Answer:
C. Is traveling on a curve in the road
Hope this helps :3
The pick up truck has a changing velocity because, it is travelling on a curve in the road. A change in direction results in its change in velocity because, velocity is a vector quantity.
What is velocity ?Velocity is a physical quantity that measures the distance covered by an object per unit time. It is a vector quantity, thus having magnitude as well direction.
The rate of change in velocity is called acceleration of the object. Like velocity, acceleration also is a vector quantity. Thus, a change in magnitude or direction or change in both for velocity make the object to accelerate.
Here, all the three vehicles are travelling with the same velocity. But, the truck is moving to a curve on the road. The curvature in the path will make a change in its velocity.
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The image related with this question is attached below:
An object rotates with period of 10s.how many revolutions will it make in25s
Answer:
2¹/2
Explanation:
if the revolution is in 10 seconds the R,=Total time÷time of the revolution
Answer:
The object will make \(2\frac{1}{2}\) (2.5) revolutions in 25s.
This indicates that it will revolve through two full revolutions before rotating a third time in the opposite direction.
Explanation:
A rotational period of 10 seconds indicates that an object completes one full rotation every 10 seconds. The object's frequency is therefore 1/10 Hz, or 0.1 Hz. We must apply the calculation to determine how many revolutions it will complete in 25 seconds:
Number of revolutions = frequency x time passed
We are informed that 25 seconds have passed. Using the following formula, we can determine the frequency:
Frequency = 1 / period.
The frequency is because the period is 10 seconds:
Frequency equals 1/10, or 0.1 Hz.
Now we can calculate the number of revolutions using the formula above:
Number of revolutions = (25 s) x (0.1 Hz) = 2.5 revolutions
It takes 10 seconds for the first complete revolution, another 10 seconds for the second full revolution, and 5 seconds for the final half revolution.
In other words, the object starts at its starting location, rotates a whole anticlockwise revolution, another full anticlockwise revolution, and then eventually rotates a further half anticlockwise revolution before returning to its initial position. As a result, the item in this instance rotates in the opposite direction of clockwise.
As a result, in 25 seconds, the object will complete 2.5 revolutions.
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Suppose that in the photoelectric-effect experiment we make a plot of the detected current versus the applied potential difference. What information do we obtain from such a plot? Can we determine from it the value of Planck's constant? Can we determine the work function of the metal?
The work function of the metal is W₀ = hν₀
The electrons on and near the surface of the metal are expelled when light of continuous intensity and frequency that is greater than the threshold frequency falls on an electrode in a vacuum glass tube. For the sake of simplicity, assume that each photon releases one electron. Now that the light is consistent in intensity, the quantity of photons released and those that collide with the surface will likewise be constant, leading to a constant quantity of electrons released from the metal surface. But because they are at various speeds, the ejected electrons each have a varied amount of kinetic energy.
Only when light strikes a metal surface at a frequency greater than the threshold frequency of the metal does the photoelectric effect take place.Therefore, from above we can said, that the minimum energy of an electron from the metal surface is known as work function.
W₀ = hν₀
In above equation, h is plank constant its value is 6.626 × 10⁻³⁴J-s and ν₀
is the frequency of incident radiation.
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If a runner maintains a constant speed of 12 km/h, how long will it take to complete a marathon race of 26.2 miles?
Answer:
below
Explanation:
First, convert 26.2 mi to km = 42.16 km
then 42.16 km / 12 km/ hr = 3.51 hr = 3 hr 30.8 m
Four long wires are each carrying 6.0 A. The wires are located
at the 4 corners of a square with side length 9.0 cm. All of
these wires are carrying current out of the page. The
magnetic field (in T) at one corner of the square is:
Answer:
\(B_T=2.0*10^-5[-\hat{i}+\hat{j}]T\)
Explanation:
To find the magnitude of the magnetic field, you use the following formula for the calculation of the magnetic field generated by a current in a wire:
\(B=\frac{\mu_oI}{2\pi r}\)
μo: magnetic permeability of vacuum = 4π*10^-7 T/A
I: current = 6.0 A
r: distance to the wire in which magnetic field is measured
In this case, you have four wires at corners of a square of length 9.0cm = 0.09m
You calculate the magnetic field in one corner. Then, you have to sum the contribution of all magnetic field generated by the other three wires, in the other corners. Furthermore, you have to take into account the direction of such magnetic fields. The direction of the magnetic field is given by the right-hand side rule.
