A 1.20 kg copper rod resting on two horizontal rails 0.90 m apart carries a
current I = 55.0 A from one rail to the other. The coefficient of static friction
between the rod and rails is μs= 0.60.
(a) What is the smallest vertical magnetic field B that would cause the rod to
slide?
(b) Suppose a B field is directed at some angle to the vertical φ, with the current
along the rod directed into the page, as shown. Find an expression for B as a
function of φ for the case when the rod is just on the verge of beginning to slide.
(c) Find the value of φ which yields the smallest value of B that would cause
the rod to slide, together with the corresponding value of B.
Answers
Answer:
Explanation:
(a) In order for the copper rod to slide, the magnetic force on it must be greater than the maximum static friction force. The magnetic force on the rod can be found using the formula F = BIL, where B is the magnetic field, I is the current, and L is the length of the rod. The maximum static friction force can be found using the formula Ff = μsN, where μs is the coefficient of static friction and N is the normal force on the rod.
Since the rod is resting on two rails, the normal force on the rod is equal to its weight, N = mg, where g is the acceleration due to gravity. Therefore, the condition for the rod to slide is:
BIL > μs mg
Solving for B, we get:
B > μs mg / IL
Substituting the given values, we get:
B > (0.60)(1.20 kg)(9.81 m/s^2) / (0.90 m)(55.0 A)
B > 0.077 T
Therefore, the smallest vertical magnetic field that would cause the rod to slide is 0.077 T.
(b) When the rod is on the verge of beginning to slide, the magnetic force on it is equal to the maximum static friction force, F = Ff = μsN. The magnetic force can be expressed as F = BIL, and the normal force can be expressed as N = mg. Therefore, we have:
BIL = μs mg
Solving for B, we get:
B = μs mg / IL
But we also know that the angle between the magnetic field and the vertical is given by φ, so we can express L in terms of φ using the formula L = d/sinφ, where d is the distance between the rails. Therefore, we have:
B = μs mg sinφ / Id
(c) To find the value of φ that yields the smallest value of B, we need to minimize the expression for B with respect to φ. Taking the derivative of B with respect to φ, we get:
dB/dφ = μs mg cosφ / Id sin^2φ
Setting this derivative equal to zero and solving for φ, we get:
tanφ = μs mg / Id
Substituting the given values, we get:
tanφ = (0.60)(1.20 kg)(9.81 m/s^2) / (0.90 m)(3000000 kg)(9.00 x 10^-7 m)
tanφ ≈ 0.12
Taking the arctan of both sides, we get:
φ ≈ 6.87°
Substituting this value of φ back into the expression for B, we get:
B = μs mg sinφ / Id
B ≈ 0.030 T
Therefore, the smallest value of B that would cause the rod to slide is approximately 0.030 T, when the magnetic field is at an angle of 6.87° to the vertical.
Related Questions
A uniform electric field makes an angle of 60.0∘ with a flat surface. The area of the surface is 6.66×10−4m2. The resulting electric flux through the surface is 4.44 N⋅m2/C.
Calculate the magnitude of the electric field.(Express your answer with the appropriate units.)
Answers
Answer:
Explanation:
The electric flux through a surface is given by the equation:
Φ = EAcos(θ)
where Φ is the electric flux, E is the electric field, A is the area of the surface, and θ is the angle between the electric field and the surface normal.
We are given Φ = 4.44 N⋅m2/C, A = 6.66×10−4 m2, and θ = 60.0∘. Substituting these values into the equation above and solving for E, we get:
E = Φ / (Acos(θ))
= 4.44 N⋅m2/C / (6.66×10−4 m2cos(60.0∘))
= 1.62×10^4 N/C
Therefore, the magnitude of the electric field is 1.62×10^4 N/C.
The magnitude of the electric field is 13,320 N/C.
What is electric flux?The electric flux through a surface is defined as the product of the electric field and the area of the surface projected perpendicular to the electric field. Mathematically, we can write:
Φ = EAcos(θ)
where Φ is the electric flux, E is the electric field, A is the area of the surface, and θ is the angle between the electric field and the surface normal.
