In the figure, if the tension in string 1 is 34 N (40 degrees to the left) and the tension in string 2 is 24 N ( to the right) what is the mass of the object shown?
Answers
Answer:
3.7 kg
Explanation:
Start off by drawing and labeling a free-body diagram for the object. I have attached an image that I drew that shows all of the relevant forces acting on the object.
On the free-body diagram, we have the tension forces (T₁ and T₂), their x and y components, and the weight force (w).
We want to start off by finding the angle theta (Θ) so that we can use this angle when using Newton's Second Law later on in the problem to calculate the mass of the object.
We can find the angle Θ by using the fact that there are no unbalanced horizontal forces acting on the object, so the net force is zero.
This means that T₁ sin(40) is equal to T₂ sin(Θ). Set them equal to each other in an equation and solve for the angle Θ. We are given the tension forces: T₁ = 34 N and T₂ = 24 N.
T₁ sin(40) = T₂ sin(Θ)34 * sin(40) = 24 * sin(Θ)Evaluate 34 * sin(40) and divide it by 24 to isolate sin(Θ).
0.9106157804 = sin(Θ)Take the inverse sine of both sides of the equation.
Θ = sin⁻¹(0.9106157804) Θ = 65.59058699°Now that we have the angle Θ, we can use this to set up an equation involving mass using Newton's Second Law.
We know that there is a weight force directed downwards on the object, and this weight force is equal to mg (mass · gravitational acceleration).
There are two forces acting upwards on the object: the x-components of the two tension forces.
Using the fact that the object is not moving vertically, we know that the net force must equal 0 (since F = ma and acceleration = 0 m/s², therefore F = 0 N).
The sum of the forces in the y-direction will be equal to 0. Setting the upwards direction to be positive and the downwards direction to be negative, we can write this equation:
∑Fᵧ = T₁ cos(40) + T₂ cos(65.59058699) - mg = 0Add mg (weight force) to both sides of the equation.
T₁ cos(40) + T₂ cos(65.59058699) = mgSubstitute 34 for T₁ and 24 for T₂.
34 * cos(40) + 24 * cos(65.59058699) = mgThe gravitational acceleration on Earth is 9.8 m/s². Substitute this value into the equation and solve for m, the mass of the object.
34 * cos(40) + 24 * cos(65.59058699) = m(9.8)Evaluate the left side of the equation.
35.96360799 = 9.8mDivide both sides of the equation by 9.8.
m = 3.669755918Round this to two significant figures since the problem gives us the tension forces to two sig figs.
m ≈ 3.7 kgThe mass of the object shown is around 3.7 kg.
Answer:
3.7 kg
Explanation:
Start off by drawing and labeling a free-body diagram for the object. I have attached an image that I drew that shows all of the relevant forces acting on the object.
On the free-body diagram, we have the tension forces (T₁ and T₂), their x and y components, and the weight force (w).
We want to start off by finding the angle theta (Θ) so that we can use this angle when using Newton's Second Law later on in the problem to calculate the mass of the object.
We can find the angle Θ by using the fact that there are no unbalanced horizontal forces acting on the object, so the net force is zero.
This means that T₁ sin(40) is equal to T₂ sin(Θ). Set them equal to each other in an equation and solve for the angle Θ. We are given the tension forces: T₁ = 34 N and T₂ = 24 N.
T₁ sin(40) = T₂ sin(Θ)
34 * sin(40) = 24 * sin(Θ)
Evaluate 34 * sin(40) and divide it by 24 to isolate sin(Θ).
0.9106157804 = sin(Θ)
Take the inverse sine of both sides of the equation.
Θ = sin⁻¹(0.9106157804)
Θ = 65.59058699°
Now that we have the angle Θ, we can use this to set up an equation involving mass using Newton's Second Law.
We know that there is a weight force directed downwards on the object, and this weight force is equal to mg (mass · gravitational acceleration).
There are two forces acting upwards on the object: the x-components of the two tension forces.
Using the fact that the object is not moving vertically, we know that the net force must equal 0 (since F = ma and acceleration = 0 m/s², therefore F = 0 N).
The sum of the forces in the y-direction will be equal to 0. Setting the upwards direction to be positive and the downwards direction to be negative, we can write this equation:
∑Fᵧ = T₁ cos(40) + T₂ cos(65.59058699) - mg = 0
Add mg (weight force) to both sides of the equation.
