Three blocks in contact with each other are pushed across a rough horizontal surface by 63 N force as shown. The acceleration of gravity is 9.8 m/s 2 kg kg 2.5 kg K = 0.1 If the coefficient of kinetic friction between each of the blocks and the surface is 0.1, find the magnitude of the force exerted on the 9 kg block by the 2.5 kg block_ Answer in units of N.
The 2.5 kg block pulls on the 9 kg block with an 87.2 N force.
Newton's Third Law, often known as the law of action and reaction, can be used to determine the force that the 2.5 kg block exerts on the 9 kg block. The force applied to the 9 kg block is equivalent to, but applied in the opposite direction from, the force applied to the 2.5 kg block. Since they are in touch, the force of friction operating on the 9 kg block is equal to the force of friction acting on the 2.5 kg block.
Calculating the friction force is as simple as multiplying the normal force, or weight of the object, by the coefficient of friction:
Step 1: Determine the normal force or weight of the object. The weight of a 9 kg object can be calculated as 9 kg x 9.8 N/kg = 87.2 N.
Step 2: Determine the coefficient of friction. In this case, the coefficient of friction is 0.1.
Step 3: Calculate the friction force by multiplying the normal force by the coefficient of friction.
Friction force = Normal force x Coefficient of friction
= 87.2 N x 0.1 = 8.72 N.
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A parachute is used to decelerate a skydiver from an initial velocity of vo = 83 m/s to a velocity of vf = 9 m/s. The deceleration produced by the parachute is a = (-0.0302) m/s2. Determine the distance in [m], As, required to reach its final speed. As = number (3 significant figures) [m]
The distance required to be covered by the skydiver to reach the final speed is found to be 378.22m.
The deceleration produced by the parachute is -0.0302m/s². The final and the initial velocity of the skydiver are 9m/s and 83m/s respectively.
Now, we know the equation of motion,
V² - U² = 2as
Where,
V and U are the final and the initial velocity,
a is the net acceleration,
s is the distance covered by the parachute.
Now, putting all the values,
(9)²-(83)² = 2(-0.0320)s
s = 378.22 m.
So, distance that should be travelled by the skydiver is 378.22m.
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Consider the point charges arranged at the corners and at the center of a square, as depicted in the figure. 1. Find the magnitude of the electric field, in newtons per coulomb, at the location of qa in the figure, given that qb= qc = qd = 5.6 nC, q = -1.3 nC, and the square is 6 cm on a side.
The magnitude of the electric field, in newtons per coulomb, at the location of qa in the figure is 32737.87 N/C.
What is electric field?
An electric field is a physical field that surrounds electrically charged particles and acts as an attractor or repellent to all other charged particles in the vicinity. It can also refer to a system of charged particles' physical field.
When charge is present in any form, every point in space has an electric field associated with it. The value of E, often known as the electric field strength, electric field intensity, or just the electric field, expresses the strength and direction of the electric field.
[tex]$$The $\mathrm{x}$ component of $\vec{E}_q$ is given as:$$\begin{aligned}\vec{E}_{q, x} & =E_q \cos 45^{\circ} \hat{x} \\& =k \frac{\left|-1.1 \times 10^{-9}\right|}{1.25 \times 10^{-3}} \times \frac{1}{\sqrt{2}} \hat{x}\end{aligned}$$And its y component is given as:$$\begin{aligned}\vec{E}_{q, y} & =-E_q \sin 45^{\circ} \hat{y} \\& =-k \frac{\left|-1.1 \times 10^{-9}\right|}{1.25 \times 10^{-3}} \times \frac{1}{\sqrt{2}} \hat{y}\end{aligned}$$[/tex]
[tex]$$Therefore, the net electric field at the location of $q_a$ is given as:$$\begin{aligned}\vec{E} & =\vec{E}_b+\vec{E}_c+\vec{E}_{d, x}+\vec{E}_{d, y}+\vec{E}_{q, x}+\vec{E}_{q, y} \end{aligned}[/tex]
[tex]& =k \times 10^{-9} \times\left(\left(-\frac{5.9}{(0.05)^2}-\frac{5.9}{\sqrt{2} \times 5 \times 10^{-3}}+[/tex] [tex]\frac{1.1}{\sqrt{2} \times 1.25 \times 10^{-3}}\right) \hat{x}+\left(\frac{5.9}{(0.05)^2}+\frac{5.9}{\sqrt{2} \times 5 \times 10^{-3}}-\frac{1.1}{\sqrt{2} \times 1.25 \times 10^{-3}}\right) \hat{y}\right) \end{aligned}[/tex]
[tex]\begin{aligned}& =\left(9 \times 10^9\right) \times 10^{-9} \times(-2572.13 \hat{x}+2572.13 \hat{y}) \\& =23149.17 \times(-\hat{x}+\hat{y}) \mathrm{N} / \mathrm{C}\end{aligned}[/tex]
[tex]$And its magnitude is given by:$$\begin{aligned}|\vec{E}| & =23149.17 \times \sqrt{1^2+1^2} \\& =23149.17 \times \sqrt{2} \\& =32737.87 \mathrm{~N} / \mathrm{C}\end{aligned}$$[/tex]
Thus, the magnitude of the electric field, in newtons per coulomb, at the location of qa in the figure is 32737.87 N/C.
