The knot at the junction is in equilibrium under the influence of four forces acting on it. The F force acts from above on the left at an angle of α with the horizontal. The 5.7 N force acts from above on the right at an angle of 50◦ with the horizontal. The 6.2 N force acts from below on the right at an angle of 44◦ with the horizontal. The 6.7 N force acts from below on the left at an angle of 43◦ with the horizontal.
1. What is the magnitude of the force F?
2. What is the angle a of the force F in the figure above?
Answers
The knot is in equilbrium, so there is no net force acting on it. Starting with the unknown force and going clockwise, denote each force by F₁, F₂, F₃, and F₄, respectively. We have
F₁ + F₂ + F₃ + F₄ = 0
Decomposing each force into horizontal and vertical components, we have
F cos(180º - α) + (5.7 N) cos(50º) + (6.2 N) cos(-44º) + (6.7 N) cos(-137º) = 0
F sin(180º - α) + (5.7 N) sin(50º) + (6.2 N) sin(-44º) + (6.7 N) sin(-137º) = 0
Recall that cos(180º - x) = - cos(x) and sin(180º - x) = sin(x), so these equations reduce to
F cos(α) ≈ - 3.22 N
F sin(α) ≈ 4.51 N
(1) Recall that for all x, sin²(x) + cos²(x) = 1. Use this identity to solve for F :
(F cos(α))² + (F sin(α))² = F ² ≈ 30.73 N² → F ≈ 5.5 N
(2) Use the definition of tangent to solve for α :
tan(α) = sin(α) / cos(α) ≈ 1.399 → α ≈ 126º
or about 54º from the horizontal from above on the left of the knot.
(a) The magnitude of the force F acting on the knot is 5.54 N.
(b) The angle α of the force F is 54.4⁰.
The given parameters:
F force at α 5.7 N force at 50⁰6.2 N force at 44⁰6.7 N force at 43⁰The net vertical force on the knot is calculated as follows;
[tex]F_y = Fsin(\alpha) + 5.7 sin(50) - 6.2 sin(44) - 6.7 sin(43)\\\\F_y = F sin(\alpha) -4.51\\\\Fsin(\alpha) = 4.51[/tex]
The net horizontal force on the knot is calculated as follows;
[tex]F_x = -F cos(\alpha) + 5.7 cos(50) + 6.2cos(44) - 6.7cos(43)\\\\F_x = -Fcos(\alpha) + 3.22\\\\Fcos(\alpha) = 3.22[/tex]
From the trig identity;
[tex]sin^2 \theta + cos^ 2 \theta = 1\\\\[/tex]
[tex](Fsin(\alpha))^2 + (Fcos(\alpha))^2 = (4.51)^2 + (3.22)^2\\\\F^2(sin^ 2\alpha + cos^2 \alpha) = 30.71\\\\F^2(1) = 30.71\\\\F = \sqrt{30.71} \\\\F = 5.54 \ N[/tex]
The angle α of the force F is calculated as follows;
[tex]Fsin(\alpha) = 4.51\\\\sin(\alpha) = \frac{4.51}{F} \\\\sin(\alpha ) = \frac{4.51}{5.54} \\\\sin(\alpha ) = 0.814\\\\\alpha = sin^{-1}(0.814)\\\\\alpha = 54.5 \ ^0[/tex]
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Related Questions
Maribel has an iron rod around which she wraps copper wire. She places the device on a table near a compass. What will happen to the compass if she sends current through the copper wire?
A.The needle of the compass will point at a right angle to the device
B. The needle of the compass will point toward the device
C. The needle of the compass will show no effect
D.The needle of the compass will spin in circles
Answers
If Maribel sends current through the copper wire in the iron rod, the needle of the compass will point toward the device.
What is electric current?Electric current is the rate of flow of electric charge.
According to this question, Maribel has an iron rod around which she wraps copper wire. She places the device on a table near a compass.
If Maribel sends current through the copper wire in the iron rod, the needle of the compass will point toward the device because the metallic needle is attracted in the direction of the current.
