she hits the water is 7.29m/s
Finally,
a = 1.152s
b = 0.817 m
c = 7.29m/s
what are the effects of cooling on the physical properties of a substance
When the liquid cools down, it loses heat energy.
What is the physical effect of cooling on liquid?As the liquid cools, it loses heat energy. As a result, its particles slow down in movement and come closer to one another. Attractive forces begin to hold particles and the crystals of a solid form.
If water is cooled, it can change into ice. If ice is warmed, it can change into a liquid state. Heating a substance makes the molecules move very fast whereas cooling a substance makes the molecules move very slowly.
Heating a liquid increases the speed of the molecules present in it. An increase in the molecule's speed competes with the attraction between molecules and results in the molecules moving apart whereas Cooling a liquid decreases the movement of the molecules.
So we can conclude that the liquid cools down when it loses heat energy.
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what are beats
a. periodic fluctuations in the velocity of sound waves
b. periodic fluctuations in the wavelength of sound waves
c. periodic fluctuations in the intensity of sound waves
d. periodic fluctuations in the frequency of sound waves
Beats can be defined as the periodic fluctuations in the frequency of sound waves. That is option D
What are sound waves?Sound waves are those waves that are produced by the vibration of an object whose energy is usually propagated through a medium.
When two sound waves of different frequencies meets, a periodic variation that occurs is called beats.
Therefore, Beats can be defined as the periodic fluctuations in the frequency of sound waves.
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What is the temperature change of The water
A motorcycle stoop is at a traffic light, when the light turns green, the motorcycle accelerates to a speed of 78 km/h over a distance of 50 m. What is the average acceleration of the motorcycle over this distance?
The average acceleration of the motorcycle over the given distance is approximately 9.39 m/s².
To calculate the average acceleration of the motorcycle, we can use the formula:
Average acceleration = (final velocity - initial velocity) / time
First, let's convert the final velocity from km/h to m/s since the distance is given in meters. We know that 1 km/h is equal to 0.2778 m/s.
Converting the final velocity:
Final velocity = 78 km/h * 0.2778 m/s = 21.67 m/s
Since the motorcycle starts from rest (initial velocity is zero), the formula becomes:
Average acceleration = (21.67 m/s - 0 m/s) / time
To find the time taken to reach this velocity, we need to use the formula for average speed:
Average speed = total distance/time
Rearranging the formula:
time = total distance / average speed
Plugging in the values:
time = 50 m / 21.67 m/s ≈ 2.31 seconds
Now we can calculate the average acceleration:
Average acceleration = (21.67 m/s - 0 m/s) / 2.31 s ≈ 9.39 m/s²
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A motorcycle, travelling cast, starts from rest, moves in a straight line with a constant acceleration and covers a distance of 64 m in 4 s.Calculate a) Its acceleration b) Its final velocity c) At what time the motorcycle had covered half the total distance d) What distance the motorcycle had covered in half the total time.
The motorcycle had covered a distance of 16 meters in half the total time.
a) To calculate the acceleration, we can use the formula:
a = (v - u) / t
where a is the acceleration, v is the final velocity, u is the initial velocity (which is 0 since the motorcycle starts from rest), and t is the time.
Given:
u = 0 m/s (initial velocity)
v = ? (final velocity)
t = 4 s (time)
s = 64 m (distance)
Using the equation of motion:
s = ut + 1/2at^2
We can rearrange the equation to solve for acceleration:
a = 2s / t^2
a = 2(64) / (4)^2
a = 128 / 16
a = 8 m/s^2
Therefore, the acceleration of the motorcycle is 8 m/s^2.
b) To find the final velocity, we can use the formula:
v = u + at
v = 0 + (8)(4)
v = 32 m/s
Therefore, the final velocity of the motorcycle is 32 m/s.
c) To determine the time at which the motorcycle had covered half the total distance, we divide the total distance by 2 and use the formula:
s = ut + 1/2at^2
32 = 0 + 1/2(8)t^2
16 = 4t^2
t^2 = 4
t = 2 s
Therefore, the motorcycle had covered half the total distance at 2 seconds.
d) To calculate the distance covered in half the total time, we use the formula:
s = ut + 1/2at^2
s = 0 + 1/2(8)(2)^2
s = 0 + 1/2(8)(4)
s = 0 + 16
s = 16 m
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6. A 25 g sample of iron (initially at 800.00°C) is dropped into 200 g of water (initially at
30.00°C). The final temperature of the system is 40.22°C. Find the specific heat of iron.