T₁ cos(40) + T₂ cos(65.59058699) = mg
Substitute 34 for T₁ and 24 for T₂.
34 * cos(40) + 24 * cos(65.59058699) = mg
The gravitational acceleration on Earth is 9.8 m/s². Substitute this value into the equation and solve for m, the mass of the object.
34 * cos(40) + 24 * cos(65.59058699) = m(9.8)
Evaluate the left side of the equation.
35.96360799 = 9.8m
Divide both sides of the equation by 9.8.
m = 3.669755918
Round this to two significant figures since the problem gives us the tension forces to two sig figs.
m ≈ 3.7 kg
The mass of the object shown is around 3.7 kg.
Related Questions
Question 2 10 points)
Blueprints were used in the year
Answers
Answer:
1842.
Explanation: Blueprints were invented a generation before the Civil War by John Herschel, a chemist, astronomer, and photographer, in 1842.
How do the offspring produced by asexual reproduction differ from those produced by sexual reproduction?
А.
Offspring produced by asexual reproduction are bigger.
В.
Offspring produced by asexual reproduction use more energy.
С.
Offspring produced by asexual reproduction are more uniform.
D
Offspring produced by asexual reproduction are produced more slowly.
Answers
Answer:
Asexual reproduction produces offspring that are genetically identical to the parent because the offspring are all clones of the original parent. During sexual reproduction the genetic material of two individuals is combined to produce genetically diverse offspring that differ from their parents.
Explanation:
A vector has an x-component
of 6.15 m and a y-component
of -3.88 m.
Find the magnitude of the
vector.
Answers
Answer:
please find attached file
Explanation:
The magnitude of the vector is 7.27m .
What is magnitude of a vector?The magnitude of a vector is the numerical value of the vector. It is represented by the length of the vector.
When a vector is resolved in two components then it is given by formula,
[tex]A = \sqrt{Ax^{2}+Ay^{2} }[/tex]
Here,
[tex]A_{x} = 6.15\\A_{y} = 3.88[/tex]
A = [tex]\sqrt{6.15^{2}+3.88^{2}[/tex]
A = 7.27m
Hence magnitude of the vector is 7.27m .
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If you are in a car that is being pulled down a 56 m path with a force of 12.5
N, what is the work being done?
Answers
Answer:
answer is 700 joules
Explanation:
work is equal to force into displacement
W=12.5*56
700 joules
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Answers
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A. The chromosomes in the daughter cells half the number from the parent cell.
B. The chromosomes in the daughter cells are the same number as the parents cell.
C. Each nuclei is identical to the parent nucleus.
D. The four main stages are prophase,metaphase,anaphase, and telophase.
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Answer:
I think its A
Explanation:
How does a balanced Chemical Equation Satisfy the Law of Conservation of Mass?
A. During a chemical reaction, the total amount of matter stays the same.
b. During a chemical reaction, matter is destroyed.
c. During a Chemical reaction, one ore more new substances formed.
d. During a chemical reaction, the total number of atoms increases.
Answers
HELPPPPP!
which of the following is a human action that could lead to decreased amounts of greenhouse gases found in the atmosphere, such as carbon dioxide?
A ) Generating energy by burning coal
B ) Deforestation
C ) Driving automobiles
D ) Planting trees
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Which of the following areas of the sun is where energy is transferred very slowly, sometimes taking up to 100,000 years, by electromagnetic radiation?
A. the radiation zone
B. the core
C. the convection zone
D. the solar flares
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What is the kinetic energy of a 25kg object moving at a velocity of 2.5 m/s
Answers
Answer:
78j
Explanation:
78.125J to be exact
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Answers
Answer:
A car
Explanation:
Determine Average Speed.
Total distance = 800 mi
Total time = 10 hr
Answers
Explanation:
Average Speed.=Total distance/Total time=800/10=80m/hour
A phonograph record 0.15 m in its radius rotates 18 times per 90 seconds what is the frequency?
Answers
Answer:
The frequency of the phonograph record is 0.2 Hz
Explanation:
The frequency of an object moving in uniform circular motion is the number of completed cycles the object makes in a specified time period
The given parameters of the phonograph record are;
The radius of the record = 0.15 m
The number of times the phonograph record rotates, n = 18 times
The time it takes the phonograph record to rotate the 18 times, t = 90 seconds
The frequency of the phonograph record, f = (The number of times the phonograph record rotates) ÷ (The time it takes the phonograph record to rotate the 18 times)
∴ The frequency of the phonograph record, f = n/t = 18/(90 s) = 0.2 Hz
The frequency of the phonograph record = 0.2 Hz.