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What is the value of 4p − 2, when p = 8? 16 24 30 34
Answers
Answer:
30
Explanation:
Plug in p to get 4(8) - 2
32 - 2 = 30
Gravity, momentum, and friction are examples of:
Answers
Answer:
Gravity,momentum & friction are examples of FORCE.
Explanation:
Hope this helps you
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(b) What are the dimensions of a and b in the relation F = a*x^0.5+ bt^2 where F is force, x is distance and t is
time.
Answers
Answer:
It is 5F
Explanation:
For a rocket traveling at 12010 m/s, by what factor does its relativistic momentum differ from its ordinary momentum
Answers
The relativistic momentum of the rocket differ from the ordinary momentum by a factor of 1.2m.
Relativistic momentum of the rocketThe relativistic momentum of the rocket is calculated as follows;
[tex]P = \frac{mv}{\sqrt{1- \frac{v^2}{c^2} } } \\\\P = \frac{m(12010)}{\sqrt{1- \frac{(12010)^2}{(3\times 10^8)^2} } } \\\\P = 12,011.2 m \ (kgm/s)[/tex]
where;
m is mass of the rocketOrdinary momentum of the rocketThe ordinary momentum of the rock is calculated from the product of mass and velocity of the rocket.
P = mv
P = 12010m (kgm/s)
Difference between the two momentumΔP = 12,011.2m - 12,010m
ΔP = 1.2m
Thus, the relativistic momentum of the rocket differ from the ordinary momentum by a factor of 1.2m.
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Define kinetic energy and write a statement about how kinetic energy is affected as velocity increases.
Answers
Answer: Kinetic energy is the energy of mass in motion. Because kinetic energy is proportional to the velocity squared, increases in velocity will have an exponentially greater effect on translational kinetic energy.
Explanation: Google
A moving object's kinetic energy is directly proportional to both its mass and the square of its velocity.
How does kinetic energy gets changed ?
An object with twice as much mass and the same speed will have twice as much kinetic energy, whereas an object with twice as much mass and the same speed will have four times as much kinetic energy.Kinetic energy is the kind of energy an object or particle has because it moves. When a net force is applied to an object, which is work that transfers energy, the object accelerates and gains kinetic energy. A moving object or particle's kinetic energy is a property that is affected by its mass as well as its motion. Translation (movement along a path from one location to another), rotation about an axis, vibration, or any combination of these motions can be the type of motion.In the meter-kilogram-second system, the joule is the energy unit. The kinetic energy of a two-kilogram mass traveling at a speed of one meter per second, which is slightly more than two miles per hour, is one joule, or something like 4.4 pounds on Earth. The unit of energy in the centimeter-gram-second system is the erg, or 10^7 joules, which is the same as the kinetic energy of a mosquito in flight. On the atomic and subatomic scale, smaller units of energy, such as the electron volt, are also utilized in specific contexts.To know more about kinetic energy check this:
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Calculate the current in a circuit if 500 C of charge passes through it in 10 minutes. *
(1 Point)
a) 0.83A
b) 0.083A
c) 8.3A
d) 83A
Answers
Answer:
Choice a. Approximately [tex]0.83\; \rm A[/tex] on average.
Explanation:
The electric current through a wire is the rate at which electric charge flows through a cross-section of this wire.
Assume that electric charge of size [tex]Q[/tex] flowed through a wire cross-section over a period of time [tex]t[/tex]. The average current in that wire would be:
[tex]\displaystyle I = \frac{Q}{t}[/tex].
For this question:
[tex]Q = 500\; \rm C[/tex], whereas[tex]t = 10\; \rm \text{minutes}[/tex].Therefore, the average current in this circuit would be:
[tex]\displaystyle I = \frac{Q}{t} = \frac{500\; \rm C}{10\; \text{minutes}} = 50\; \rm C /\text{minute}[/tex].
However, the units in the choices are all in [tex]\rm A[/tex] (for Amperes.) One Ampere is equal to one [tex]\rm C / \text{second}[/tex]. It will take some unit conversations to change the unit of [tex]I = 50\; \rm C/ \text{minute}[/tex] (coulombs-per-minute) to coulombs-per-second.
