Find the tension in the ropes shown in the figure if the supported object weighs 600N.
Answers
By Newton's second and third laws, we have the following net forces at
point A:[tex]\sum F_x = -T_1 \cos(60^\circ) + T_2 \cos(60^\circ) = 0[/tex]
[tex]\sum F_y = T_1 \sin(60^\circ) + T_2 \sin(60^\circ) - 600 \,\mathrm N = 0[/tex]
Together, these equations tell us [tex]\boxed{T_1=T_2\approx 346 \,\mathrm N}[/tex].
point B:[tex]\sum F_x = T_3 \cos(20^\circ) - T_2 \cos(60^\circ) - T_5 = 0[/tex]
[tex]\sum F_y = T_3 \sin(20^\circ) - T_2 \sin(60^\circ) = 0[/tex]
point C:[tex]\sum F_x = -T_4 \cos(20^\circ) + T_1 \cos(60^\circ) + T_5 = 0[/tex]
[tex]\sum F_y = T_4 \cos(20^\circ) - T_1 \sin(60^\circ) = 0[/tex]
Combining the horizontal force equations for points B and C and using the fact that [tex]T_1=T_2[/tex] gives
[tex](T_3 \cos(20^\circ) - T_2 \cos(60^\circ) - T_5) + (-T_4 \cos(20^\circ) + T_1 \cos(60^\circ) + T_5) = 0 + 0[/tex]
[tex]\implies (T_3 - T_4) \cos(20^\circ) = 0 \implies T_3=T_4[/tex]
Then combining the vertical force equations for B and C, we find
[tex](T_3 \sin(20^\circ) - T_2 \sin(60^\circ)) + (T_4 \sin(20^\circ) - T_1 \sin(60^\circ)) = 0 + 0[/tex]
[tex]\implies 2 T_3 \sin(20^\circ) - 2 T_1 \sin(60^\circ) \implies T_3 = \dfrac{\sin(60^\circ)}{\sin(20^\circ)} T_1[/tex]
so that [tex]\boxed{T_3 = T_4 \approx 877 \,\mathrm N}[/tex]
Lastly solve for [tex]T_5[/tex] using either horizontal force equation for B or C.
[tex]-T_4 \cos(20^\circ) + T_1 \cos(60^\circ) + T_5 = 0[/tex]
[tex]\implies T_5 = \left(\dfrac{\sin(60^\circ)}{\sin(20^\circ)} - \cos(60^\circ)\right) T_1 \implies \boxed{T_5 \approx 651\,\mathrm N}[/tex]
Related Questions
What happens to the light in a
concave lens?
a. the light diverges when it passes
through the lens.
b. the light diverges before it enters the
lens.
c. the light converges when it enters the
lens.
Answers
Answer:
a. the light diverges when it passes through the lens.
Explanation:
All the light rays after passing through the concave lens diverge and when produced backwards appear to meet at a point on the principal axis of the lens. This point is known as principal focus of a concave lens.
Type the correct answer in the box.use numerals instead of words. if necessary, use / for the fraction bar. δabc is a right triangle in which ∠b is a right angle, ab = 1, ac = 2, and bc = . cos c × sin a =
Answers
From the diagram The value of cos C × sin A = [tex]\frac{3}{4}[/tex]
Determine the numerical value of cos C × sin AFirst step : determine the values of cos C and sin A
cos C = adjacent / hypotenuse
= a / b
= [tex]\sqrt{3} / 2[/tex]
= √3/2
sin A = sin 60⁰
= √3/2
Therefore the numerical value of cos C * sin A = [tex]\frac{3}{4}[/tex]
In conclusion From the diagram The value of cos C × sin A = [tex]\frac{3}{4}[/tex]
Learn more about right angle : https://brainly.com/question/24323420
#SPJ1
A boat crossing a 153.0 m wide river is directed so that it will cross the river as quickly as possible. The boat has a speed of 5.10 m/s in still water and the river flows uniformly at 3.70 m/s. Calculate the total distance the boat will travel to reach the opposite shore.
