Answers
Answer:
170 kg
Explanation:
Free-Body Diagram:Let's start by drawing a free body diagram for this problem. Let's call the tension in the left rope [tex]T_1[/tex] and the tension in the right rope [tex]T_2[/tex].
Now we can construct a free body diagram using the horizontal and vertical components of the two tension forces.
Let's start with the left tension force:
Horizontal component (x): [tex]T_1 \cdot cos(30)[/tex]Vertical component (y): [tex]T_1 \cdot sin(30)[/tex]The right tension force:
Horizontal component: [tex]T_2 \cdot cos(45)[/tex]Vertical component: [tex]T_1 \cdot sin(45)[/tex]In order to see what these forces look like on the diagram, look at the first image attached. (1)
Now, we can create the FBD using the components of the tension forces and the force of gravity pulling on the crate, known as w.
The horizontal components of [tex]T_1[/tex] and [tex]T_2[/tex] go on the left and right of the FBD, respectively. The two vertical components go on top, and the weight force is on the bottom. We know that weight = mg.
To see what the free body diagram should look like, see the second image attached. (2)
Now that we have the FBD, we can write a system of equations using the sum of forces in both the x- and y-direction.
Since the crate is not moving in either the horizontal or vertical direction, we can say that the net force acting on the crate is 0.
[tex]F_\text{net} = 0[/tex]This means that the sum of x forces and the sum of y forces are both 0. Let's set the top and right to be the positive direction and the bottom and left to be the negative direction. Now we can write the system of equations:
[tex]\sum F_x = T_2 \cdot cos(45) - T_1\cdot cos(30) = 0[/tex] [tex]\sum F_y = T_1 \cdot sin(30) +T_2\cdot sin(45) - mg = 0[/tex]There are many ways to solve this system of equations, but I will be showing the top two ways that I tend to solve these types of problems.
Method 1:Solve for [tex]T_1 \cdot sin(30)[/tex] and [tex]T_1 \cdot cos(30)[/tex] in both equations.
[tex]T_1 \cdot cos(30) = T_2 \cdot cos(45)[/tex] [tex]T_1\cdot sin(30) = mg - T_2 \cdot sin(45)[/tex]We know that [tex]\frac{sin\theta}{cos\theta}[/tex] = [tex]tan\theta[/tex], so we can reorder both equations and divide them.
[tex]T_1\cdot sin(30) = mg - T_2 \cdot sin(45)[/tex] [tex]T_1 \cdot cos(30) = T_2 \cdot cos(45)[/tex] [tex]tan(30)=\frac{mg-T_2\cdot sin(45)}{T_2\cdot cos(45)}[/tex]Note that [tex]\frac{T_1}{T_1}[/tex] cancels, leaving us with tan(30).
Now that we have this equation, we can plug in known values. We are trying to solve for m, the largest mass of the crate that the ropes can support. We know that:
[tex]g=9.8\ \frac{m}{s^2}[/tex] [tex]T_2=1500\ \text{N}[/tex]Let's substitute these values into our equation:
[tex]tan(30)=\frac{m(9.8)-(1500)\cdot sin(45)}{(1500)\cdot cos(45)}[/tex]Multiply 1500 * cos(45) to both sides of the equation.
[tex]tan(30) \cdot (1500 \cdot cos(45)) =9.8m-(1500 \cdot sin(45))[/tex]Add 1500 * sin(45) to both sides of the equation.
[tex]tan(30) \cdot (1500 \cdot cos(45)) + 1500 \cdot sin(45)) =9.8m[/tex]Divide both sides of the equation by 9.8.
[tex]\frac{tan(30) \cdot (1500 \cdot cos(45)) + (1500 \cdot sin(45)) }{9.8}= m[/tex]Simplify.
[tex]\frac{1673.032607}{9.8}=m[/tex] [tex]m=170.717613[/tex]The largest mass the ropes can support is around 170 kg (round down, not up).
Method 2:We can use the system of equations again.
[tex]T_1 \cdot cos(30) = T_2 \cdot cos(45)[/tex] [tex]T_1\cdot sin(30) = mg - T_2 \cdot sin(45)[/tex]This time, let's do a little guess and check. Using the first equation, plug in 1500 N for T2 and solve for T1.
[tex]T_1 \cdot cos(30) = (1500) \cdot cos(45)[/tex]Divide both sides of the equation by cos(30).