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How can you show respect of others intellectual property?
Answer:
You can show respect for others' intellectual property by:
Acknowledging the source of the material and giving credit to the original creator or owner.Obtaining permission before using or reproducing any protected material, such as patents, trademarks, copyrights, or trade secrets.Following all laws and regulations related to intellectual property, such as the Digital Millennium Copyright Act (DMCA).Not infringing on others' intellectual property rights by creating or distributing counterfeit or fake products.Being mindful of others' rights and taking steps to protect their intellectual property, just as you would want others to respect your own.The measured total pressure for each trial is the sum of the vapor pressure of the liquid and the pressure due to any air trapped in the flask (see equation 1 in the introduction) a) What happens to the air pressure in higher temperature flasks? Explain in terms of molecular motion. b) Calculate corrected air pressures for any of the trials that were not performed at the same temperature as the atmospheric pressure data. Hint: P1/T1 = P2/T2
As the temperature of the flask increases, the molecules in the air become more energetic, resulting in an increase in air pressure.
Given the total pressure measured for the each trail = vapor pressure of liquid + pressure due to any air trapped in the flask.
a) The pressure of the gas rises because the molecules collide with the container walls more frequently as a result of the faster collisions between the molecules and the walls. This is because the molecules are moving faster and collide more often with the walls of the flask, creating a greater force.
b) To calculate the corrected air pressure, the ideal gas law can be used (P1/T1 = P2/T2). The atmospheric pressure (P1) and temperature (T1) must be known for the trial and the temperature (T2) of the flask must be known. The corrected air pressure (P2) can then be calculated.
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a star with 0.5 apparent magnitude would appear how many times brighter than a star with 5.5 apparent magnitude? Therefore the star with apparent magnitude 0.5 must be how many times farther away?
The star with an apparent magnitude of 0.5 appears approximately 100.06 times brighter than the star with an apparent magnitude of 5.5. It is approximately 10 times closer to us.
The magnitude scale used in astronomy is logarithmic, which means that each whole number increase or decrease in magnitude represents a difference in brightness by a factor of approximately 2.512. Therefore, to determine the relative brightness between two stars, we can calculate the difference in magnitude and then use this factor.In this case, the difference in apparent magnitude between the two stars is 5.5 - 0.5 = 5 magnitudes. Using the factor of 2.512, we can calculate the relative brightness:Brightness factor = 2.512^(difference in magnitude) = 2.512^5 ≈ 100.06So, the star with an apparent magnitude of 0.5 would appear approximately 100.06 times brighter than the star with an apparent magnitude of 5.5.To determine the distance between the two stars, we can use the inverse square law of light. Since brightness decreases with distance squared, if one star appears 100.06 times brighter, it must be approximately [tex]\sqrt{ 100.06}[/tex] ≈ 10 times closer to us than the star with apparent magnitude 5.5.For more questions on magnitude
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body a of mass 4m moving with speech u colldes with another body b of mass 2m, at rest the collisn on and elastic nature. after collision the fracyion of energy lost by the colding body a is
a.1/9
b.8/9
c.4/9
d.5/9
The fraction of energy lost by the colliding body is 8/9.
In an elastic collision, the total kinetic energy of the system before the collision is equal to the total kinetic energy of the system after the collision.