Answers
We have the relation
[tex]\vec v_{B \mid E} = \vec v_{B \mid R} + \vec v_{R \mid E}[/tex]
where [tex]v_{A \mid B}[/tex] denotes the velocity of a body A relative to another body B; here I use B for boat, E for Earth, and R for river.
We're given speeds
[tex]v_{B \mid R} = 5.10 \dfrac{\rm m}{\rm s}[/tex]
[tex]v_{R \mid E} = 3.70 \dfrac{\rm m}{\rm s}[/tex]
Let's assume the river flows South-to-North, so that
[tex]\vec v_{R \mid E} = v_{R \mid E} \, \vec\jmath[/tex]
and let [tex]-90^\circ < \theta < 90^\circ[/tex] be the angle made by the boat relative to East (i.e. -90° corresponds to due South, 0° to due East, and +90° to due North), so that
[tex]\vec v_{B \mid R} = v_{B \mid R} \left(\cos(\theta) \,\vec\imath + \sin(\theta) \, \vec\jmath\right)[/tex]
Then the velocity of the boat relative to the Earth is
[tex]\vec v_{B\mid E} = v_{B \mid R} \cos(\theta) \, \vec\imath + \left(v_{B \mid R} \sin(\theta) + v_{R \mid E}\right) \,\vec\jmath[/tex]
The crossing is 153.0 m wide, so that for some time [tex]t[/tex] we have
[tex]153.0\,\mathrm m = v_{B\mid R} \cos(\theta) t \implies t = \dfrac{153.0\,\rm m}{\left(5.10\frac{\rm m}{\rm s}\right) \cos(\theta)} = 30.0 \sec(\theta) \, \mathrm s[/tex]
which is minimized when [tex]\theta=0^\circ[/tex] so the crossing takes the minimum 30.0 s when the boat is pointing due East.
It follows that
[tex]\vec v_{B \mid E} = v_{B \mid R} \,\vec\imath + \vec v_{R \mid E} \,\vec\jmath \\\\ \implies v_{B \mid E} = \sqrt{\left(5.10\dfrac{\rm m}{\rm s}\right)^2 + \left(3.70\dfrac{\rm m}{\rm s}\right)^2} \approx 6.30 \dfrac{\rm m}{\rm s}[/tex]
The boat's position [tex]\vec x[/tex] at time [tex]t[/tex] is
[tex]\vec x = \vec v_{B\mid E} t[/tex]
so that after 30.0 s, the boat's final position on the other side of the river is
[tex]\vec x(30.0\,\mathrm s) = (153\,\mathrm m) \,\vec\imath + (111\,\mathrm m)\,\vec\jmath[/tex]
and the boat would have traveled a total distance of
[tex]\|\vec x(30.0\,\mathrm s)\| = \sqrt{(153\,\mathrm m)^2 + (111\,\mathrm m)^2} \approx \boxed{189\,\mathrm m}[/tex]
A bus starts from rest.if the acceleration is 2m/s square, find
i.the distance travelled
ii.the velocity after 2 seconds.
Answers
Answer:
The velocity after 2 seconds can be found through:
V = u +a*t
Where V is final velocity, u is initial velocity, a is acceleration and t is time.
V = 0 + 2* 2= 4 meters/second
The distance (s) can be found through:
V^2= u^2 +2*a* s
Where V is final velocity, u is initial velocity, a is acceleration.
4^2= 0^2 + 2 *2*s
16= 0 + 4s
s= 4 meters
Distance (s) can also be found through:
s= ut + 1/2 at^2
s= 0+ 1/2 *2*2^2= 1 *2*2
s= 4 meters
Explanation:
to complete the statement.
Atoms of elements in the same group have the same number of
chemical properties.
This is why they have similar chemical properties.
Answers
Answer:
Valence electrons
Explanation:
I don't exactly understand the question. However, I do know that the main commonality between elements of the same group (column) is their valence electrons. Valence electrons are very important when it comes to bonding, ionization, etc.