If you assume that the magnetic field is measured in the up-right corner of the square, the wire to the left generates a magnetic field (in the corner in which you measure B) with direction upward (+ j), the wire down (down-right) generates a magnetic field with direction to the left (- i) and the third wire generates a magnetic field with a direction that is 45° over the horizontal in the left direction (you can notice that in the image attached below). The total magnetic field will be:
\(B_T=B_1+B_2+B_3\\\\B_{T}=\frac{\mu_o I_1}{2\pi r_1}\hat{j}-\frac{\mu_o I_2}{2\pi r_2}\hat{i}+\frac{\mu_o I_3}{2\pi r_3}[-cos45\hat{i}+sin45\hat{j}]\)
I1 = I2 = I3 = 6.0A
r1 = 0.09m
r2 = 0.09m
\(r_3=\sqrt{(0.09)^2+(0.09)^2}m=0.127m\)
Then you have:
\(B_T=\frac{\mu_o I}{2\pi}[(-\frac{1}{r_2}-\frac{cos45}{r_3})\hat{i}+(\frac{1}{r_1}+\frac{sin45}{r_3})\hat{j}}]\\\\B_T=\frac{(4\pi*10^{-7}T/A)(6.0A)}{2\pi}[(-\frac{1}{0.09m}-\frac{cos45}{0.127m})\hat{i}+(\frac{1}{0.09m}+\frac{sin45}{0.127m})]\\\\B_T=\frac{(4\pi*10^{-7}T/A)(6.0A)}{2\pi}[-16.67\hat{i}+16.67\hat{j}]\\\\B_T=2.0*10^-5[-\hat{i}+\hat{j}]T\)
If you walk 17.8m at an angle of 63 degree north of east how far north are you from your starting position
Answer:
Sy = S sin θ = 17.8 sin 63 = 15.9 m north of east from the start
An object with a mass of 2 kg is moving with a velocity of 3 m/s when a 5 N net force
acts upon it. What will the object's velocity be if the force acts for 7 S?
By Newton's second law, the net force exerted on the object makes it undergo an acceleration a such that
(2 kg) a = 5 N
so that it is accelerated a = 2.5 m/s^2.
Since the object starts with velocity 3 m/s, after 7 s its acceleration will make it speed up to
3 m/s + (2.5 m/s^2) (7 s) = 20.5 m/s
1)What is the pressure at point D in kPa ?
2)Temperature at point D
3)What is the net work done on the gas as it is taken through four cycles?
4)What is the internal energy of the gas when it is at point A?
5)What is the total change in internal energy of this gas during four complete cycles?
The answer is 1) The pressure at point D is 80 kPa. 2) The temperature at point D is 800 K. 3) The net work done on the gas over four cycles is zero. 4) The internal energy of the gas at point A is 100 J. 5) The total change in internal energy during four complete cycles is zero.
The total change in internal energy of this gas during four complete cycles is zero. The given diagram represents the Carnot cycle involving four stages. The four stages of the Carnot cycle are reversible and follow an ideal gas that is placed in a cylinder with a movable piston.Let's solve each question asked one by one.1) From the graph, it can be observed that the pressure at point D is 0.08 M Pa, which is equal to 80 kPa. Hence, the pressure at point D in kPa is 80 kPa.2) Temperature at point D The isotherm at point D is about 800 K. Hence, the temperature at point D is 800 K.3) The net work done on the gas as it is taken through four cycles is zero because the Carnot cycle is a cycle that has four stages. In each cycle, the net work done is the area enclosed by the cycle. Therefore, for a complete cycle, the net work done is zero because the area enclosed is a loop.4) The internal energy of the gas when it is at point A is 100 J because the internal energy of the gas is directly proportional to the temperature and volume. Here, at point A, the temperature is 500 K, and the volume is 2 m³, so the internal energy of the gas when it is at point A is 100 J.5) The Carnot cycle is a reversible cycle that is used to determine the efficiency of heat engines. It is a closed cycle that does not involve any net energy exchange with the surroundings. Therefore, the total change in internal energy of this gas during four complete cycles is zero since the initial and final states are the same. Hence, the total change in internal energy of this gas during four complete cycles is zero.For more questions on the Carnot cycle, click on:
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Are we within Earth's Roche limit?