Here in the Question,
We are given the electric flux Φ = 4.44 N·m^2/C, the area A = 6.66×10^-4 m^2, and the angle θ = 60.0°. We can solve for the magnitude of the electric field E by rearranging the equation as follows:
E = Φ / (A*cos(θ))
Substituting the given values, we get:
E = 4.44 N·m^2/C / (6.66×10^-4 m^2*cos(60.0°))
Simplifying the denominator, we get:
E = 4.44 N·m^2/C / (6.66×10^-4 m^2*0.5)
E = 13,320 N/C
Therefore, 13,320 N/C is the magnitude of the electric field.
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Select in the ticker-timer a frequency of 25 Hz or 50 Hz. Determine the period of the ticker-timer.
Answers
Answer:
The period of a ticker-timer is the time interval between two consecutive dots made by the ticker.
If the frequency of the ticker-timer is 25 Hz, then it makes 25 dots in one second. Therefore, the period of the ticker-timer can be calculated as:
Period = 1/frequency = 1/25 Hz = 0.04 seconds
If the frequency of the ticker-timer is 50 Hz, then it makes 50 dots in one second. Therefore, the period of the ticker-timer can be calculated as:
Period = 1/frequency = 1/50 Hz = 0.02 seconds
So, the period of the ticker-timer is 0.04 seconds for a frequency of 25 Hz and 0.02 seconds for a frequency of 50 Hz
Explanation:
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Find the density of seawater at a depth where
I the pressure atm
at the
the
surface is 1050 kg/m³. Seawater has a bulk
modulus of 2.3 x 10° N/m². Bulk modulus is
defined to be
B =
Po AP
Ap
Answers
Answer:
To find the density of seawater at a certain depth, we need to use the following equation:
P = P0 + ρgh
where:
P0 = pressure at the surface (given as 1 atm = 101325 Pa)
ρ = density of seawater at the depth we're interested in
g = acceleration due to gravity (9.81 m/s^2)
h = depth below the surface
We also need to use the bulk modulus equation to find the change in pressure with depth:
B = (ρ/ρ0)(P-P0)/P
where:
ρ0 = density of seawater at the surface (given as 1050 kg/m^3)
P = pressure at the depth we're interested in
Combining these two equations, we get:
B = (ρ/ρ0)((P0 + ρgh) - P0)/P
B = ρgh/P
ρ = (BP)/(gh)
Substituting the given values, we get:
ρ = (2.3 x 10^9 N/m^2)(101325 Pa)/(9.81 m/s^2)(1050 kg/m^3)(1 atm)
ρ ≈ 1031.4 kg/m^3
Therefore, the density of seawater at a depth where the pressure is 1 atm and the density at the surface is 1050 kg/m^3 is approximately 1031.4 kg/m^3.
A body moving at 50m/s decelerates uniformly at 2/ms? until it comes to rest. What distance does it cover from the time it starts to decelerate to the time it comes to rest.
Answers
Answer:
625
Explanation:
To solve this problem, we can use the following kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s since the body comes to rest)
u = initial velocity (50 m/s)
a = acceleration (-2 m/s^2 since the body is decelerating)
s = distance
We want to find the distance (s) that the body covers from the time it starts to decelerate to the time it comes to rest. We can rearrange the equation to solve for s:
s = (v^2 - u^2) / (2a)
Substituting the values we have:
s = (0^2 - 50^2) / (2 x (-2)) = 625 meters
Therefore, the body covers a distance of 625 meters from the time it starts to decelerate until it comes to rest.
A Car accelerate Cuniformly from) 13 ms -1 to 31ms-1 while entering the motor way Covering the distance 220m
Answers
Answer:
3.84 m/s^2.
Explanation:
To solve this problem, we can use the following kinematic equation:
v^2 = u^2 + 2as
where:
v is the final velocity (31 m/s)
u is the initial velocity (13 m/s)
a is the acceleration (which is assumed to be constant)
s is the distance traveled (220 m)
We want to solve for the acceleration, so we can rearrange the equation as follows:
a = (v^2 - u^2) / 2s
Substituting the given values:
a = (31^2 - 13^2) / (2 x 220)
a = 3.84 m/s^2
Therefore, the acceleration of the car is 3.84 m/s^2.
please rate
When a ball is thrown into the air, its kinetic energy is lowest
A at its highest point.
B. at the moment it is released.
C. as it begins to fall back to the ground.
Answers
What is a force that acts upon a projectile launched into the air?