How does the kinetic energy from the forward motion of a car traveling at 16 m/s
compare with the kinetic energy of the same car traveling at 8 m/s?
(A) It is 2 times greater.
(C) It is 8 times greater.
(B) It is 4 times greater.
(D)
It is 16 times greater.
Answers
The kinetic energy in the first case is 4 times more than the second case.
Hence, option D)It is 4 times greater is the correct answer.
What is Kinetic Energy?Kinetic energy is simply a form of energy a particle or object possesses due to its motion.
It is expressed as;
K = (1/2)mv²
Where m is mass of the object and v is its velocity.
Given that;
For the first case, velocity v = 16m/sFor the second case, velocity = 8m/sLet the mass of the car be mFor the first case, kinetic energy of the car will be;
K = (1/2)mv²
K = (1/2) × m × (16m/s)²
K = (1/2) × m × 256m²/s²
K = mass × 128m²/s²
For the second case, kinetic energy of the car will be;
K = (1/2)mv²
K = (1/2) × m × (8m/s)²
K = (1/2) × m × 64m²/s²
K = mass × 32m²/s²
Comparing the kinetic energy of the car with the same mass but different velocity, we can see that the kinetic energy in the first case is 4 times more than the second case.
Hence, option D)It is 4 times greater is the correct answer.
Learn more about kinetic energy here: brainly.com/question/12669551
#SPJ1
A car with a mass of 1000 kg is moving on an un-banked ramp with a radius of 100 m. what is the maximum speed the car can move without skidding if the coefficients of static and kinetic friction are 0.80 and 0.60 respectively
Answers
The maximum speed the car can move without skidding is determined as 28 m/s.
Maximum speed of the car
The maximum speed of the car moving in a circular path is provided by static frictional force.
Fs = μFₙ = mv²/r
μFₙ = mv²/r
mv² = μFₙr
v² = μFₙr/m
[tex]v_{max} = \sqrt{\frac{\mu_s F_n r}{m} } \\\\v_{max} = \sqrt{\frac{\mu_s (mg) r}{m} } \\\\v_{max} = \sqrt{\mu_sgr} \\\\v_{max} = \sqrt{(0.8)(9.8)(100)}\\\\v_{max} = 28 \ m/s[/tex]
Learn more about maximum speed here: https://brainly.com/question/4931057
#SPJ1
Shyam saw a cylindrical copper rod in his store room he realise that it can be used for various purposes it can be used as a flower ways by covering it one side face with any metal it can be used as a conductor or it can be used as a cylindrical box by covering both the side face with metal he measure the radius of the rod with 3% and length of rod with 7% error error percentage is measuring the volume of the cylinderical box is
Answers
The error percentage in measuring the volume of the cylindrical box is 6.3 x 10⁻³ %
Error percentage in measuring the volume of the cylinder
The total error percentage in measuring the volume of the cylinder is calculated as follows;
Volume of cylinder = πr²h
Volume of cylinder = π(0.03r)²(0.07h)
Volume of cylinder = (6.3 x 10⁻⁵)πr²h
Error in measuring the volume = 6.3 x 10⁻⁵ x 100% = 6.3 x 10⁻³ %
Learn more about percentage error here: https://brainly.com/question/5493941
#SPJ1
Which two options would INCREASE the electric force between two charged particles?
A. Increase the distance between the particles. B. Decrease the charge of one of the particles. C. Decrease the charge of both particles
D. Decrease the distance between the particles
E. Increase the charge of one of the particles.
Answers
The electric force between two charged particles can be increased by decreasing the distance between the two particles.
How to increase electric force between two charged particles.The technique of decreasing the separation distance between objects increases the force of attraction or repulsion between the objects. while
increasing the separation distance between objects decreases the force of attraction or repulsion between the objects.
Read more on Electric Force:
https://brainly.com/question/17692887
#SPJ1
Question 1 of 10
What is the wavelength of a wave with a frequency of 262 Hz and a speed of
343 m/s?