Answer:
Yes
Explanation:
Within the Earths Roche is our mass and body.
The Earth rotates once every day. What is the velocity of a person on its surface, if the radius of Earth is 6 million meters
Answer:
v = ω R
number of seconds in 24 hrs = 24 * 3600 = 86400 s / da = T (period)
f = 1 / T
ω = 2 Π f = 2 Π / T = 2 Π / 86400
v = 2 Π / 8.64E4 * 6.0E6 = 436 m / s
Check:
S = 2 Π * 6.0E6 = 3.77E7 m/da
S / T = 3.77E7 m/da / 8.64E4 s/da = 436 m / s
At low pressures and high temperatures, the density of a gas
Answer:
Higher denisty
Explanation:
High pressure=high denisty
The diagram below shows the velocity vectors for two cars that are moving
relative to each other.
45 m/s west
25 m/s east
Car 1
Car 2
From the frame of reference of car 1, what is the velocity of car 2?
OA. 20 m/s west
OB. 70 m/s east
C. 70 m/s west
D. 20 m/s east
The relative velocity of the car 2 with respect to car 1 is 70 m/s west. So, the correct option is C.
Velocity of the car 1 with respect to the ground, v₁ = 45 m/s west
Velocity of the car 2 with respect to the ground, v₂ = 25 m/s east
Let the direction towards the east be positive and the opposite direction towards the west be negative.
The expression for the relative velocity of the car 2 with respect to car 1 is given by,
v₂₁ = v₂ - v₁
v₂₁ = 25 - (-45)
Therefore, the relative velocity,
v₂₁ = 70 m/s west
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Attaching the image file here.
A person standing on the roof of a building drops a 0.125 Kg ball on the ground. A
child on eight floor saw the ball passing with a speed of 33.1 m/s. The first floor of the building
is 12.0 m high and each successive floor is 8.00 m high. Determine the total numbers of floors
in the building. How fast was the ball falling just before it hit the ground? What was its kinetic
energy just before it hit the ground?
Answer:
V = a t velocity after time t
t = 33.1 / 9.80 = 3.38 sec (time ball had been falling)
S = 1/2 a t^2 = 55.9 m
So the ball had been falling for 7 * 8 = 56 m
The child was 7 floors from the top
Since he was on the eight floor the floors below him were
7 * 8 + 12 = 68 m total floors below child
68 + 56 = 124 m total height of building
Total floors in building = 7 + 7 + 1 = 15 floors
PE at top = KE at bottom
KE = m g h = .125 * 9.80 * 124 = 152 Joules
A hiker walks 4.30 km east, turns 90.0º due south and walks an additional 2.48 km. What distance did the hiker travel? *
24.64 km
6.78 km
1.82 km
4.96 km
Answer:
6.78 km
Explanation:
Length of path due east = 4.3km
Length of path south = 2.48km
Unknown:
Distance covered = ?
Solution:
The distance covered is the total length of path from start to finish. It takes cognizance of the turns and every direction moved.
Unlike displacement which only considers the net direction from start to finish, distance sums up the total path.
So;
Distance = 4.3km + 2.48km = 6.78km
A dragster crosses the finish line with a velocity of 140m/s . Assuming the vehicle maintained a constant acceleration from start to finish, what was its average velocity for the race?
Answer:
Answer is attached
The average velocity for the race is 70 m/s if the dragster crosses the finish line with a velocity of 140 m/s.
What is linear acceleration?It is defined as the rate of change in linear velocity with respect to time. It is also known as linear acceleration.
It is given that:
A dragster crosses the finish line with a velocity of 140m/s.
The vehicle maintained a constant acceleration from start to finish.