How do you determine the height of a wave?
Answers
Answer:
Wave height is the vertical distance between the crest (peak) and the trough of a wave. Some other definitions: Still-Water Line is the level of the lake surface if it were perfectly calm and flat. Crest is the highest point on the wave above the still-water line.
Explanation:
When a baseball is thrown straight upward, what is its acceleration at its greatest height? Please explain your answer.
9.8 m/s2 downward
9.8 m/s2 upward
9.8 m/s2 horizontally
0 m/s2
Answers
Answer: A
Explanation:
The acceleration of gravity is always 9.8 m/s^2 downwards, even if the velocity is 0 m/s.
Why does refraction occur?
A. Light travels through different materials at different speeds.
B. Different colors of light travel at different speeds.
C. Different materials physically twist light around.
D. Light from different sources travels at different rates.
Answers
Answer:
The answer is C.
Explanation:
Let's take a glass of water as an example. Now, shine a flashlight on it. See it bend the light into a rainbow? That is a example of refraction. When the light enters the water, the water actually slows down and changes its direction, causing the light to come out the other side in a different way. Since water is very dense, it can bend the water and make it different.
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Very briefly describe the way an electromagnet works.
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Answer:
Because the electromagnet is made up of moving coils, when an electric current passes through, the coils act like a magnet.
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What is the effect of temperature on the solubility of a solid in a liquid? Check all correct elements that you included in your question. format: "What is the effect of X on Y?" materials: solid dissolved in a liquid independent variable: temperature dependent variable: solubility
Answers
Answer:
materials: solid dissolved in a liquid
independent variable: temperature
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I got it right
Rafael lives near a road at the bottom of the hill. His parents are concerned that soil will wash off the hill and rocks will fall onto the road. Rafeal converts an investigation to find out if grass growing on a hillside will help stop soil erosion. He collects two samples of the same size and type of soil. One sample of soil has grass growing on it and the other does not. He places each sample of soil in a small tray. For his investigation, Rafael pours the same amount of water onto both samples of soil. He uses a large tray to collect water that may flow through the soil. Which practice shows the best way for Rafael to set up this investigation?
Answers
Answer:
The first picture/option
Explanation:
The first picture/option shows the best way for Rafael to set up the investigation.
The experimental set-up must be in a sloppy position in order to simulate the condition that is characteristic of the bottom of the hill where he stays. Hence, the two soil samples must be tilted in order to determine if the grass can help to stop the washing down of the soil from the top of the hill.
The two options following the first option do not fulfill the condition of the same treatment. Both soil samples must be subjected to the same treatment condition in order for the outcome to be valid. The last option could have also been admissible but did not simulate the hill/slope conditions of where Rafael stays.
To set up his investigation on whether grass can help stop soil erosion on a hillside, Rafael can follow these steps: 1. Collect two samples of the same size and type of soil. This ensures that the only difference between the two samples is the presence of grass.
2. Place each sample of soil in a small tray. This allows Rafael to contain the soil and prevent it from mixing with each other.
3. Pour the same amount of water onto both samples of soil. This ensures that the water input is consistent for both samples, allowing Rafael to compare the effects of grass on soil erosion.
4. Use a large tray to collect water that may flow through the soil. This allows Rafael to measure and compare the amount of water runoff from both samples. By collecting the water, Rafael can determine if the grass on the hillside helps to retain more water and prevent soil erosion.
By following these steps, Rafael can compare the water runoff and soil erosion between the sample with grass and the sample without grass. This will provide him with evidence to determine if grass can effectively help stop soil erosion on a hillside.
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Ammonia is a covalent compound used in many cleaners. What is its chemical formula? N2O H2O NH3 HO3
Answers
Explanation:
NH3 is the correct answer
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Describe how computer climate models help scientists understand possible future climate changes. How reliable are these computer models in making predictions about global warming? Discuss any limitations in these models.
Answers
Now a new evaluation of global climate models used to project Earth's future global average surface temperatures over the past half-century answers that question: most of the models have been quite accurate.
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I got a 100% on this assignment copy it and put it on your notes then go sentence by sentence copy but dont highlight any "." you will not be able to paste it into the box add the "." after you paste it, it one sentence.