O A. 1.3 m
OB. 89,866 m
O C. 1.11 x 10-5 m
O D. 0.76 m
SUBMIT
Answers
Answer:
V = λ f (wavelength * frequency)
λ = V / f = 343 m/s / 262 / s = 1.3 m
An engineer is working to design a bouncy ball that conserves all of its kinetic and potential energy. She drops the ball to the ground from a height of 3 meters. If it really works, how high should the ball bounce
Answers
If potential energy is conserved or remain the same, the ball will bounce 3 m high.
Conservation of energyThe principle of conservation of energy states energy can neither be created nor destroyed but can be converted from one form to another.
If we apply the principle of conservation of energy, the total potential energy will remain the same.
P.E(initial) = P.E(final)
Thus, If potential energy is conserved or remain the same, the ball will bounce 3 m high.
Learn more about potential energy here: https://brainly.com/question/1242059
#SPJ4
After travelling 4.0 km, the train reaches its maximum speed. it continues at this constant speed on the next section of the track where the track follows a curve which is part of a circle.
state the direction of the resultant force on the train as it follows the curved path.
Answers
Answer:
toward the center of the circular curve
Explanation:
An object will follow a circular path at constant speed if and only if its net acceleration is constant and directed toward the center of the curved path.
__
The result force is directed toward the center of the circle.
_____
Additional comment
If any part of the result force is in the direction of motion, the speed will not be constant. If the center-directed force is not constant, the path will not be circular.
a student investigates the efficiency of a scale model of an electricity generating wind turbine using the equipment in figure 1.
the student changed the number of sales on the turbine and measures the power output from the turbine's generator. the air blower is supplied with 533w and has efficiency of 0.62.
when using two sails, the efficiency of turbine was 13%. calculate the power generated.
Answers
The power generated or output power of the turbine is determined as 42.96 W.
Power generated
The power generated or output power of the turbine is calculated as follows;
eff = 0utput power/1nput power x 100%
13 = 0utput power/(0.62 x 533)
0.13 = 0utput power/330.46
0utput power = 0.13 x 330.46
0utput power = 42.96 W
Thus, the power generated or output power of the turbine is determined as 42.96 W.
Learn more about 0utput power here: https://brainly.com/question/20038729
#SPJ1
75m X A car moves with a uniform velocity 21 ms-1 from position P and a truck moves from rest with uniform acceleration 2 ms-2 from position Q in the same time in the same direction.
i) Determine the distance travelled in 20 seconds.
ii) How many times the private car will meet? Analyze mathematically.
Answers
Velocity after 20s for both
Car=21m/sTruck=2(20)=40m/s.Distance traveled for car
20(21)=420mDistance traveled by truck=
s=ut+1/2at²s=1/2(2)(20)²s=400m#b
Distance from Q
for car
420-75=345mFor truck
400mThe truck will meet the car after 75/21≈4s
Then for 6s the car keeps meeting because after 7 s Truck will archive 22m/s velocity
Total meet ups=6+1=7timeson which factor potential energy depends?
Answers
[tex]\large{\underline{\underline{\pmb{\frak {\color {red}{Question:}}}}}}[/tex]
[tex] \sf \red{what \: is \: potential \: energy}[/tex]
[tex]\large{\underline{\underline{\pmb{\frak {\color {blue}{Answer:}}}}}}[/tex]
Potential energy: A type of energy which is possessed by an object due its position.
Example: A raised weight or when we raise any weight is a potential energy.
[tex]\large{\underline{\underline{\pmb{\frak {\color {red}{Question:}}}}}}[/tex]
[tex] \sf \red{on \: which \: factor \: potential \: energy \: depends}[/tex]
[tex]\large{\underline{\underline{\pmb{\frak {\color {blue}{Answer:}}}}}}[/tex]
Potential energy depends upon three factors. They are:
Mass of an object. Height of an object. Gravitational force upon an object.[tex] \boxed{ \huge \frak \red{brainlysamurai}}[/tex]
During the time interval from 0.0 to 10.0 s, the position vector of a car on a road is given by x(t) = a + bt + ct2, with a = 17.2 m, b = -10.1 m/s, and c = 1.10 m/s2. What is the car’s velocity as a function of time? What is the car’s average velocity during this interval?
im stuck with this :(
Answers
The car’s velocity as a function of time is b + 2ct and the car’s average velocity during this interval is 0.9 m/s.