1. Centripetal
2. Gravity
3. Trajectory
Answers
The force that acts upon a projectile launched into the air is gravity.
What is gravity?Gravity is a fundamental force of nature that causes all physical objects to attract each other. It is the force that pulls objects towards each other, and it is the reason why objects with mass are attracted towards the center of the Earth.
When an object is launched into the air, it is subject to the force of gravity, which pulls the object down towards the Earth. As the object moves through the air, the force of gravity causes it to follow a curved path, known as a trajectory, until it eventually hits the ground. While other forces such as air resistance may also act upon the projectile, gravity is the primary force that determines the path of the projectile.
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A student uses 800 W microwave for three seconds how much energy does a student use
Answers
Answer:
The student use 2400 Joules
Explanation:
From the formula E = pt
p = 800W
t = 3 seconds
=> E = 800*3 = 2400J
10. The energy states of an electron in a hydrogen atom is given by:
�
�
=
−
13.6
�
�
�
2
En=
n
2
−13.6 eV
Which of the following is not a possible energy of an emitted photon of the atom for an electron that is initially at
�
=
4
n=4?
0.66 eV
1.89 eV
2.55 eV
12.8 eV
Answers
Because it is less than the required minimum energy difference of 1.51 eV, the energy of 0.66 eV is not feasible. Hence, 0.66 eV is the correct answer.
When the hydrogen atom's energy in its ground state is 13.6 eV, what is the energy of the third excited state?The electron is first assumed to be in the ground state (n=1) in a hydrogen atom. Hence, the electron's energy in its ground state is 13.6 eV. This means that 12.75eV is needed to transfer electrons from the ground state to the third excited state.
The following equation provides the energy levels:
En = -13.6/n² eV
where n is the main quantum number.
An electron can move from the n=4 level to the n=3, n=2, or n=1 level after initialization. For each of these transitions, the relevant photon energies and energy differences are as follows:
n=4 to n=3: ΔE = En=3 - En=4 = (-13.6/3²) - (-13.6/4²) = 1.51 eV
n=4 to n=2: ΔE = En=2 - En=4 = (-13.6/2²) - (-13.6/4²) = 3.40 eV
n=4 to n=1: ΔE = En=1 - En=4 = (-13.6/1²) - (-13.6/4²) = 10.2 eV
As a result, the released photons could have energies of 1.51 eV, 3.40 eV, or 10.2 eV.
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A gas is contained in a cylinder with a frictionless moveable piston at a pressure of 2.7 * 105 pascals and a volume of 0.04 cubic meters. What is the work done by the gaseous system if the volume is increased to 0.12 cubic meters ?
Answers
The work done by the gaseous system if the volume is increased to 0.12 cubic meters is given as 21,600 joules
How to solve for the workdoneTo find the work done by the gas, we can use the formula:
W = PΔV
where W is the work done, P is the pressure of the gas, and ΔV is the change in volume.
At the initial state, the pressure is P = 2.7 × 10^5 Pa and the volume is V1 = 0.04 m^3. At the final state, the volume is V2 = 0.12 m^3.
The change in volume is ΔV = V2 - V1 = 0.12 m^3 - 0.04 m^3 = 0.08 m^3.
Substituting these values into the formula, we get:
W = PΔV = (2.7 × 10^5 Pa) × (0.08 m^3) = 21,600 J
Therefore, the work done by the gaseous system is 21,600 joules (J).
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Answer:
4.6x10^4 joules
Explanation:
A crate of mass
m = 26 kg
rides on the bed of a truck attached by a cord to the back of the cab as in the figure below. The cord can withstand a maximum tension of 69 N before breaking. Neglecting friction between the crate and truck bed, find the maximum acceleration the truck can have before the cord breaks. (Enter the magnitude of the maximum acceleration in the forward direction.)
m/s2
Answers
Answer:
Explanation:
The maximum tension the cord can withstand is 69 N, so we know that the tension in the cord cannot exceed this value. The tension in the cord is related to the acceleration of the truck through Newton's second law:
ΣF = ma
where ΣF is the net force on the crate, m is the mass of the crate, and a is the acceleration of the truck.
In this case, the only force acting on the crate in the horizontal direction is the tension in the cord. Therefore, we can write:
ΣF = T = ma
where T is the tension in the cord.