Before the collision, the total kinetic energy of the system is given by:
[tex]K1 = 0.5 * m1 * u^2[/tex]
After the collision, the total kinetic energy of the system is given by:
[tex]K2 = 0.5 * m_{1} * v_{1} ^2 + 0.5 * m_{2} * v_{2}^2[/tex]
where m1 is the mass of body A, u is its initial velocity, v1 is its final velocity, m2 is the mass of body B, and v2 is its final velocity.
Conservation of momentum also applies in this case. The momentum of the system before the collision is equal to the momentum of the system after the collision.
Before the collision, the momentum of the system is given by:
[tex]p_{1} = m_{1} * u[/tex]
After the collision, the momentum of the system is given by:
[tex]p_{2} = m_{1} * v_{1} + m_{2} * v_{2}[/tex]
From the conservation of momentum, we have:
[tex]m_{1} * u = m_{1} * v_{} + m_{2} * v_{2}[/tex]
Solving for v1 and v2, we find:
[tex]v_{1} = u * (m_{1} - m_{2}) / (m_{1} + m_{2})[/tex]
[tex]v_{2} = 2 * u * m_{1} / (m_{1} + m_{2})[/tex]
Substituting these values into the equation for K2, we find:
[tex]K_{2} = 0.5 * m_{1} * u^2 * (m_{1} - m_{2})^2 / (m_{1} + m_{2})^2[/tex]
The fraction of energy lost by body A is given by:
[tex](K_{1} - K_{2}) / K_{1} = 1 - K_{2} / K_{1}[/tex]
= [tex]1 - 0.5 * m_{1} * u^2 * (m_{1} - m_{2})^2 / (m_{1} + m_{2})^2 / (0.5 * m_{1} * u^2)[/tex]
= [tex]1 - (m_{1} - m_{2})^2 / (m_{1} + m_{2})^2[/tex]
= 1 - (4 - 2)^2 / (4 + 2)^2
= 1 - (2)^2 / (6)^2
= 1 - 4/36 = 1 - 1/9 = 8/9
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A 5.0 Ω, 10.0 Ω, 12.0 Ω, and 16.0 Ω resistor are connected in series to a 120 V voltage source. What is the current of the circuit?
A) 2.8 A
B) 4.4 A
C) 44 mA
C) 28 mA
Answer:
2.8 A
Explanation:
since the resistances are in series, the net resistance will be,
R = R1 + R2 + R3 + .....
R = ( 5+10+12+16)Ω
R = 43Ω
From Ohm's law,
V = iR
120 = i * 43
i = 120/43 A
i = 2.8A
Assuming all of the resistors have the same resistance, which of the following correctly ranks the equivalent resistance of the circuits shown?
A. b < d < c < a
B. d < b < a < c
C. a < c < d < b
D. c > a > d > b
E. a = b = c = d
The correct answer is (A) b < d < c < a.
How to determine the equivalent resistance of the circuit?we need to consider the placement of the resistors.
In circuits a, b and c, resistors are connected in series. The corresponding resistance of resistors combined in series is the sum of the particular resistances. So the equivalent resistance for these circuits is:
a) 3R + R + 3R = 7R
b) R + R + 3R + 3R = 8R
c) 3R + R + R + 3R = 8R
In circuit d, resistors are connected in parallel. The equivalent resistance of resistors connected in parallel is given by the formula
1/request = 1/R + 1/R + 1/R = 3/R
Therefore Req = R/3. Comparing the values of the equivalent resistors reveals the following:
b < d < c < a
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I need help answering these questions on this worksheet
The density measures the compactness of a substance. Here the density of an object of mass 60 g and volume 150 cm³ is 0.4 g/cm³.
What is density?The mass of an object contained per unit volume is defined as the density. The SI unit of density is kg / m³. The equation used to calculate density is:
Density = Mass / Volume
= 60 / 150 = 0.4 g/cm³
The objects which have same volume, but different masses have different densities. If greater the mass, more dense will be the object.
Thus the density of the object is 0.4 g/cm³.
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suppose that the apparatus used in the demonstration is placed on a moving cart. the cart moves with a constant acceleration a, and the spring is activated when the cart crosses point p. which ball will hit the ground first?a. Ball A and Ball B hit the ground simultaneously b. Ball Ac. Ball B
The ball will hit the ground first if the cart moves with a constant acceleration a, and the spring is activated when the cart crosses point P as Ball A and Ball B hit the ground simultaneously.
Thus, the correct option is A.