ONE SENTENCE AT A TIME NO ". ' - or :" AT ALL
An aircraft flying at a steady velocity of 70 m/s eastwards at a height of 800 m drops a package of supplies. a) Express the initial velocity of the package as a vector
Answers
Answer:
Explanation:
If unit vector towards east is represented by i in the present case ,
initial horizontal velocity of aircraft towards east is 70 m /s . The package dropped by the aircraft will also have same velocity while getting separated from the aircraft . Hence its velocity is represented by the vector ,
v = 70 i .
Its vertical velocity of package at that time will be zero so
v = 70 i + 0 j
= 70 i
Initial Velocity can be defined as the velocity at which the motion starts.
Initial Velocity for the package is [tex]70i[/tex].
Given that an aircraft flying at a steady velocity of 70 m/s eastwards at a height of 800 m.
Here we express the steady velocity as [tex]u\;\rm m/s[/tex]. Distance is expressed by [tex]d\;\rm meter[/tex]. Initial Velocity can be expressed as [tex]v\;\rm m/s[/tex].
Initial velocity can be calculated by the formula given below.
[tex]v\;=\;u\;+\;at[/tex]
In the above formula, [tex]a[/tex] is expressed the acceleration and [tex]t[/tex] is expressed the time of the motion.
For the initial velocity, time [tex]t\;=\;0[/tex] because motion starts in the vertical direction. Let us assume that unit vector can be expressed by [tex]i[/tex] and [tex]j[/tex].
Initial velocity formula in vector form is given below.
[tex]v\;=\;ui\;+\;atj[/tex]
By substituting all the values in the above formula, initial velocity is
[tex]v\;=\;ui\;+\;a\times0j\\v\;=\;ui\\v\;=\;70i[/tex]
So the initial velocity of the package is 70[tex]i[/tex].
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What type of reaction feels cold to the touch? A. Endothermic, because energy is being released into the surroundings B. Endothermic, because energy is being absorbed from the surroundings C. Exothermic, because energy is being released into the surroundings D. Exothermic, because energy is being absorbed from the surroundings
Answers
Answer:
D. Exothermic, because energy is being absorbed from the surroundings
Explanation:
This is true about the Exothemic reaction due to the fact that, the reaction occurs outside the body. During this reaction, the energy being absorbed from the surrounding environment will hit the body surface thereby creating the coldness due to the heat given out from the body being minimal.
Answer:
Endothermic, because energy is being absorbed from the surroundings.
Explanation:
It is recommended to use air container for storing oil for long time . Give scientific reason.
Answers
What is the force on a 1000 kg elevator that is falling freely at 9.8 m/ sec²?
Answers
Answer:
f=m.a 1000*9.8=9800newton
ILL GIVE BRAINLIEST !!!!!!!!!!! Do some research, and look up the difference between the zinc-carbon battery described on the
previous page, and the alkaline battery (shown at the left), which is another common dry cell that we
use every day. What are the electrodes made of in the alkaline battery? The electrolyte? Does one type
have an advantage over the other?
Create a few paragraph essay describing your findings to your teacher.
Answers
Answer:
The alkaline battery gets its name because it has an alkaline electrolyte of potassium hydroxide instead of the acidic ammonium chloride or zinc chloride electrolyte of the zinc-carbon batteries. An electrolyte is a substance that produces an electrically conducting solution when dissolved in a polar solvent, such as water. The dissolved electrolyte separates into cations and anions, which disperse uniformly through the solvent. Electrically, such a solution is neutral.Advantages. One of the advantages of alkaline batteries over other primary batteries and rechargeable batteries is that it has higher energy density. It has longer shelf life than batteries with chloride-type electrolyte. It could last to up to seven years unused, losing about five percent of its energy every year.
Explanation:
ASNWER THIS OR ILL KIDNAPP YOUR DOG AND REVEAL YOUR SEARCH HISTORY!!
Name 3 different forces that act on objects on the Earth
Answers
Answer:
Applied Force.
Gravitational Force.
Normal Force.
Frictional Force.
Air Resistance Force.
Tension Force.
Spring Force.
Explanation:
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Which of the following has the most kinetic energy?
A. stretching a rubber band
B. a jet flying through the air
C. throwing a paper airplane
D. pitching a baseball
Answers
Throwing an paper airplane & A jet flying through the air.