[tex]T_1=\frac{1500 \cdot cos(45)}{cos(30)}[/tex]Simplify.
[tex]T_1=1224.744871 \ \text{N}[/tex]Now plug in 1500 N for T1 and solve for T2.
[tex](1500) \cdot cos(30) = T_2 \cdot cos(45)[/tex]Divide both sides by cos(45).
[tex]T_2=\frac{1500\cdot cos(30)}{cos(45)}[/tex] [tex]T_2=1837.117307 \ \text{N}[/tex]Since the tension cannot exceed 1500 N without the rope breaking, we must use the first substitution, where [tex]T_1=1224.744871[/tex] and [tex]T_2=1500 \ \text{N}[/tex].
Now we can use these known values and plug them into the second equation: [tex]T_1\cdot sin(30) = mg - T_2 \cdot sin(45)[/tex]
Add [tex]T_2 \cdot sin(45)[/tex] to both sides of the equation.
[tex]mg=T_1 \cdot sin(30) + T_2 \cdot sin(45)[/tex]Divide both sides of the equation by g.
[tex]m=\frac{T_1 \cdot sin(30) + T_2 \cdot sin(45)}{g}[/tex]Plug in known values and solve for m.
[tex]m=\frac{(1224.744871) \cdot sin(30) + (1500) \cdot sin(45)}{9.8}[/tex]Simplify.
[tex]m=\frac{1673.032607}{9.8}[/tex] [tex]m=170.717613[/tex]As you can see, we get the same answer with either method. The largest mass the ropes can support is 170 kg.
Related Questions
Based on the law of conservation of energy, which statement is correct?
Answers
Answer:
D. Energy in an isolated system remains constant
General Formulas and Concepts:
Physics
Law of Conservation of Energy - Energy is neither created or destroyedExplanation:
According to the Law of Conservation of Energy, it cannot be created or destroyed.
Therefore, we can eliminate choices A and B right off the bat.
We need to choose between C and D. We know that even though energy cannot be created or destroyed, it can be changed into a different form. Therefore, the correct answer is D.
A heat engine operating between the
temperatures T1 and T2 takes in Qı calories at
temperature T1 and gives up Q2 calories at
temperature T2. The efficiency of this heat
engine is
(Q1 - Q2)/Q2.
(Q1 - Q2)/Q1.
(T2 - T1/T2.
Q2/(Q1 - Q2).
O T1/(T1-T2).
Answers
Answer:
(Q1 - Q2)/Q1
Explanation:
The efficiency of any device can be given by the following formula:
[tex]Efficiency = \eta[/tex] = Output/Input
Now, for engine the output is the mechanical work that it does and the input is the heat that it absorbs. Let:
W = Work Done by the engine
Q₁ = Heat Absorbed by the System
Q₂ = Heat Rejected by the System (Because According to 2nd Law of Thermodynamics, engine can not convert the entire heat into work without rejection of some heat)
Therefore, the equation becomes:
[tex]\eta = \frac{W}{Q_{1}}[/tex]
but, the work can be written as the difference between the absorbed heat and the rejected heat. Hence,
[tex]\eta = \frac{Q_{1} - Q_{2}}{Q_{1}}[/tex]
Therefore, the correct option is:
(Q1 - Q2)/Q1
An object in static equilibrium has a coefficient of static friction as 0.110. If the normal force acting on the object is 95.0 newtons, what is the mass of the object? A. 9.70 kilograms B. 10.5 kilograms C. 85.3 kilograms D. 95.0 kilograms E. 1.00 × 102 kilograms
Answers
Answer:
9.70 kilograms
Explanation:
I got a 100% on my test
The mass of the object is 9.7 kg. Option (A) is correct.
What is normal force?Every day, we experience the normal force. For instance, when a book is placed on a table, the usual response force prevents the book from falling through the table, even though gravity is pulling the book downward. That implies that there is a force acting to push it upward. The word "normal force" refers to the force. Normal in this context refers to being perpendicular to the ground.
Given parameters:
the normal force acting on the object is: N = 95.0 newtons.
coefficient of static friction: μ = 0.110.
We have to find mass of the object: m = ?
We know that:
Normal force = weight of the object
⇒ N = mg
⇒ m = N/g = 95.0/9.8 kg = 9.7 kg
Hence, the mass of the object be 9.7 kg.