Average velocity of the carThe average velocity of the car is calculated as follows;
x(t) = a + bt + ct2
v = dx/dt
v(t) = b + 2ct
v(0) = -10.1 m/s + 2(1.1)(0) = -10.1 m/s
v(10) = -10.1 + 2(1.1)(10) = 11.9 m/s
Average velocityV = ¹/₂[v(0) + v(10)]
V = ¹/₂ (-10.1 + 11.9 )
V = 0.9 m/s
Thus, the car’s velocity as a function of time is b + 2ct and the car’s average velocity during this interval is 0.9 m/s.
Learn more about velocity here: https://brainly.com/question/4931057
#SPJ1
How many starlink satellites are in orbit right now.
Answers
Answer:
Currently 1,915
Explanation:
I don't know if this is still exactly accurate to date, but when I answered this question, an astronomer had been tracking that many constallations
A delivery van has 80000j of kinetic energy. if the brakes can supply a force of 12,500n to bring the van to stop, how far will the van travel while coming to rest after the brakes are applied?
Answers
The distance, van travels while coming to rest after brake applied is 6.4m
What is Work energy theorem?It states that the Work done in moving a body is equal to the change in kinetic energy of the body
Given is a delivery van whose kinetic energy K.E = 80000J and the force applied to brake F = 12500 N.
The brakes are applied to stop the van, so, final velocity is zero. Then, change in kinetic energy will be
According to work energy theorem, work done is
W = ΔK.E = K.Ef - K.Ei
W = - 80000J
Work done is also defined as the product of force applied and the distance it travelled.
W = Fs
80000 = 12500 x s
s = 6.4 m
Thus, the distance, van travels while coming to rest after brake applied is 6.4m
Learn more about work energy theorem.
https://brainly.com/question/10063455
#SPJ1
A 0.3Kg mass of liquid is heated from 20°C to 53°C. The specific heat capacity of the
liquid is 22001/Kg C. How much energy is transferred to the liquid?
Answers
The total energy is transferred to the liquid is = 217809.9 J
Given:-It is given in the question that—
weight of the liquid= 0.3kg
specific heat capacity=22001/kg C
temperature changes between 20°C to 53°C
Solution:-we can easily solve this problem by using the formula of the calorimetry principle.
The formula is —
Q= m×s×t [Q=total energy is transferred, m= mass of the substance, s= specific heat, t= final temperature - initial temperature]
by putting the value on what is given in this question —
Q= 0.3×22001×(53-20)
= 217809.9 J
So energy transferred to the liquid is=217809.9 J
If the net force acting on a moving object CAUSES NO CHANGE IN ITS VELOCITY, what happens to the object's momentum?
A. It decreases.
B. It remains equal to the force.
C. It increases.
D. It stays the same.
Answers
If the net force acting on a moving object causes no change in its velocity, the object's momentum will stay the same.
What is momentum?Momentum of a body in motion refers to the tendency of a body to maintain its inertial motion.
The momentum is the product of its mass and velocity.
This suggests that if the net force acting on a moving object causes no change in its velocity, the momentum of the object will remain the same.
Therefore, if the net force acting on a moving object causes no change in its velocity, the object's momentum will stay the same.
Learn more about momentum at: https://brainly.com/question/13554527
#SPJ1
Calculate the total distance travelled by the motorcyclist over 0-60
Answers
the unit of energy is a derived unit give reasons.
Answers
Answer:
ioinl
Explanation:
mention part of generetor and write the uses of each part
Answers
Answer:
Explanation:
If generator really means alternator as used in cars, the following can be said:
The rotor is fed with a variable voltage ranging from 0 volt to 12 volts. The 2 brushes (fixed, not rotating, like the stator) make contact with two rings that are rotating with the rotor. The rotor acts like a fixed magnet, but the magnetic field strength is constantly updated to provide a constant output voltage, even if the load current change or the motor speed change.