As we know,
The average velocity can be given as:
V(avrg) = (v1 + v2)/2
v1 = 140 m/s
v2 = 0 m/s
v(avrg) is the average of the velocity.
V(avrg) = (140 + 0)/2
V(avrg) = 140/2
V(avrg) = 70 m/s
Thus, the average velocity for the race is 70 m/s if the dragster crosses the finish line with a velocity of 140 m/s.
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5. You are pulling a rubber sneaker along concrete
a. Calculate force of static friction between your sneakers (2kg) and sidewalk if coefficient of
static friction is 0.9
Answer:
Fs = 17.66 N
Explanation:
The force of static friction is given by the following formula:
\(F_s = \mu R = \mu W\\\)
where,
Fs = The force of static friction = ?
μ = coefficient of static friction = 0.9
W = weight of sneakers = mg
m = mass of sneakers = 2 kg
g = acceleration due to gravity = 9.81 m/s²
Therefore,
\(F_s = \mu mg\\F_s = (0.9)(2\ kg)(9.81\ m/s^2)\\\)
Fs = 17.66 N
A toy cars engine pushes it forward at a constant speed. What happens if the force provided by the engine decreases?
If the force provided by the engine of a toy car decreases, the car will slow down and eventually come to a stop.
1. The force provided by the engine of a toy car is responsible for propelling it forward at a constant speed. This force overcomes any friction or resistance acting on the car.
2. When the force provided by the engine decreases, there is a reduction in the overall force acting on the car. As a result, the force can no longer counteract the resistance and friction effectively.
3. The resistance and friction acting on the toy car, such as air resistance and the friction between the wheels and the surface, start to have a greater impact on the car's motion.
4. With a reduced force from the engine, the car begins to slow down gradually. The deceleration occurs because the opposing forces now have a greater influence on the car's motion.
5. As the force continues to decrease, the opposing forces eventually surpass the remaining force from the engine. Consequently, the toy car slows down even more and eventually comes to a complete stop.
6. If the force provided by the engine becomes extremely low or nonexistent, the opposing forces will completely overpower the forward force, causing the toy car to stop moving altogether.
In summary, when the force provided by the engine of a toy car decreases, the car's speed decreases, and it eventually comes to a stop due to the increased influence of opposing forces.
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An experiment is performed in which a force is applied to two objects (A and B) and the resulting acceleration is measured. The
graph below summarizes the results. Answer the following questions:
a. What is the relationship between force and acceleration?
b. What are the units for the slope of the line? Show you work below:
acceleration (m/s2)
Force (N)
c. Using the line equation (y = mx +b), derive a general equation that describes the relationship between force and
acceleration.
d. What does the equation you derived above tell you about the relationship between mass and acceleration?
your answer is second hope it's helpful to you
1. A ball is at rest on the top of a hill (see the figure).
At the top of the hill, the ball will have [the maximum value of its, no, the minimum value of its] gravitational potential energy and [no, the maximum value of its] kinetic energy. If the ball rolls down the hill then, its [gravitational potential energy, kinetic energy] is converted to [gravitational potential energy, kinetic energy] when it gets to the ground.
2. Get your stopwatch ready and prepare to drop the object from the height h you selected in the previous step. You should drop the object so its [bottom, top, middle] part is initially at the height h. The initial speed of the ball [zero, 9.8 m/s, 9.8 m/s^2, depends on the height h] You'll need to measure the time from when the ball leaves your hand to exactly when it hits the ground [ for the first time it bounces, after it bounces and then comes to rest, both the first time and then after it bounces; then average the two times]
.