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A car and driver weighing 5060N passes a sign stating "Bridge out 27.5 meters ahead." She slams on the brakes and the car decelerates at a constant rate of 14 m/s^2. The acceleration of gravity is 9.8 m/s^2. What is the magnitude of the work done stopping the car if the car just stops in time to avoid diving into the water?
Answer in units of J.
Answers
Answer:
198785.714286 Joules
Explanation:
[tex]W=f*d[/tex]
[tex]F=ma\\F=516.326530612*-14\\F=-7228.57142857 N\\[/tex]
To find work:
Now that the force and the distance are known, plug and chug:
[tex]W=f*d\\W=-7228.57142857*27.5\\W=-198785.714286J[/tex]
Note that the question is asking for the magnitude of work, so the negative can be discarded as it is a directional component.
So, your answer is
198785.714286 Joules
A 420N force act on a 400N object, and the force is from the north.
In what direction will the object move?
Forward
Backboard
North
South
Answers
Answer:
I believe its forward or south :D
Explanation:
What compound is a product of photosynthesis?
Group of answer choices
Water
Carbon Dioxide
Glucose
Sunlight
Answers
Answer: Glucose
Explanation:
According to the law of conservation of mass, what is the mass of aluminum
oxide (Al2O3) formed in this reaction?
-
2A1 +
53.96 g
302
96.00 g
2A1203
?
A. 84.08 grams
B. 117.96 grams
C. 203.92 grams
D. 101.96 grams
Answers
D. 101.96 grams. Molar mass of Al2O3=2× Atomic mass of aluminium + 3× atomic mass of oxygen. =2×27+3×16=54+48=102g.
What happens when Al2O3 reacts?Sodium aluminate and water are produced when aluminum oxide Al 2 O 3 interacts with sodium hydroxide solution.Between 900 and 1100 ° C is the temperature at which this reaction occurs.Aluminum oxide functions as just an acid in this reaction.
How is Al2O3 produced from aluminum?Bauxite is the name of the aluminum ore (Al 2O 3).Bauxite is refined to create aluminum oxide, commonly known as alumina, which can be used to extract aluminum.Electrolysis is used to remove the metal, but first the aluminum oxide must be heated in order for electricity to flow through it.
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Answer: The CORRECT Answer is : 203.92 grams
Explanation: I took the test
Dominic has a brain injury. Why is this MOST likely to be a serious injury?
Answers
If Dominic has a brain injury, then he must have sustained a serious injury.
Functions of the brainThe brain coordinates all the activities in the body such as speech, locomotion, coordination and intelligence. This makes the brain the master point of control in the body.
Brain injuryWhenever there is an injury to the brain, various parts of the body could be affected. Functions such as speech, locomotion and general coordination may become largely impaired.
Therefore, if Dominic has a brain injury, then he must have sustained a serious injury.
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Question 9 of 20
Which sentence best describes the function of an electric motor?
A. An electric motor uses electrical energy to produce magnetic
force.
B. An electric motor uses electrical energy to produce mechanical
energy
C. An electric motor uses mechanical energy to produce electrical
energy
D. An electric motor uses magnetic force to produce electrical
energy
Answers
Option B. An electric motor uses electrical energy to produce mechanical energy.
An electric motor is used to transform electric electricity into mechanical power. An electric-powered motor is an electrical device that converts electric energy into mechanical electricity.
Maximum electric-powered motors operate thru the interaction among the motor's magnetic field and electric-powered contemporary in a wire winding to generate force inside the form of torque implemented on the motor's shaft.
Electric motors are devices that convert electrical strength into mechanical power, commonly in the form of rotational motion. In easy terms, they may be devices that use electric powered power to generate reason strength.
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how does the vertical component of a projectiles compare to the motion of vertical free fall when air resistance is neglected?
Answers
In which direction does the gravity of the earth act?
why do the satellite not fall while revolving around the earth.
Answers
Answer:
Satellites don't fall from the sky because they are orbiting Earth. Even when satellites are thousands of miles away, Earth's gravity still tugs on them. Gravity--combined with the satellite's momentum from its launch into space--cause the satellite go into orbit above Earth, instead of falling back down to the groundv
Explanation:
lily can travel 60 miles in 1.5 hours. if her speed is reduced by 5 mph. how far can she travel in 3 hours?
Answers
Answer:
3 hours.