We can solve this equation for the acceleration:
a = T/m
We know that the tension cannot exceed 69 N, so the maximum acceleration the truck can have before the cord breaks is:
a = 69 N / 26 kg
a ≈ 2.65 m/s^2
Therefore, the maximum acceleration the truck can have before the cord breaks is 2.65 m/s^2.
What factors would create an ideal circuit?
Answers
An ideal circuit is a theoretical representation of an electrical circuit, where all components are perfect and all parameters such as resistance, capacitance, and inductance are zero.
The ideal circuit also has no energy losses, making it an ideal electrical system. To create an ideal circuit, the following factors must be considered:
1. Perfectly Conductive Wires: The wires and other conductors used in the circuit should be perfect conductors, which means the resistance should be zero. This will ensure that no energy is lost in the form of heat.
2. Zero Inductance: Inductance is a property of a circuit which causes a voltage drop when current flows through it. The ideal circuit should have no inductance so that the current can flow freely.
3. Zero Capacitance: Capacitance is a property in which electric charge builds up when current passes through it. To create an ideal circuit, the capacitance should be zero.
4. Zero Impedance: Impedance is the opposition to the flow of current in an electrical circuit. The ideal circuit should have zero impedance so that the current can flow freely.
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A rock with a mass of 10.0 kg is balanced on top of a large boulder. Describe the forces acting on the rock, and use the concept of forces to explain why it stays on top of the boulder.
Answers
There are two forces acting on the rock: the force of gravity pulling it downward and the force of the boulder supporting it from underneath.
What is the force of gravity?The force of gravity is the gravitational attraction between the rock and the Earth. It pulls the rock downward with a force equal to its weight, which is given by the equation Fg = mg, where Fg is the force of gravity, m is the mass of the rock, and g is the acceleration due to gravity (approximately 9.81 m/s^2).
Why do boulder stays on top?The concept of forces explains why the rock stays on top of the boulder because the forces are balanced. The force of gravity pulling the rock downward is equal and opposite to the force of the boulder supporting it from underneath. As a result, the rock remains in equilibrium, or a state of balance, on top of the boulder. If either force were to change, the equilibrium would be disrupted, and the rock would either fall to the ground or be pushed off the boulder.
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Why do you think the pylon in Figure 24 is designed the way it is, and not in the way shown in Figure 25?
Answers
They are specifically made tο be ideal fοr cοnducting live electrical lines because οf their electrical insulatiοn and mechanical tοughness. A structure called an electric pylοn οf hοt-rοlled steel bevels οr gusset plates.
What kinds οf patterns are used tο create electrical pylοns?Other materials, such as cοncrete and wοοd, may alsο be utilised in additiοn tο steel. Transmissiοn tοwers can be divided intο fοur main categοries: suspensiοn, terminal, tensiοn, οr transpοsitiοn.
Whο was the electrical pylοn's designer?This Central Electricity Bοard held a cοmpetitiοn in 1927, and the winning entry was chοsen by the classical designer Sir Reginald Blοοmfield. He settled οn an A-frame structure with latticewοrk that was οffered by the American cοmpany Milliken Brοthers and is still in use tοday.
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Complete question:
A student uses 800 W microwave for 30 seconds how much energy does a student use
Answers
Answer:
The student used 24000 Joules of energy.
Explanation:
We can use the Energy Power equation to solve this example.
[tex]\sf E=Pt[/tex]
Where
[tex]\sf E[/tex] is the energy in Joules (J)
[tex]\sf P[/tex] is the power in Watts (W)
[tex]\sf t[/tex] is the time in seconds (s)
Numerical Evaluation
In this example we are given
[tex]\sf P=800\\t=30[/tex]
Substituting our given values into the equation yields
[tex]\sf E=800 \cdot 30[/tex]
[tex]\sf E=24000[/tex]
24000 Joules
[tex]\Large\bold{SOLUTION}[/tex]
To calculate the energy used by the student in this scenario, we can use the formula:
[tex]\sf{Energy\: (in\: Joules) = Power\: (in\: Watts) \times Time\: (in\: seconds)}[/tex]
Given that the student uses an 800 W microwave for 30 seconds, we can plug in these values to the formula:
[tex]\sf Energy = 800\: W \times 30\: s = 24,000\: J[/tex]
Therefore, the student uses 24,000 Joules of energy in this scenario.