[tex]\begin{aligned}I &= 50\; \rm C/ \text{minute} \\ &= \frac{50\; \rm C}{1\; \rm \text{minute}} \times \frac{1 \; \text{minute}}{60\; \rm \text{seconds}} \approx 0.83\; \rm C/ \text{second} = 0.83 \; \rm A\end{aligned}[/tex].
Hence, the most accurate choice here would be choice a.
Which event causes the formation of trenches in Earth’s crust?
magma rising
mantle emerging
volcanoes erupting
lithosphere colliding
Answers
Answer:
D lithosphere colliding
Reason:
Image result for what causes the formation of trenches in Earth’s crust
Trenches are formed by subduction, a geophysical process in which two or more of Earth's tectonic plates converge and the older, denser plate is pushed beneath the lighter plate and deep into the mantle, causing the seafloor and outermost crust (the lithosphere) to bend and form a steep, V-shaped depression.
The formation of trenches in Earth's crust is caused by the collision of lithospheric plates, so the correct answer is "lithosphere colliding."
What are trenches in Earth's crust?Trenches are long, narrow depressions or canyons in the Earth's crust that form at subduction zones, where one lithospheric plate is forced beneath another plate into the Earth's mantle. Trenches are primarily found on the ocean floor, where they can be several kilometers deep and hundreds of kilometers long.
Trenches are formed by the process of subduction, which occurs when one tectonic plate moves beneath another plate. As the denser plate sinks into the mantle, it creates a deep trench in the ocean floor. This process is associated with volcanic activity, as the sinking plate often triggers the melting of rock in the mantle, which can then rise to the surface and form volcanic islands or arcs.
Trenches are important features of the Earth's crust because they provide evidence for the movement and interaction of tectonic plates over time. Additionally, they are often associated with earthquakes and can serve as warning signs of potential seismic hazards in the surrounding region.
Therefore, lithosphere colliding causes the formation of trenches in Earth’s crust.
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What effect does the finite of the black paper have on the field?
Answers
The effect of black papper on the field is that the black paper have a form of chimney effect. Thid is because the black paper heat up the space between the field and the body in order to allow an upward air current like a chimney. This air current adds to the cooling of the field.
Black paper absorb heat from the surrounding and generate it to current flow in the field.
What is a Field?A field refer to a egion in which each point has a physical quantity like time or gravitational or space which are connected and associated with the region.
Therefore, the black paper allow air current flow.
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Discuss the methods of linear measures in Surveying
Answers
Various methods coming under the direct method of linear measurement are:
1 Linear Measurement by Pacing
2 Linear Measurement by Passometer
Linear Measurement by Pedometer
Linear Measurement by Odometer and speedometer
Linear Measurement by Chaining
a person drops two objects from the same height one object weighs 15n and the other weighs 10 n how does the mass of the object relate to the force of gravity on them
Answers
Answer:
Since the gravitational force is directly proportional to the mass of both interacting objects, more massive objects will attract each other with a greater gravitational force. So as the mass of either object increases, the force of gravitational attraction between them also increases.
Explanation:
sorry if this is wrong or is incorrect... but at least I tried right.
fill in the corresponding transcription and translation for each organism and determine the amino acid for which the dna is coded and the organism that would result from their protein synthesis
Answers
The process of transcription and translation forms part of the central dogma of molecular biology which describes protein synthesis from genes.
What is transcription?Transcription is the process whereby RNA molecules are synthesized from DNA.
The RNA produced is messenger RNA written as mRNA
The mRNA produced is used then used to synthesize proteins at the ribosomes in a process known as translation.
Amino acids which are used to make the proteins are code for by three nucleotides known as codons.
Therefore, the process of transcription and translation is used for protein synthesis from genes.
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A motorcycle travels a distance of 420 miles in 8.5 hours. Give the average speed of the motorcycle
Answers
Answer:
As per Provided Information
Distance travelled by motorcycle is 420 miles
Time taken by motorcycle is 8.5 hours
we have been asked to determine the average speed of the motorcycle .