90
Answer:
\(c=0.45\ J/g^{\circ} C\)
Explanation:
Given that,
A 25 g sample of iron (initially at 800.00°C) is dropped into 200 g of water (initially at 30.00°C). The final temperature of the system is 40.22°C.
We need to find the specific heat of iron.
It can be calculated as:
Cooler water gains = hot metal loses
mc∆T = - mc∆T
Put all the values,
\(200g(4.184\ J/g^{\circ} C)(T_f-T_i) = -25g(c)(T_f-T_i) \\\\200g(4.184 )( 40.22-30.00) = -25\times (c)\times (40.22-800.00)\\\\8552.096 = 18994.5c\\\\c=\dfrac{8552.096 }{18994.5}\\\\c=0.45\ J/g^{\circ} C\)
So, the specific heat of iron is \(0.45\ J/g^{\circ} C\)
Two parallel rods are each 0.69 m in length. They are attached at their centers to a spring that is initially neither stretched nor compressed. The spring has a spring constant of 130 N/m. When 1200 A of current is in each rod in the same direction, the spring is observed to be compressed by 3.0 cm. Treat the rods as long, straight wires and find the separation between them when the current is present.
Answer:
Explanation:
Let the separation required be d .
Force between rod = 10⁻⁷ x 2 I₁ I₂ L / d
where I₁ and I₂ are current in them , d is distance of separation and L is length of wire .
Force between rod = 10⁻⁷ x 2 x 1200 x 1200 x .69 / d
= .1987 /d
Restoring Force by spring = k x where k is force constant and x is compression .
= 130 x .03
= 3.9 N
For balancing
Restoring Force by spring = Force between rod
.1987 /d = 3.9
d = .1987 /3.9
= .0509 m
= 5.09 cm .
An airbys A380 airliner lands at 30 m/s. Partially loaded, its mass is 480000 kg. The engines apply reverse thrust for 12s to slow the plane to 25 m/s.How much thrust did the engines apply?
To determine the thrust applied by the engines, we can use Newton's second law of motion, which states that force (thrust) is equal to mass times acceleration. In this case, we need to calculate the force required to decelerate the plane from 30 m/s to 25 m/s in 12 seconds.
First, we calculate the change in velocity (∆v):
\(\displaystyle\sf \Delta v=25\,m/s-30\,m/s=-5\,m/s\)
Next, we calculate the acceleration (∆a) using the formula:
\(\displaystyle\sf \Delta a=\frac{\Delta v}{\Delta t}\)
where ∆t is the change in time, which is 12 seconds in this case.
\(\displaystyle\sf \Delta a=\frac{-5\,m/s}{12\,s}\)
Now, we can determine the force (thrust) applied by the engines using Newton's second law:
\(\displaystyle\sf F=m\cdot a\)
where m is the mass of the airplane, which is 480000 kg.
\(\displaystyle\sf F=480000\,kg\cdot \left(\frac{-5\,m/s}{12\,s}\right)\)
Calculating the result:
\(\displaystyle\sf F=-200000\,N\)
Therefore, the engines applied a thrust of -200000 Newtons (N) to decelerate the plane. The negative sign indicates that the thrust is in the opposite direction of the motion.
What is the function of the Brachistochrone curve ?
Answer:
The brachistochrone curve is an idealized curve that provides the fastest descent possible.
Explanation:
There is actually an analytical solution to this case or, with some derivation work, we can use the PDE functionality of COMSOL Multiphysics to solve the problem.
Using filters, a physicist has created a beam of light that consists of three wavelengths: 400 nm (violet), 500 nm (green), and 650 nm (red). He aims the beam so that it passes through air and then enters a block of crown glass. The beam enters the glass at an incidence angle of
1 = 43.9°.
The glass block has the following indices of refraction for the respective wavelengths in the light beam.
wavelength (nm) 400 500 650
index of refraction
n400 nm = 1.53
n500 nm = 1.52
n650 nm = 1.51
(a)
Upon entering the glass, are all three wavelengths refracted equally, or is one bent more than the others?
400 nm light is bent the most
500 nm light is bent the most
650 nm light is bent the most
all colors are refracted alike
(b)
What are the respective angles of refraction (in degrees) for the three wavelengths? (Enter each value to at least two decimal places.)
(i)
400 nm
°
(ii)
500 nm
°
(iii)
650 nm
°
I need help with this questionPossible answers for each below1. 0 N 150 N100 N50 N2. leftright neither3. acceleratestay at constant velocity4. unbalanced forcebalanced force
Applying newton's second law:
\(\Sigma Fx=100N-50N=50N_{\text{ }}to_{\text{ }}the_{\text{ }}right\)Now, we can answer the questions.
1.
Answer:
50N
2.