[tex]\rule{200pt}{5pt}[/tex]
A porter can climb 10 staircase of 30cm each in 10 sec by carrying a 50kg bag. Calculate the power of the porter
Answers
Therefore, the power of the porter is 441,450 J/s, or approximately 441.5 watts.
What is work done?The work done by the porter in lifting the 50 kg bag up the stairs can be calculated as the product of the force applied and the distance moved.
The force applied is the weight of the bag, which is given by:
F = m * g
where m is the mass of the bag and g is the acceleration due to gravity, which is approximately 9.81 m/s². Substituting the given values, we get:
F = 50 kg * 9.81 m/s²
F = 490.5 N
The distance moved by the porter in lifting the bag up one staircase is 30 cm, and the porter climbs 10 staircases in 10 seconds, which gives a speed of:
v = (10 * 30 cm) / 10 s
v = 30 cm/s
The power of the porter is the rate at which work is done, which can be calculated as:
P = W / t
where W is the work done and t is the time taken. Substituting the values, we get:
P = F * d * v / t
P = 490.5 N * 10 * 30 cm * 30 cm/s / 10 s
P = 441,450 J/s
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if an 80 kg person is 5 m away from a 100 kg person, what is the force of gravity between them?
Answers
The force of gravity between the 80 kg person and the 100 kg person, who are 5 meters apart, is approximately 1.07269 × 10^-6 Newtons.
To find the force of gravity between them?The force of gravity between two objects is given by the formula:
F = G(m1*m2)/r^2
Where
F is the force of gravity G is the gravitational constant (6.67430 × 10^-11 N·(m/kg)^2) m1 and m2 are the masses of the two objectsr is the distance between themPlugging in the given values, we get:
F = 6.67430 × 10^-11 N·(m/kg)^2 * (80 kg) * (100 kg) / (5 m)^2
Simplifying this expression, we get:
F = 1.07269 × 10^-6 N
Therefore, the force of gravity between the 80 kg person and the 100 kg person, who are 5 meters apart, is approximately 1.07269 × 10^-6 Newtons.
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Two asteroids are suspended in space 50 meters apart. The masses of the asteroids are 2000000 kg and
3000000 kg.
Answers
Answer:
Explanation:
What is the gravitational force between them?
To calculate the gravitational force between two objects, we can use the formula:
F = G * (m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (6.6743 x 10^-11 N * m^2 / kg^2), m1 and m2 are the masses of the two objects, and r is the distance between them.
Plugging in the given values, we get:
F = (6.6743 x 10^-11 N * m^2 / kg^2) * (2000000 kg) * (3000000 kg) / (50 m)^2
F = 0.8046 N
Therefore, the gravitational force between the two asteroids is approximately 0.8046 N.
Use the data in the table to determine the identities of the two gasses that you found could be components of water. Provide evidence to support your claim.
Answers
The two gases that could be components of water are indeed hydrogen and oxygen.
Evidence to support this claim:
1. The chemical formula for water is H2O, which means that it is composed of two hydrogen atoms and one oxygen atom.
2. The table of elements shows that hydrogen (H) and oxygen (O) are both elements that exist in nature.
3. The atomic mass of hydrogen (1.008) and oxygen (15.999) matches the molecular mass of water (18.015).
4. Water is produced when hydrogen gas (H2) is burned in the presence of oxygen gas (O2), according to the following equation: 2H2 + O2 → 2H2O.
Overall, the evidence supports the conclusion that hydrogen and oxygen are the two gases that could be components of water.
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Before a collision, a 200-kg Honda is driving 30 m/s towards a
600-kg Toyota that is not moving. After the crash, the two cars
are stuck together. What is their velocity?
m/s
Answers
As a result, the combined Honda-Toyota system's post-collision speed is 7.5 m/s.
How can you calculate the entire momentum prior to a collision?The system's center of mass was v/2 before to the collision since one automobile had a velocity of v and the other zero. The total momentum is equal to the entire mass times the velocity of the center of mass, or (2m)(v/2) = mv before and after.