[tex] \bf \: Speed_{(Average)} = \cfrac{total \: distance \: travelled}{time \: taken} [/tex]
Now let's put the given value to find the average speed of motorcycle
[tex] \longrightarrow \sf \: Speed_{(Average)} \: = \cfrac{420}{8.5} \\ \\ \\ \longrightarrow \sf \: Speed_{(Average)} \: = \cfrac{4200}{85} \\ \\ \\ \longrightarrow \sf \: Speed_{(Average)} \: = \cancel\cfrac{4200}{85} \\ \\ \\ \longrightarrow \sf \: Speed_{(Average)} \: = 49.41 \: miles \: per \: hour[/tex]
Therefore,
Average speed of the motorcycle is 49.41 miles per hour .1. Based on the score you got in our previous activity, do you consider yourself physically fit? Explain your answer.
2. Why is it important to be physically fit? 3. What do you think are the implications of having a physically fit body?
4. What can you do to become physically fit?
Answers
Regular exercise and physical activity is responsible for strong muscles and bones.
What can you do to become physically fit?Exercise and physical activity improves respiratory, cardiovascular, and overall health of an individual. Staying active can help in maintaining a healthy weight, reduce your risk of diabetes, heart disease, and reduce risk for cancers so we can conclude that regular exercise and physical activity is responsible for strong muscles and bones.
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Lome people predict that California will sink into the ocean. Is this idea consistent with the theory of plate tectonics?
Answers
Answer:
No!
Explanation:
The sliver of California west of the San Andreas fault is slowly moving northwestward with the Pacific plate; movement is essentially horizontal.
A motorcycle accelerates at 10 m/s2 to reach a final velocity of 50 m/s from rest. How much time passed during the acceleration?
Answers
Answer:
t = 5 s
Explanation:
We'll need this equation:
Vf = Vi + at
Rearranging the equation to solve for time, we get:
t = ( Vf - Vi ) / a
Plugging in what we know, we get:
t = ( 50 m/s - 0 m/s ) / 10 m/s^2
t = 5 s
state and explain parallelogram Law of vector addiction
Answers
Answer:
Parallelogram law of vector addition states that. if two vectors are considered to be the adjacent sides of a parallelogram, then the resultant of the two vectors is given by the vector that is diagonal passing through the point of contact of two vectors.
You are given the right triangle shown. Which of the following equations would be a correct way to solve for the missing information
A. I and then II or III
B. I and II only
C. II or III only
D. You must use all
Answers
Answer:
Option A. I and then II or III
Explanation:
From the question given above, the following data were obtained:
Angle = θ
Opposite = 16 m/s
Adjacent = 24 m/s
Hypothenus = v
i. The value of θ can be obtained by using Tan ratio as show below:
Tan θ = Opposite / Adjacent
Opposite = 16 m/s
Adjacent = 24 m/s
Tan θ = 16 / 24
ii. Cos θ = Adjacent /Hypothenus
Adjacent = 24 m/s
Hypothenus = v
Cos θ = 24 / v
Cross multiply
v × Cos θ = 24
Divide both side by Cos θ
v = 24 / Cos θ
iii. Sine θ = Opposite /Hypothenus
Opposite = 16 m/s
Hypothenus = v
Sine θ = 16 / v
Cross multiply
v × Sine θ = 16
Divide both side by Sine θ
v = 16 / Sine θ
From the above illustrations, we can use (i) to obtain θ then we can use (ii) or (iii) to obtain the value of v.
Hello question for JungKookLuver and jguzman577. What’s my favorite color don’t answer! Or you get reported!
Answers
Answer: Green!
Explanation: ThankYou bro
A car with a mass of 1,400 kg is traveling at a speed of 40 m/s. What is its momentum?
(P=m*v) P=momentum, m=mass, and v=Velocity.
Answers
Answer:
The answer is
56,000 kgm/sExplanation:
The momentum of an object can be found by using the formula
momentum = mass × velocityFrom the question
m = 1400 kg
v = 40 m/s
We have
momentum = 1400 × 40
We have the final answer as
56,000 kgm/sHope this helps you
Please help!!!!!!!
A tennis racket hits a tennis ball forward by exerting a force of 55 N on the ball.
What force does the ball exert on the tennis racket during the hit?