Answer:
Right
3.
Answer:
Accelerate
4.
Answer:
Unbalanced force
When you mix red and blue pigment, you produce the color:
orange
black
red
violet
Answer:
violet
Explanation:
A thin uniform rod has a length of 0.480 m and is rotating in a circle on a frictionless table. The axis of rotation is perpendicular to the length of the rod at one end and is stationary. The rod has an angular velocity of 0.37 rad/s and a moment of inertia about the axis of 3.10×10−3 kg⋅m2. A bug initially standing on the rod at the axis of rotation decides to crawl out to the other end of the rod. When the bug has reached the end of the rod and sits there, its tangential speed is 0.132 m/s. The bug can be treated as a point mass.
(a) What is the mass of the rod?
(b) What is the mass of the bug?
(a) To solve for the mass of the rod, we can use the formula for rotational kinetic energy:
KE = (1/2) * I * w^2
where KE is the rotational kinetic energy, I is the moment of inertia, and w is the angular velocity.
At the beginning, when the bug is at the axis of rotation, the rotational kinetic energy of the rod is:
KE1 = (1/2) * I * w^2 = (1/2) * (3.10×10−3 kg⋅m^2) * (0.37 rad/s)^2 = 0.036 J
When the bug reaches the other end of the rod, the rotational kinetic energy is:
KE2 = (1/2) * I * w^2 = (1/2) * (3.10×10−3 kg⋅m^2) * (0.132 m/s)^2 / (0.480 m)^2 = 3.62×10^-5 J
The change in kinetic energy is due to the work done by the bug as it crawls along the rod. The work done by the bug can be calculated as the product of the force it exerts on the rod and the distance it crawls:
W = F * d
The force the bug exerts on the rod can be calculated using Newton's second law for rotational motion:
τ = I * α
where τ is the torque, α is the angular acceleration, and I is the moment of inertia.
Since the rod is rotating with a constant angular velocity, its angular acceleration is zero, so the net torque on the rod must be zero. This means that the torque exerted by the bug on the rod must be equal and opposite to the torque due to the angular momentum of the rod:
τ_bug = τ_rod
F * d = I * w
F = I * w / d
Substituting the values given, we get:
F = (3.10×10−3 kg⋅m^2) * (0.37 rad/s) / (0.480 m) = 0.0237 N
Now we can use the work-energy principle to find the mass of the rod:
W = KE2 - KE1 = F * d = (1/2) * m * v^2
where m is the mass of the rod and v is the tangential velocity of the bug at the end of the rod.
Substituting the values given, we get:
(1/2) * m * (0.132 m/s)^2 = 3.62×10^-5 J - 0.036 J
Simplifying and solving for m, we get:
m = 0.221 kg
Therefore, the mass of the rod is 0.221 kg.
(b) To find the mass of the bug, we can use the same equation we used to calculate the force it exerted on the rod:
F = I * α / d
where α is the angular acceleration of the rod caused by the bug crawling along it.
Since the rod is a thin uniform rod, its moment of inertia can be calculated as:
I = (1/3) * m * L^2
where L is the length of the rod.
Substituting the values given, we get:
I = (1/3) * (0.221 kg) * (0.480 m)^2 = 0.0202 kg⋅m^2
Now we can calculate the angular acceleration caused by the bug crawling along the rod. Since the rod is rotating with a constant angular velocity, its angular acceleration is given by:
α
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α = (w_f^2 - w_i^2) / (2 * θ)
where w_i is the initial angular velocity of the rod, w_f is the final angular velocity of the rod after the bug has crawled to the end, and θ is the angle through which the bug crawls, which is equal to the length of the rod:
θ = L = 0.480 m
Substituting the values given, we get:
α = (0.132 m/s)^2 / (2 * 0.480 m) = 0.072 rad/s^2
Now we can calculate the force exerted by the bug on the rod:
F = I * α / d = (0.0202 kg⋅m^2) * (0.072 rad/s^2) / (0.480 m) = 0.00303 N
Finally, we can use Newton's second law to find the mass of the bug:
F = m * a
where a is the tangential acceleration of the bug, given by:
a = r * α
where r is the distance from the bug to the axis of rotation, which is equal to the length of the rod minus the distance the bug has crawled, or:
r = L - d = 0.480 m - 0.480 m = 0 m
Therefore, the tangential acceleration of the bug is zero, and its mass is:
m = F / a = 0.00303 N / 0 m/s^2 = undefined
This means that the force exerted by the bug on the rod is not enough to cause any tangential acceleration, and therefore the mass of the bug is negligible compared to the mass of the rod. We can assume that the bug has zero mass for practical purposes.