Initial momentum of Honda = m1 * v1
= 200 kg * 30 m/s
= 6000 kg·m/s
Final momentum of combined system = (m1 + m2) * v_final
Setting the two momenta equal to each other, we get:
6000 kg·m/s = 800 kg * v_final
Solving for v_final, we get:
v_final = 6000 kg·m/s / 800 kg
= 7.5 m/s
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Contamination of food in a storage area can be reduced by: making sure that the temperature is kept at 98°F removing all wrapping from food before storage putting cardboard on the floor of the store room to keep food off the floor keeping raw and ready to eat food separated
Answers
Of the options provided, keeping raw and ready-to-eat food separated is likely the most effective way to reduce contamination of food in a storage area.
When raw meat and ready-to-eat foods come into contact with each other, there is a risk of cross-contamination, which can lead to foodborne illness. This can happen if bacteria from the raw meat are transferred to the ready-to-eat food, where they can grow and cause illness.
Keeping raw and ready-to-eat food separated helps to reduce this risk by preventing direct contact between the two types of food. This can be done by storing raw meat on the bottom shelf of a refrigerator or in a separate area from ready-to-eat food in a storage room.
While keeping the temperature at 98°F can help prevent the growth of some types of bacteria, it may not be effective in preventing contamination from other sources. Removing wrapping from food before storage and putting cardboard on the floor can also help with cleanliness and organization, but may not directly address the issue of cross-contamination.
Overall, it is important to use a combination of food safety practices to prevent contamination of food in a storage area. This includes proper storage, handling, and preparation of food, as well as maintaining a clean and organized storage environment.
Convert the BCD number given to its Excess-3 equivalent: 1001 0011 1000.
Answers
To convert a BCD number to Excess-3, we add 3 to each BCD digit.
The BCD number given is: 1001 0011 1000
Adding 3 to each digit, we get:
1011 0100 1111
Therefore, the Excess-3 equivalent of the given BCD number is: 1011 0100 1111.
An athlete whirls a 7.66 kg hammer tied to the end of a 1.4 m chain in a simple horizontal circle where you should ignore any vertical deviations. The hammer moves at the rate of 0.372 rev/s. What is the tension in the chain? Answer in units of N.
Answers
The hammer's centripetal acceleration is therefore 100.59 m/s².
Using an example, what is acceleration?An object has positive acceleration when it is going faster than it was previously. Positive acceleration was demonstrated by the moving car in the first scenario. Positive forward motion is being made by the car.
Hammer mass, m, is 6.55 kg. chain length, including the length of the arms, r = 1.3 m, Hammer's angular velocity is given by the formula: = 1.4 rev/s = 8.79646 rad/s (1 rev = 6.28 rad).
The formula a = V2/r, where V is the transverse velocity of the hammer, yields the centripetal acceleration.
V = r, hence
As a result, a = r²
A = 1.3 x 8.796462, or 100.59 m/s², is obtained by substituting the supplied numbers in the equation above.
The hammer's centripetal acceleration is therefore 100.59 m/s².
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Is this statement is correct ?? According to Newton's 4rd law, Action and reaction never start from the same point.
help me...
Answers
Explanation:
I'm sorry, but the statement you provided is incorrect. There is no such thing as Newton's 4th law. Newton's laws of motion consist of three laws, which are:
An object at rest tends to stay at rest, and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
The acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass.
For every action, there is an equal and opposite reaction.
None of these laws state that action and reaction never start from the same point. However, it is true that the action and reaction forces act on different objects, not necessarily at the same point. This is because Newton's third law states that every action has an equal and opposite reaction, which means that when one object exerts a force on another object, the second object exerts an equal and opposite force back on the first object.
What are some examples of conservation of energy?
Answers
Answer:
power plant
collision
Battery
Burning wood
speaker
Beating drum
HELP ME!!!!If a researcher is designing an electromagnet for a life-saving medical application, which properties of the magnet will she need to take into account?
Select two answers!!
Wether or not magnetic field is constant.
Number of could of conducting wire.
Wether or not domains are present in iron core.
Metal composition of conducting wire.
Answers
Answer:
Number of coils of conducting wire and whether or not domains are present in iron core are the two properties of the electromagnet that the researcher will need to take into account.
Explanation:
The number of coils of conducting wire affects the strength of the magnetic field produced by the electromagnet. More coils will produce a stronger magnetic field, while fewer coils will produce a weaker magnetic field. The researcher will need to determine the appropriate number of coils to produce the desired strength of the magnetic field for the medical application.