A. The ball exerts an equal backward force on the racket.
B. The ball is light, so it exerts almost no force on the racket.
C. The ball causes drag on the racket with a small forward force as it flies away.
D. The ball exerts a smaller force that alternates forward and backward to vibrate the racket.
Answers
A 2kg rock is at the edge of a cliff 20m above the surface of a lake. What is its potential energy at the top of the cliff?
Please show work!
Answers
Answer:
392 j
Explanation:
potential energy (PE) is equal to the mass of the object multiplied by the acceleration due to gravity multiplied by the height of the object.
PE=mgh (g=9.8 m/s/s)
PE= (2 kg)(9.8 m/s/s)(20 m)
PE= 392 j
j= joules
1. An express train, traveling at 36 m/s, is accidentally sidetracked onto a local train track. The express engineer spots a local train 100 m ahead on the same track and traveling in the same direction at a constant 11 m/s. The local engineer is unaware of the situation. The express engineer jams on the brakes and slows the express at 3.0 m/s2. (a) To determine whether the trains collide, use kinematics to calculate their positions when the express train stops: i. How much time will it take the express train to stop? ii. In that time, how far will the express train have moved? iii. In that time, how far will the local train have moved? iv. Based on the results of ii. and iii., do the trains collide? Explain.
Answers
Answer:
(i) 12 seconds
(ii) 216 meters from the initial position
(iii) 132 meters from the initial position
(iv) No
Explanation:
Speed of express train =36 m/s
Speed of local train =11 m/s
The initial distance between the local train and passenger train =100 m.
Due to the application of breaks, the express train slows at the rare of [tex]3.0 m/s^2.[/tex]
So, the acceleration of the express train, [tex]a=-3 m/s^2[/tex].
(i) Let t be the time the express train takes to stop.
From the equation of motion,
v=u+at
where, v: final velocity, u: initial velocity, a: constant acceleration, t: time taken to change the speed from u to v.
In this case, v=0, u=36 m/s, [tex]a=-3 m/s^2[/tex]
So, 0=36+(-3)t
[tex]\Rightarrow t= 36/3=12[/tex] seconds.
(ii) To compute the distance traveled, s, till the express train stops, using
[tex]v^2=u^2+2as[/tex]
[tex]\Rightarrow 0^2=36^2+2(-3)s[/tex]
[tex]\Rightarrow s=\frac{36\times36}{6}[/tex]
[tex]\Rightarrow s=216[/tex] meters.
(iii) The local train is moving at a speed of 11 m/s
So, in 12 seconds, the distance, d, traveled by the local train
d= 11x12=132 meters [as distance= speed x time]
(iv) Let 0 be the reference position which is the initial position of the express train.
So, at the initial time, the position of the local train is at 100m.
After 12 seconds:
The position of the express train is at 216 m [using part (ii)]
and the position of the local train is at 100+132=232m [using part (iii)].
So, the local train is still ahead of the express train, hence the trains didn't collide.
the speed of sound in air at a temperature of -40c° ?
Answers
Answer:
304.87 m/s
Explanation:
v2 = v1 × √T2÷√T2
v2 = 330 × √233÷√273
v2 = 304.87 m/s
Which type of force is a noncontact force?
O A. Buoyancy
O B. Any normal force
O C. Air resistance
O D. Any fundamental force
Answers
Answer:D>D>D>D>D>D>D>D>>D>D>D>D>D>D>D>D>D>
Explanation:
Answer:
O D. Any fundamental force
Explanation:
got it right on the test
A cat jumps up and sits on the lap of a woman who is sitting in the chair. The cats weight is 40 newtons. What is the reaction force provided by the chair now?
Answers
Answer:
540 newtons.The weight of the chair is 90 N. Action-reaction pairs include the cat-woman’s lap, the woman- chair, the chair-strongman, and the strongman-ground.
Explanation:
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A 7.50 kg bowling ball moving
6.42 m/s strikes a 1.60 kg bowling
pin at rest. After, the ball moves
5.43 m/s at a 12.0° angle. What is
the x-component and y-component of the pin's final
velocity?
Answers
Answer:
Explanation:
To solve this problem we need to know the direction in which the ball was moving to start with.
The answer will be different depending n the original angle of the ball's movement.