What is constant acceleration?Аccelerаtion is the rаte of chаnge in velocity, which is а vector, therefore, chаnges in this quаntity cаn influence its mаgnitude аnd/or direction. Аlthough аccelerаtion cаn be null, positive, or negаtive, it is, often, misunderstood аs а synonym for speeding up. This is true when аccelerаtion is positive for а strаight-line motion. In this type of motion, а negаtive аccelerаtion meаns thаt the object is slowing down, аnd а null аccelerаtion meаns thаt the speed does not chаnge.
Thus, when the cart moves with a constant acceleration a, and the spring is activated when the cart crosses point P, Ball A and Ball B hit the ground simultaneously.
Your question is incomplete, but most probably your full question can be seen in the Attachment.
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a motorized pulley lifts an object of mass m at a constant velocity v. assuming that all frictional forces are abscent, find average power
The vertical component of acceleration at time tm can be determined by taking the second derivative of the vertical position vector with respect to time.
What is velocity?Velocity is a vector quantity that measures the rate and direction of change in an object's position. It is typically expressed in units of meters per second (m/s). Velocity is equal to the distance traveled divided by the time it takes to travel that distance. Velocity is also related to acceleration, which is the rate of change of velocity.
At time tm, the vertical component of acceleration for the module would be the derivative of the vertical velocity vector with respect to time, which is the change in vertical velocity over time. This can be calculated by taking the second derivative of the vertical position vector with respect to time. Since the position vector is a function of time, the acceleration can be determined by taking the second derivative of the position vector with respect to time, which is defined as the rate of change of the velocity with respect to time. Therefore, the vertical component of acceleration at time tm can be determined by taking the second derivative of the vertical position vector with respect to time.
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What is the maximum distance we can shoot a dart, provided our toy dart gun gives a maximum initial velocity of 9.12m/s?
The distance that is covered is 8.5 m.
What is the maximum distance?We have to note that the movement of the dart would be the movement of a parabola. We would need to know that in this case, the first thing that we should find is the time that has been taken;
t = u sin 45/0.5 * 9.8
t = 9.12 sin 45/0.5 * 9.8
t = 1.32 s
Then we have that;
R = Vxt
Thus the distance that is covered is;
R = 9.12 cos45 * 1.32
R = 8.5 m
We can see that the projectile movement of the dart would cover a horizontal distance of about 8.5 m
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1. An object was launched from the ground to the top of a building at a
distance of 65 m from its foot on a horizontal plane at an angle of 60
degrees. Using SOHCAHTOA, find the height of the building the
projectile was launched to from the ground.
Using SOH,CAH,TOA, we can calculate the height of the building by taking the sine of the launch angle (60°) and the distance traveled (65 m). The height of the building is 56.9 m.
What is SOH,CAH,TOA?SOH,CAH,TOA stands for Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse and Tangent = Opposite/Adjacent. This is a set of trigonometric ratios that can be used to solve for angles and lengths of sides of a right triangle. It is used when the angle and length of two sides of a right triangle are known, but the length of the third side needs to be calculated.
Calculation using SOH, CAH, TOA
The distance from the ground to the top of the building is 65 m and the angle is 60 degrees. the height (h) of the building.has to be found
Using the trigonometric ratio of Sine, calculate the height of the building:
Sin(60°) = Opposite/Hypotenuse
h/65 = sin(60°)
h = 65sin(60°)
h = 65(0.866)
h = 56.59 m
Therefore, the height of the building the projectile was launched to from the ground is 56.59 m.
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suppose that two runners run a 100-meter dash, but the first runner reaches maximum speed more quickly than the second runner. both runners maintain constant speed once they have reached their maximum speed and cross the finish line at the same time. which runner has the larger maximum speed
The runner who reaches their maximum speed more quickly has the larger maximum speed. In a 100-meter dash, reaching maximum speed more quickly generally indicates a higher level of acceleration, which is related to maximum speed.
The runner who reaches their maximum speed more slowly may have a longer time to build up speed, but once both runners have reached their maximum speed, they are both running at the same speed.
So, the runner who reached maximum speed more quickly will have had a higher maximum speed.
Speed is known as the rate of change of position of an object in any direction. Speed is calculated as the ratio of distance to the time in which the distance was covered.
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true/false. relationship between the strength of the attractions between particles and the number of particles you expect to be in the gas phase at a given temperature.
put the parts or regions of the neuron in order from the direction of where a stimulus is first received to where a response stimulus is conducted.