The presence of domains in the iron core is also an important consideration. The iron core of the electromagnet helps to concentrate the magnetic field and increase its strength. The domains in the iron core align with the magnetic field produced by the current flowing through the wire, and this alignment reinforces the magnetic field. If the iron core does not have domains, the magnetic field produced by the electromagnet will be weaker. Therefore, the researcher will need to ensure that the iron core has domains to maximize the strength of the magnetic field for the medical application.
Suppose the angles shown in Fig. 5.31 are 52° and 25°. If the left-hand mass is 2.5 kg, what should the right-hand mass be so that it accelerates (a) downslope at 0.64 m/s2 and (b) upslope at 0.76 m/s2?
Answers
Downslope at 0.64 m/s², m = 12.4 kg
Upslope at 0.76 m/s², m = 6.35 kg
Define Mass?In Physics, mass is the most basic property of matter, and it is one of the fundamental quantities. Mass is defined as the amount of matter present in a body. The SI unit of mass is the kilogram (kg). The formula of mass can be written as:
Mass = Density × VolumePart A)
The sum of forces on the left-hand mass
T - mgsin(angle) = ma
T - (2.6) (9.8) (sin 70) = 2.6(.64)
T = 25.6 N
m = left mass.........M = right mass
T - mg×sin70 = ma
Mg×sin16 - T = Ma
Mg×sin16 - mg×sin70 = a×(M+m)
M×g×sin16 - mg×sin70 = Ma + ma
M× (g×sin16 -a) = m× (a + gsin70)
M = m× (a + gsin70) / (g×sin16 -a)
a) a = 0.64
M = 10.98 Kg
b) M = 11.82 kg
For the right-hand mass, the sum of forces...
mgsin(angle) - T = ma
m (9.8) (sin 16) - 25.6 = m (.64)
2.7m - 25.6 = .64m
m = 12.4 kg
Part B)
For the left-hand mass
mgsin(70) - T = ma
(2.6) (9.8) (sin 70) - T = (2.6) (.76)
T = 21.97 N
Then for the right-hand mass
T - mgsin(16) = ma
21.97 - m (9.8) (sin 16) = m (.76)
21.97 - 2.7m = .76m
m = 6.35 kg
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The right-hand mass should be 3.3 kg to accelerate up the slope at 0.76 m/s². To solve this problem, we need to use the principles of Newton's laws of motion and trigonometry.
We know that the force of gravity acting on the mass is equal to its weight, which can be calculated using the formula Fg = mg, where Fg is the force of gravity, m is the mass, and g is the acceleration due to gravity (which is approximately 9.8 m/s²).
To find the force acting down the slope, we need to calculate the component of the weight that acts down the slope, which is given by Fg sin θ, where θ is the angle of the slope. Using the given angle of 52°, we can calculate the force acting down the slope for the left-hand mass as:
Fdown = Fg sin θ
Fdown = (2.5 kg)(9.8 m/s²) sin 52°
Fdown = 18.9 N
To find the required mass for the right-hand mass to accelerate at 0.64 m/s^2 down the slope, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass times its acceleration (F = ma). Therefore, we can calculate the required force for the right-hand mass as:
F = ma
F = (m)(0.64 m/s²)
Since the force acting down the slope is 18.9 N, we can set these two equations equal to each other and solve for the mass:
F = Fdown
(m)(0.64 m/s²) = 18.9 N
m = 29.5 kg
Therefore, the right-hand mass should be 29.5 kg to accelerate down the slope at 0.64 m/s².
To find the required mass for the right-hand mass to accelerate at 0.76 m/s² up the slope, we can use the same approach, but this time we need to use the component of the weight that acts up the slope, which is given by Fg cos θ, where θ is the angle of the slope. Using the given angle of 25°, we can calculate the force acting up the slope for the right-hand mass as:
Fup = Fg cos θ
Fup = (m)(9.8 m/s²) cos 25°
Setting this equal to the force required for the right-hand mass to accelerate up the slope, we get:
Fup = ma
(m)(0.76 m/s²) = (m)(9.8 m/s²) cos 25°
m = 3.3 kg
Therefore, the right-hand mass should be 3.3 kg to accelerate up the slope at 0.76 m/s².
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How did Newton discovered gravity?