It might be reasonable to assume that the ball is meant to approach along the x-axis,
but if so, the initial speed of 6.42m/s would be irrelevant to the answer.
So I will solve the problem for the general case of two objects colliding at arbitrary angles, and
tell you how to specialize it for any assumption about the initial conditions.
Let
m1 = 7.5 kg be the mass of the ball,
m2 = 1.6 kg be the mass of the pin,
v1 = 6.42 m/s be the velocity of the ball before the strike,
v2 = 0 m/s be the velocity of the pin before the strike,
α1 be the angle of v1,
α2 be the angle of v2,
w1 be the velocity of the ball after the strike,
w2 = 14.8 m/s be the velocity of the pin after the strike,
β1 be the angle of w1,
β2 = -47° be the angle of w2.
By conservation of momentum:
m1v1 + m2v2 = m1w1 + m2w2
Since the velocities are vectors, the addition is vector addition, and the equality is vector equality.
"Vector equality" means that the x-coordinates are equal and the y-coordinates are equal.
The problem cares only about y-coordinates, specifically the y-coordinate of w1, which is w1sin(β1).
(In general, the y-coordinate of any vector is obtained by multiplying the vector's norm by the sine of its angle.)
Conservation of momentum in the y-coordinate is then
m1v1sin(α1) + m2v2sin(α2) = m1w1sin(β1) + m2w2sin(β2)
Expressing the sought quantity
w1sin(β1) = (m1v1sin(α1) + m2v2sin(α2) - m2w2sin(β2))/m1
Substituting known quantities:
w1sin(β1) = (7.5×6.42×sin(α1) + 1.6×0×sin(α2) - 1.6×14.8×sin(-47°))/7.5
= (48.15×sin(α1) + 17.3)/7.5
In the above expression we do not know α1.
If we assume that the ball is approaching along the x-axis then α1 = 0, and
w1sin(β1) = 17.3/7.5 = 2.3
Under that assumption the y-component of the ball's final velocity is 2.3 m/s;
being positive, it is opposite the direction of the pin.
please help in 5 mintues
Which component uses the core muscles of your stomach?
a. Muscular endurance
b. Flexibility
c. BMI
d. Abdominal endurance
Answers
Answer:
a. Muscular endurance
is correct answer
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Rank the six combinations of electric charges on the basis of the electric force acting on q1.
a.
q1= +1nC
q2= -1nc
q3= -1nc
b.
q1= -1nC
q2= +1nc
q3= +1nc
c.
q1= +1nC
q2= +1nc
q3= +1nc
d.
q1= +1nC
q2= +1nc
q3= -1nc
e.
q1= -1nC
q2= -1nc
q3= -1nc
f.
q1= +1nC
q2= -1nc
q3= +1nc
Answers
Answer:
Largest; options A & B
2nd largest; Option F
3rd Largest; Option D
Smallest; Options E & C
Explanation:
Looking at the charges, basically, the net force of the charge q1 is the sum of charges q2 and q3.
When 2 charges are opposite, the force will be attractive but if they are same, then the force will be repulsive.
Thus, the order of the forces is;
I) Largest: q1= +1nC, q2= -1nc, q3= -1nc and (q1= -1nC, q2= +1nc, q3= +1nc)
II) Second largest is: q1= +1nC, q2= -1nc, q3= +1nc
III) Third largest: q1= +1nC, q2= +1nc, q3= -1nc
IV) Smallest: (q1= -1nC, q2= -1nc, q3= -1nc) and (q1= +1nC, q2= +1nc, q3= +1nc)
Meat-eating desert reptiles depend on which of the following biotic factors to supply their needs?
Daytime temperature ranges above 30 degrees Celsius
Condensation of moisture on plants for drinking water
OSmall animals in their habitat on which they feed
Plants that bear fruits during the summer months
Answers
Meat-eating desert reptiles depend on small animals in their habitat on which they feed.
What is the need of meat eating desert reptiles?Meat-eating desert reptiles depend on small animals that lives to their surrounding. On these animals, these meat eating desert reptiles feed and fulfill their requirements of food so we can conclude that meat eating reptiles needs small animals present in the desert for feeding.
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