Explanation:
If speed is reduce of 5, then she drive at 35 mph.
so 35*3 = 105 miles in 3 hours.
Therefore, we get 3 hours.
Which of the following is an example of a double replacement reaction?
A. 3Fe + 2O2 → Fe3O4
B. BaCl2 + K2CO3 → BaCO3 + 2KCl
C. NiCO3 → NiO + CO2
D. Cl2 + 2NaBr → 2NaCl + Br2
Answers
Answer:B
Explanation:please like this bc I just did it and got it right
. A ventilation fan has blades 0.25 m long rotating at 20 rpm (revolutions per minute). What is the centripetal acceleration of a point on the outer tip of a blade
Answers
Answer:
The centripetal acceleration of a point on the outer tip of a blade is 1.097 m/s²
Explanation:
Given;
length of the fan blade, r = 0.25 m
angular speed = 20 rpm
The angular speed in rad/s is given as;
[tex]\omega = \frac{20 \ rev}{ \ \ \min} \ \times \ \frac{2\pi}{1 \ rev} \ \times \ \frac{1 \ \min}{60s} = 2.095 \ rad/s \\\\[/tex]
The centripetal acceleration of a point on the outer tip of a blade is given as;
[tex]\alpha_c = \frac{v^2}{r} = \omega ^2r[/tex]
[tex]\alpha _c = (2.095)^2(0.25)\\\\\alpha _c =1.097 \ m/s^2[/tex]
Therefore, the centripetal acceleration of a point on the outer tip of a blade is 1.097 m/s²
Answer:
The centripetal acceleration = [tex]1.1m/s^2[/tex]Explanation:
Given
[tex]rpm = 20[/tex]
therefore,
[tex]20rpm = \frac{20*2\pi}{60}\\\\=2.1 rad/s = w[/tex]
From,
[tex]V = rw\\\\V = 0.25 * 2.1\\\\V = 0.525m/s[/tex]
Centripetal acceleration,
[tex]a_c = \frac{V^2}{r}\\\\a_c = \frac{0.525^2}{0.25}\\\\a_c = 1.1m/s^2[/tex]
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the amplitude of an oscillator decreases to 36.8% of its initial value in 10.0 s. what is the value of the time constant
Answers
Answer:
τ = 5 s
Explanation:
When a vibrating body is damped. Its amplitude starts to decrease. This decrement is exponential. And it is given as follows:
[tex]X = X_{0}e^{-\frac{t}{2\tau}[/tex]
where,
τ = Time Constant = ?
X = Instantaneous value of amplitude
X₀ = Initial Value of amplitude
t = time interval = 10 s
The ratio of decrement is given as:
[tex]\frac{X}{X_0} = 36.8\% = 0.368[/tex]
therefore, using these values, we get:
[tex]\frac{X}{X_{0}} = 0.368 = e^{\frac{10\ s}{2\tau}}[/tex]
Taking natural log (ln) on both sides, we get:
[tex]ln(0.368) = \frac{10\ s}{2\tau}\\\\\tau = \frac{10\ s}{2ln(0.368)}[/tex]
τ = 5 s
The value of the time constant for the decrease in the amplitude of this oscillator is 5.
Given the following data:
Decrease in amplitude = 36.8% = 0.368Time = 10.0 seconds.To determine the value of the time constant:
Mathematically, the amplitude for damped harmonic motion is given by the formula:
[tex]X = X_o e^\frac{t}{2 \tau}[/tex]
Where:
t is the time.[tex]\tau[/tex] is the time constant.X is the instantaneous value of amplitude.[tex]X_o[/tex] is the initial value of amplitude.Rearranging the formula, we have:
[tex]\frac{X}{X_o} = e^{-\frac{t}{2 \tau}}[/tex]
Substituting the given parameters into the formula, we have;
[tex]0.368 = e^\frac{-10}{2 \tau}\\\\ln(0.368) = \frac{-10}{2 \tau}\\\\-0.9997 = \frac{-10}{2 \tau}\\\\2 \tau \times -0.9997 = 10\\\\-1.9994\tau=-10\\\\\tau =\frac{-10}{-1.9994} \\\\\tau = 5.0[/tex]
Time constant = 5
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Prior Knowledge
1. What do a light bulb, a toaster, a radio, and a computer all have in common?
Answers
Answer:
They all have electrical currents
Answer:
They have electronic parts and currents