A block suspended from a spring is oscillating vertically with a frequency of 4 Hz and an amplitude of 7 cm. A very small rock is placed on top of the oscillating block just as it reaches its lowest point. Assume that the rock has no effect on the oscillation. At what distance above the block’s equilibrium position does the rock lose contact with the block? (hint this occurs when the rock’s acceleration equals the value of gravity) What is the speed of the rock when it leaves the block? What is the greatest distance above the block’s equilibrium position reached by the rock? (Let t = 0 be when the rock is placed on the block)
Answer:
v = - 1,715 m / s , x = 0.0156 m
Explanation:
This is an oscillatory movement exercise, which is described by the expression
x = A cos (wt + Ф)
we can assume that the block is released from its maximum elongation, so the phase constant (Ф) is zero
As we are told that the stone does not affect the movement of the spring mass system, the amplitude and angular velocity do not change, in the upward movement the stone is attached to the mass, but in the downward movement the mass has an acceleration greater than g leave the stone behind, let's look for time, for this we use the definition of speed and acceleration
v = dx / dt
v = - A w sin wt
a = - Aw² cos wt
a = -g
-g = - Aw² cos wt
wt = cos⁻¹ (g / Aw²)
t = 1 / w cos⁻¹ (g / Aw²)
angular velocity and frequency are related
w = 2π f
w = 2π 4
w = 8π rad / s
remember that the angles are in radians
t = 1 / 8π cos⁻¹ (9.8 / (0.07 64π²))
t = 0.039789 1.3473
t = 0.0536 s
let's find the speed for this time
v = - A w sin wt
v = - 0.07 8π sin (8π 0.0536)
v = - 1,715 m / s
the distance is
x = A cos wt
x = 0.07 cos (8π 0.0536)
x = 0.0156 m
how long does the guided discovery stage of the drawing in phase last? in training program
Answer:
2 to 3 weeks
Explanation:
A 2.1 x 103 kg car starts from rest in a driveway. An average force of 4.0 x 103 N act on the car so that the car’s speed at the end of the driveway is 3.8 m/s. What was the length of the driveway?
Answer:
Explanation:
We can use the kinematic equation v^2 = u^2 + 2as to solve for the length of the driveway. Here, u = 0 (since the car starts from rest), v = 3.8 m/s, a = F/m = 4.0 x 10^3 N / 2.1 x 10^3 kg = 1.9 m/s^2. Solving for s, we get:
s = (v^2 - u^2) / 2a = (3.8^2) / (2 x 1.9) = 3.8 m
So the length of the driveway is 3.8 meters.
Select the correct answer.
A boat moves 60 kilometers east from point A to point B. There, it reverses direction and travels another 45 kilometers toward point A. What are the total
distance and total displacement of the boat?
O A.
OB.
O C.
O D.
The total distance is 105 kilometers and the total displacement is 45 kilometers east.
The total distance is 60 kilometers and the total displacement is 60 kilometers east.
The total distance is 105 kilometers and the total displacement is 15 kilometers east.
The total distance is 60 kilometers and the total displacement is 45 kilometers east.
The total distance is 105 kilometers and the total displacement is 15 kilometers east. Option C
How to solve for the total distanceTo calculate the total distance, we add the distances traveled in each leg of the journey: 60 kilometers (from A to B) + 45 kilometers (from B back to A) = 105 kilometers.
However, displacement refers to the change in position of an object in a straight line from its starting point to its ending point. In this case, since the boat starts and ends at the same point (A), the total displacement is zero.
Hence The total distance is 105 kilometers and the total displacement is 15 kilometers east.
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Which of the following is true at the point where you reach the top of your jump on a trampoline?
The mechanical energy is zero
he potential energy is at maximum
The kinetic energy and potential energy are equal.
The potential energy is zero.
The potential energy is at the maximum when you reach the top of your jump on a trampoline. The correct answer is option B.
What is Potential EnergyPotential Energy is the type of energy an object possesses by virtue of its position relative to others, stresses within itself, electric charge, and other factors. Potential energy exists in various forms, including gravitational potential energy, elastic potential energy, chemical potential energy, and electrical potential energy.
This type of energy can be converted into another type of energies. Examples, a charged battery has potential energy and it can be used as electrical potential energy. Petrol, diesel and and gas have chemical potential energy and be used as kinetic energy.
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2. Kevin works as a janitor, and he is pushing a fully-
loaded recycling bin that weighs 557 N across the
floor. He applies a force of 410 N at an angle of 15°
below the horizontal. The coefficient of kinetic friction
between the recycling bin and the floor is 0.46. How
long does it take him to move the bin 6.5 meters,
assuming the bin starts from rest?
The time taken for him to move the bin 6.5 m is 2.30 s.