In sequence from the position of where a stimulation is initially absorbed to whether a reply stimulus is conducted, dendrites, cell body and soma, axon hillock, axon, and synaptic terminal sections or areas of the neuron.
Describe dendrites.Dendrites are extensions made to receive messages from nearby cells. They appear to have a tree-like shape because they produce projections that are activated by numerous other neurons and carry the electromagnetic gradient to the neurone.
What are the functions of dendrites?Dendrites receive impulses from numerous other neurons and pass them on to the nerve cell. If a neuron is sufficiently active, it will emit an electrical impulses, an electrical impulse that excites additional neurons. Huge networks of these neurons are set up, and they communicate among themselves in order to create ideas and actions.
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A ball is thrown straight up. It reaches its highest point and then falls back. Which of the following is the correct statement?(a) Throughout its motion, the ball's velocity is zero(b) At the highest point in its motion, the ball's acceleration is zero(c) At the highest point in its motion, the ball's velocity is zero(d) Throughout its motion, the ball's acceleration is zero(e) At the highest point in its motion, the ball's velocity and acceleration.
The correct statement is (c): At the highest point in its motion, the ball's velocity is zero.
This is due to the fact that when anything is thrown straight up, it has a starting velocity and then accelerates as it descends towards the Earth. Its velocity is equal to zero as it reaches its highest point (due to the gravitational pull of the Earth). The ball's acceleration varies continuously as it travels because it accelerates towards the Earth when it is travelling upward and decelerates when it is travelling downward.
The ball is briefly at rest, and the only force acting on it is the gravitational pull of the Earth, therefore at its fastest point in motion, the acceleration is equal to zero.
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assuming you start at the top of the ramp that is 10 m tall with velocity of 10 m/s and your car has a mass of 1000 kg, what is your pe g
The gravitational potential energy of the car at the top of the ramp is 98,000 Joules.
How to calculate the potential energy?The gravitational potential energy (PE) of an object of mass m at ground level h is given by
PE = mgh
where g is the acceleration due to gravity, approximately 9.8 m/s^2 near the surface.
In this case, the car has a mass of 1000 kg and a height of 10 m above the ground. Therefore, the gravitational potential energy (PEg) is:
PEg = mgh = 1000kg * 9.8m/s^2 * 10m = 98,000J
Therefore, the gravitational potential energy of the car at the top of the ramp is 98,000 Joules.
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Suppose the activity of a sample of radioactive material was 100, B, q,100Bq at the start. What would you divide 100, B, q,100Bq by to obtain the activity at:
n half-lives after the start?
please get back quick its due in form tomorrow
After n half-lives, its radioactivity will be 100× [tex]2^{-n}[/tex] Bq.
What is radioactivity?A characteristic of some forms of matter known as radioactivity is the spontaneous emission of energy and subatomic particles. In essence, it is a characteristic of particular atomic nuclei.
The radioactivity of the material is 100 Bq, that means, the radioactivity of the material is 1000 disintegration per second.
the relation between radioactivity and half-life is : A = A₀ 2^-n
Hence, after n half-lives, its radioactivity will be = 100 × 2^-n Bq.
Therefore, after n half-lives, its radioactivity will be 100× [tex]2^{-n}[/tex] Bq.
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an investor is building a hydropower station. it's 5 megawatt capacity and utility is paying 26 cents per kilowatt hour. how much revenue will the hydropower station make per year? PLEASE TRY TO SOLVE
Answer:
1,300dollars
Explanation:
5megawatt= 5*10^6watts=5,000,000W
26cents/1000watts (10^3=kilo)
total amount=26cents/1000watts*5,000,000W
=130000cents
=1300 dollars
Might be wrong but you can try this
A 0.600-kg ball traveling at 4.00 m/s to the right collides with a 1.00-kg ball traveling at 5.00 m/s to the left. After the collision, the lighter ball is traveling 7.25 m/s to the left. What is the velocity of the heavier ball after the collision?
Answer:
Explanation:
The velocity of each ball after the collision can be determined using the law of conservation of momentum. The law of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces are acting on the system. In this case, the two balls form an isolated system before and after the collision, so their total momentum must be conserved.