Answers
Answer:
Isaac Newton, the English physicist, mathematician, and astronomer, discovered the concept of gravity in the late 17th century. The story of his discovery of gravity is one of the most famous in scientific history.
The most well-known anecdote is that Newton was sitting under an apple tree when an apple fell from the tree and hit him on the head. This event, however, is likely to be a myth created to make the story more memorable. Nonetheless, it is true that Newton began to wonder why objects fall to the ground instead of flying off into space.
Newton's curiosity led him to conduct experiments to understand the behavior of falling objects. He reasoned that the same force that caused an apple to fall to the ground was responsible for holding the moon in orbit around the Earth.
Newton's breakthrough came when he realized that the force that causes objects to fall to the ground is the same force that governs the motion of the planets in the solar system. He described this force as "gravity" and formulated his famous law of universal gravitation, which states that every object in the universe attracts every other object with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them.
Newton's discovery of gravity was a major scientific achievement that revolutionized our understanding of the physical world. It laid the foundation for the development of classical mechanics, and the law of gravitation has since been used to explain a wide range of phenomena in physics, from the motion of planets to the behavior of subatomic particles.
In summary, Newton discovered gravity through a process of curiosity, experimentation, and mathematical reasoning. Although the apple falling on his head is unlikely to be true, his discovery has had a profound impact on our understanding of the universe.
Answer:
Isaac Newton did not "discover" gravity, as it was already known that objects were attracted to each other. However, he did discover the law of universal gravitation, which states that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of their separation distance.
State each of Newton's Laws of Motion and explain how each can be observed during the flight of a space craft, from liftoff until the craft enters space.
Answers
newton 3th law of motion and newton's law of universal gravitation
Answer: 1. Newton's First Law of Motion (Law of Inertia): An object at rest will remain at rest, and an object in motion will remain in motion with a constant velocity unless acted upon by an external force.
During liftoff, the spacecraft is initially at rest. However, the rocket engines generate a force that propels the spacecraft forward and overcomes its initial state of rest. Once the spacecraft is in motion, it will continue to move forward with a constant velocity unless acted upon by other external forces, such as air resistance or gravity.
2. Newton's Second Law of Motion: The acceleration of an object is directly proportional to the force applied to it, and inversely proportional to its mass.
As the rocket engines burn fuel, they generate a force that propels the spacecraft forward. The acceleration of the spacecraft is directly proportional to the force generated by the engines, and inversely proportional to the mass of the spacecraft. As fuel is consumed and the spacecraft becomes lighter, its acceleration will increase, allowing it to reach escape velocity and enter space.
3. Newton's Third Law of Motion: For every action, there is an equal and opposite reaction.
During liftoff, the rocket engines generate a powerful force that propels the spacecraft forward. However, the engines also generate an equal and opposite reaction force, pushing back against the rocket and causing it to shake and vibrate. This force is also responsible for the loud noise and exhaust plumes that are visible during liftoff.
These are the three laws of motion developed by Sir Isaac Newton, and they explain how objects move and interact with one another. They can be observed in the launch and flight of a spacecraft, from the initial state of rest to the forces that drive it forward, to the equal and opposite forces that shake the rocket during liftoff.
Imagine that scientists placed a satellite at the Earth-Moon L1 Lagrangian
point, which is a point between Earth and the Moon where the gravitational
pulls from the two bodies are equal and opposite. What would happen if a
satellite at this position drifted slightly closer to Earth?
O A.
A. The gravitational pull from the Moon would correct the satellite
and bring it back to the Lagrangian point.
OB. The satellite would stop drifting and would remain fixed in this
position because of its tangential velocity.
OC. The satellite would continue to drift toward Earth as Earth's pull
became stronger than that of the Moon.
OD. The gravitational pull from the Sun would eventually pull the
satellite from this point and cause it to directly orbit the Sun.
Answers
Answer:
Explanation:
A. The gravitational pull from the Moon would correct the satellite and bring it back to the Lagrangian point.
At the Earth-Moon L1 Lagrangian point, the gravitational pulls from the Earth and the Moon are balanced, and the satellite is in a stable equilibrium. If the satellite drifted slightly closer to Earth, the gravitational pull from the Earth would become stronger, but the gravitational pull from the Moon would also increase due to its closer distance, and this would correct the satellite's motion and bring it back to the Lagrangian point.