The stator is basically 3 coils and 6 diodes that convert the 3 phases of AC output to an almost ripple-free DC.
Note that as more energy is extracted from the alternator (for example, adding 10 amps by turning on the headlights) the shaft resists more rotation. This can be easily tested by holding an alternator in your hand, and trying to rotate the shaft by hand with no load (rotate easily, keep rotating for a few seconds), then short-circuiting the output (much harder to rotate, stop rotating immediately). The quest for magical perpetual energy where a motor is powered by an alternator is a child's dream.
A uniform cylindrical rod is 0.63m long and it has cross sectional area of 0.1m. calculate the depth of immersion
Answers
The depth of immersion of the uniform cylindrical rod is 0.63m.
What is Depth of immersion?This is defined as the distance in which a body reaches when it is submerged.
Depth of immersion = Volume/Cross-sectional area
Volume = Cross-sectional area × length
= 0.1m² × 0.63m = 0.063m³
Depth of immersion = 0.063m³ / 0.1m²
= 0.63m
Read more about Depth of immersion here https://brainly.com/question/13554650
#SPJ4
Which is one factor that contributes to the formation of polar, temperate, and tropical zones?
the angle of the Sun’s rays
the direction of seasonal winds
the presence of prevailing winds
the movement of wind near a mountain
help im timed
Answers
Answer:
The angle of the Sun's rays:
At about June 21 the sun is directly overhead at about 23 deg north of the equator
On about Dec 21 the sun is directly overhead at about 23 deg south of the equator
It is this tilt 23 deg to the ecliptic (path of earth about sun) that causes the major temperature changes on earth
17. what does it mean if a personality
test is reliable?
a. a reliable test will give consistent
results over time.
b. a reliable test reveals forgotten
experiences.
c. a reliable test has strong personal
bias.
d. a reliable test accurately predicts?
your actions.
Answers
A Personality test is said to be reliable because (A). a reliable test will give consistent results over time.
Meaning of Personality testPersonality test can be defined as a test that can be used to verify or ascertain an individuals personality.
Personality test is a test that is carried out by different organizations to help to help them know the individuals in that organization and to help others know how to relate and work with them.
In conclusion, A Personality test is said to be reliable because a reliable test will give consistent results over time.
Learn more about Personality test: https://brainly.com/question/1360758
#SPJ1
Answer:
a.
Explanation:
Is the universe endless?
Answers
The universe may indeed have an end one day according but it is yet to be shown in science.
Is the universe endless?While there is certainly no way a person will live long enough to know if the universe will end or not, nevertheless certain scientific calculations are helpful.
From astronomical calculations, the universe is anticipated to have existed for about 13.8 million years. Thus, the universe may indeed have an end one day according but it is yet to be shown in science.
Learn more about the universe:https://brainly.com/question/15844073
#SPJ1
sandra is riding a bice at 10.0 meters/second. she slows down to 2.0 meters/second in 10 seconds. her acceleration is blank meters/seconds^2
Answers
Explanation:
[tex]a = \frac{v - v _{i} }{t} [/tex]
Her intial velocity is 10
Her final velocity is 2
Time is 10 seconds.
[tex]a = \frac{2 - 10}{10} [/tex]
[tex]a = - \frac{4}{5} [/tex]
The frequency of a wave does not change as it passes from one medium to another.
What will most likely happen if a light wave moves from the air into a solid?
The wavelength of the light wave will increase.
O The speed of the light wave will decrease
The wavelength of the light wave will remain the same.
O The speed of the light wave will remain the same.
Mark this and return
Save and Exit
Next
Answers
Answer:
The speed of the wave will decrease (due to a shorter wavelength after passing from air to a more dense medium)
Would young rocks be found near a volcano?
Answers
Answer:
maybe
Explanation:
young rocks may be found near volcanoes