Let's call the velocity of the heavier ball after the collision "v". The total momentum before the collision is given by:
p_i = (0.600 kg)(4.00 m/s) + (1.00 kg)(-5.00 m/s) = -2.00 kg m/s
The total momentum after the collision is given by:
p_f = (0.600 kg)(v) + (1.00 kg)(-7.25 m/s) = 0.600 kg v - 7.25 kg m/s
Since the total momentum is conserved, we can set the initial momentum equal to the final momentum and solve for v:
p_i = p_f
-2.00 kg m/s = 0.600 kg v - 7.25 kg m/s
Adding 7.25 kg m/s to both sides and dividing both sides by 0.600 kg, we get:
v = (2.00 kg m/s + 7.25 kg m/s) / 0.600 kg = 9.25 m/s
So, the velocity of the heavier ball after the collision is 9.25 m/s.
Answer:
The velocity of the heavier ball after the collision is 3.05 m/s
Explanation:
This is an example of partially elastic collision. In a partially elastic collision, momentum is conserved and the objects move at different speeds. A portion of the initial kinetic energy is still retained by the colliding objects after the impact.
The conservation of momentum states that the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision.
The formula for momentum is
[tex]p=mv[/tex]
We can conclude that
[tex]m_1v_{1i} +m_2v_{2i}=m_1v_{1f} +m_2v_{2f}[/tex]
Let object 1 be the 0.600 kg ball.
Let object 2 be the 1.00 kg ball.
We are given
[tex]m_1=0.600\\v_{1i} =4.00\\m_2=1.00\\v_{2i} =5.00\\v_{1f} =7.25[/tex]
Inserting our given values into the equation gives us
[tex](0.600*4.00)+(1.00*5.00)=(0.600*7.25)+\left(1.00*v_{2f}\right)[/tex]
Lets solve for [tex]v_{2f}[/tex].
Evaluate each set of parenthesis.
[tex]2.4+(1.00*5.00)=(0.600*7.25)+\left(1.00*v_{2f}\right)[/tex]
[tex]2.4+5=(0.600*7.25)+\left(1.00*v_{2f}\right)[/tex]
[tex]2.4+5=4.35+\left(1.00*v_{2f}\right)[/tex]
Anything multiplied by 1 stays the same.
[tex]2.4+5=4.35+v_{2f}[/tex]
Add 2.4 and 5.
[tex]7.4=4.35+v_{2f}[/tex]
Subtract 4.35 from both sides of the equation.
[tex]3.05=v_{2f}[/tex]
what concept in the video of the Big Bang Theory show which demonstrated operant conditioning that is incorrect?
Answer:
getting chocolate is a positive reinforcement
Explanation:
Which of the following statements are true regarding the similarities between heat and work?
-both heat and work are path functions
-both heat and work can cross the boundary of a system
-both heat and work are associated with a process
-both heat and work are associated with a thermodynamic state
-systems possess energy including heat and work
Heat and work are path functions because their values depend on the path taken from the initial to the final state of a system.
What is Heat?Heat is a form of energy that is transferred from one object to another due to a difference in temperature. Heat is a form of kinetic energy, the energy of motion, and can be transferred from one object to another by conduction, convection, and radiation.
Both heat and work can cross the boundary of a system, as energy transfer in the form of heat or work can occur when a system interacts with its surroundings.
Heat and work are associated with a process, which is a change in the state of a system from one thermodynamic state to another.
Heat and work are also associated with a thermodynamic state, as the amount of heat and work exchanged between a system and its surroundings is determined by the thermodynamic state of the system.
Finally, systems possess energy in the form of heat and work, which can be exchanged between a system and its environment.
Therefore, all the given option is correct
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1/1 For the 3500-lb car, determine (a) its mass in slugs, (6) its weight in newtons, and (c) its mass in kilograms. W = 3500 lb Problem 1/1 1/2 Determine your mass in slugs. Convert your weight to newtons and calculate the corresponding mass in kilograms. 1/3 For the given vectors V, and V2, determine V1 + V2, Vi + VV-V, V, V, V, X V1, and V.V. Consider the vectors to be nondimensional. у V2 = 12 V1 = 15 3 60° x
1/1. For the 3500-lb car, its mass in slugs is 108.7 slug, its weight in newtons 15540 N, and its mass in kilograms is 1584 kg. 1/2. For my weight, mass in slug is 3.421 slug, weight in newton is 488.4 N, and corresponding mass in kg is 49.786 kg. 1/3. Based on the given vectors\vec{V1}+\ \vec{V2}=18i+\left(9+6\sqrt3\right)j, \vec{V1}-\ \vec{V2}=6i+\left(9-6\sqrt3\right)j, \vec{V1}\ast\ \vec{V2}=165.53\ units, \vec{V1}\ x\ \ \vec{V2}=\left(72\sqrt3-54\right)k, and \vec{V2}\ x\ \ \vec{V1}=\left(54-\ 72\sqrt3\right)k.