The given parameters;
weight of the load, w = 557 Nforce applied , F = 410 Nangle of force, = 15°coefficient of kinetic friction = 0.46distance moved, d = 6.5 mThe net horizontal force on the recycling bin is calculated as follows;
\(Fcos\theta - F_k = ma\)
where;
m is the mass of the recycling bin\(F_k\) is the frictional forceW = mg
\(557 = 9.8m\\\\m = \frac{557}{9.8} \\\\m = 56.84 \ kg\)
The net horizontal force on the recycling bin is calculated as;
\(Fcos \theta - F_k = ma\\\\Fcos\theta - \mu_kF_n = ma\\\\410\times cos(15) \ - \ 0.46(557) = 56.84 a\\\\139.8 = 56.84a\\\\a = \frac{139.8}{56.84} \\\\a = 2.46 \ m/s^2\)
The time taken for him to move the bin 6.5 m is calculated as follows;
\(s = v_0t + \frac{1}{2} at^2\\\\6.5 = 0 + \frac{1}{2} \times 2.46\times t^2\\\\6.5 = 1.23 t^2\\\\t^2 = \frac{6.5 }{1.23} \\\\t^2 = 5.285\\\\t = \sqrt{5.285} \\\\t = 2.30 \ s\)
Thus, the time taken for him to move the bin 6.5 m is 2.30 s.
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What do you picture in your mind when you read this simile?
Bolt runs as fast as lighting.
Bolt runs very fast.
Bolt runs in a straight line.
Bolt runs in a wavy manner.
Bolt's each step produces thunder.
When reading the simile "Bolt runs as fast as lightning," the most appropriate visual interpretation would be that "Bolt runs very fast."
This simile compares Bolt's speed to that of lightning, which is known for its incredible swiftness. The intention is to emphasize Bolt's exceptional speed by equating it to the rapid movement of lightning.
While the simile highlights Bolt's remarkable speed, it does not specify the manner in which he runs or the impact of each step. Therefore, the options suggesting Bolt runs in a straight line, in a wavy manner, or that each step produces thunder are not directly implied by the simile itself. These additional details go beyond the comparison of speed and introduce elements that are not explicitly mentioned.
Hence, the most accurate interpretation based solely on the simile is that Bolt runs very fast, comparable to the speed of lightning.
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Given that two vectors A = 5i-7j-3k, B = -4i+4j-8k find A×B
\(\textbf{A}×\textbf{B}= 68\hat{\textbf{i}} + 52\hat{\textbf{j}} - 8\hat{\textbf{k}}\)
Explanation:
Given:
\(\textbf{A} = 5\hat{\textbf{i}} - 7\hat{\textbf{j}} - 3\hat{\textbf{k}}\)
\(\textbf{B} = -4\hat{\textbf{i}} + 4\hat{\textbf{j}} - 8\hat{\textbf{k}}\)
The cross product \(\textbf{A}×\textbf{B}\) is given by
\(\textbf{A}×\textbf{B} = \left|\begin{array}{ccc}\hat{\textbf{i}} & \hat{\textbf{j}} & \hat{\textbf{k}} \\\:\:5 & -7 & -3 \\ -4 & \:\:4 & -8 \\ \end{array}\right|\)
\(= \left|\begin{array}{cc}-7 & -3\\\:4 & -8\\ \end{array}\right|\:\hat{\textbf{i}}\:+\:\left|\begin{array}{cc}-3 & \:\:5\\-8 & -4\\ \end{array}\right|\:\hat{\textbf{j}}\:+\: \left|\begin{array}{cc}\:\:5 & -7\\-4 & \:\:4\\ \end{array}\right|\:\hat{\textbf{k}}\)
\(= 68\hat{\textbf{i}} + 52\hat{\textbf{j}} - 8\hat{\textbf{k}}\)
I have an idea that I will ask a question a day and see who will answer best now today I have the trolly question. There is a trolly going down two tracks it cant be stopped, on one of the tracks is only 1 person who is your best friend, on the other track there are five people you don't know, will you choose to hit one person or five people?
Answer:
I would go for the one person, but not because I'd rather risk one life over five.
Explanation:
But instead, I think it would be a lot easier to warn the one person to move out the way of the trolly, than to try and get the attention of five different strangers on the other track.
Not to mention there'd be much less confusion and chaos, if you just signal to your friend to get out the way, because you only need that one person to hear you.
I hope you like my answer :)
Which vector is the sum of vectors à and b?
The vectors addition permits locating the perfect result for the sum of the two vectors in option B). See attached and the vector is directed to the right and up.
Vector addition is the operation of adding or extra vectors together into a vector sum. The so-known as parallelogram regulation gives the rule for vector addition of or greater vectors. for two vectors and, the vector sum is received via placing them head to tail and drawing the vector from the loose tail to the unfastened head.
A vector is an amount or phenomenon that has impartial residences: importance and direction. The time period also denotes the mathematical or geometrical representation of the sort of quantity. Examples of vectors in nature are velocity, momentum, force, electromagnetic fields, and weight.
Vectors are used in technological know-how to describe something that has a direction and a magnitude. they're commonly drawn as pointed arrows, the length of which represents the vector's importance
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Which vector is the sum of vectors à and b?
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What is the direction of magnetic field lines inside any magnet?
A.
They travel from north to south.
B.
They travel from south to north.
C.
They travel in a loop.
D.
They travel back and forth within the magnet.
E.
They do not travel through the magnet.
Answer:
c
Explanation:
A plank AB 3m long weighing 20kg and with center of gravity 2m from the end A carries a load of mass 10kg at the end A it rests on two supports CandD.
1, compute the values of the reaction forces R1 and R2 at C and D.
2, how far from D and on which side of it must a mass of 24kg be placed on the plank so as to make the reactions equal? What are their values.
3,without this 24kg what vertical force applied at B will just lift the plank clear of D? What is then the reaction at C.
The answers are 1) The value of R2 is not relevant as it implies a downward force on the plank, 2) The reactions at C and D are 66.3 N and 90 N, respectively, and 3) The vertical force at B to lift the plank clear of D is 686.4 N. The reaction at C is zero, and the reaction at D is 61.4 kg.
1) R1 and R2 at C and D respectively are given by the equation R2 = (m1 + m2)g - R1, where m1 and m2 are the masses of the plank and load, respectively, and g is the acceleration due to gravity. Hence, substituting values R2 = (20 + 10) × 9.81 - R1 = 294.3 - R1. Now, taking moments about D, the following equation can be obtained: (20 × 1 + 10 × 3)g = R1 × 2 + R2 × 3 = 2R1 + 3 × (294.3 - R1) = 882.9 - R1, from which R1 = 343.7 N and R2 = 294.3 - 343.7 = -49.4 N. Since the support at D can only push the plank upwards and cannot pull it downwards, a negative value for R2 implies that the plank is actually being pulled downwards by an external force. Therefore, the value of R2 is not relevant. 2) The total weight of the plank and the load acting at the end A is 20 + 10 = 30 kg. For the reactions at C and D to be equal, the 24 kg mass must be placed at a distance x from D such that x × 30 = 24 × 6, from which x = 12/5 = 2.4 m. Since the 24 kg mass is being placed to the left of the plank, it will cause the reaction at C to decrease and that at D to increase. Thus, if R is the vertical force applied at B, then taking moments about D gives 20g × 1 - 10g × 3 + R × 6 = 0, from which R = 90 N. Taking moments about C gives R × 3 - 10g × 2 = 0, from which R = 66.3 N. 3) The vertical force applied at B that will just lift the plank clear of D is the weight of the plank and the load acting at the end A plus the weight of the part of the plank that is to the right of D. The weight of the plank and the load acting at the end A is 20 + 10 = 30 kg, and the weight of the part of the plank that is to the right of D is 24 × 1.6 = 38.4 kg. Therefore, the vertical force applied at B that will just lift the plank clear of D is (20 + 10 + 38.4)g = 686.4 N. The reaction at C is zero because the plank is not being supported there anymore. The reaction at D is the same as the weight of the plank and the load acting at the end A plus the weight of the part of the plank that is to the right of D, which is 20 + 10 + 24 × 1.6 = 61.4 kg.For more questions on acceleration
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