1/1. The weight of the car in pounds is given as 3500 lb. According to the unit conversion, as 1 lb is equal to 0.0311, the mass of the car in slugs is:
Mass = 3500 x 0.0311 = 108.7 slug
As 1 lb is equal to 4.44 N, the weight of car in newtons is:
Weight = 3500 x 4.44 = 15540 N
The equation for weight is given by:
W = mg where m is mass in kg and g is the gravity equal to 9.81 m/s^2
Hence, the mass is given by:
m= W/g=15540/9.81=1584 kg
1/2. My weight in pounds = 110 pounds
Mass in slug = 110 x 0.0311 = 3.421 slug
Weight in newton = 110 x 4.44 = 488.4 N
Corresponding mass in kg is:
m=488.4/9.81=49.786 kg
1/3. The magnitude of vector 1 = 15 units
The magnitude of vector 2 = 12 units
The angle of inclination of vector 2 from the horizontal θ = 60∘
The vector 1 is given by:
\vec{V1}=V1\ast\left(\frac{4}{5}\right)i+V1\ast\left(\frac{3}{5}\right)j=15\ast\left(\frac{4}{5}\right)i+15\ast\left(\frac{3}{5}\right)j=12i+9j
The vector 2 is given by:
\vec{V2}=V2\ cos\theta i+V2sin\theta j=12cos60i+12sin60j=6i+6\sqrt3j
Sum of the two vectors is:
\vec{V}=\ \vec{V1}+\ \vec{V2}
\vec{V}=(12i+9j)+(6i+6\sqrt3j)
\vec{V}=\ 18i+(9+6\sqrt3)j)
Difference of the two vectors is:
\vec{V}=\ \vec{V1}-\ \vec{V2}
\vec{V}=\left(12i+9j\right)-(6i+6\sqrt3j)
\vec{V}=\ 6i+(9-6\sqrt3)j)
The dot product of the two vectors is:
\vec{V}=\ \vec{V1}\ast\ \vec{V2}
\vec{V}=\left(12i+9j\right)\ast(6i+6\sqrt3j)
\vec{V}=\ 165.530\ unit
The cross product of the two vectors is:
\vec{V}=\ \vec{V1}\ x\ \vec{V2}
\vec{V}=\left(12i+9j\right)x(6i+6\sqrt3j)
\vec{V}=\ 72\sqrt3k-54k=(72\sqrt3-54)k
The cross product of the two vectors is:
\vec{V}=\ \vec{V2}\ x\ \vec{V1}\
\vec{V}=(6i+6\sqrt3j) x \left(12i+9j\right)
\vec{V}=\ 54k-\ 72\sqrt3k=(54-\ 72\sqrt3)k
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Compare the force of gravity on the Moon due to the Earth, and the force of gravity on the Earth due to the Moon.
A. The force on the Moon is greater than the force on the Earth.
B. The forces are equal and opposite.
C. The force on the Earth is greater than the force on the Moon.
After comparing the force of gravity on the Moon due to the Earth, and the force of gravity on the Earth due to the Moon, we find that The forces are equal and opposite. Thus, option B is correct.
What is gravity?The force that unites all matter is called gravity (which is anything you can physically touch). The gravitational pull of objects with a lot of matter, such as planets, moons, and stars, increases with their mass.
The quantity of matter in something is determined by its mass. Everything has a gravitational pull, and this pull increases with mass. The Earth pulls on us as we walk on its surface, and we yank back in response. The Earth's pull can cause us to fall to the ground, whereas our pull is insufficient to move the Earth because it is so much heavier than we are.
In this system both the objects have mass so the gravitational force between them is,
[tex]$\mathrm{F = \frac{GM_1M_2}{R_2} }[/tex]
For the earth moon system,
[tex]$\mathrm{F_{e/m} = \frac{GM_eM_m}{R_2} }[/tex] and [tex]$\mathrm{-F_{m/e} = \frac{GM_eM_m}{R_2} }[/tex]here negative sign stands for opposite direction.
According to Newton's third law of motion, gravitational forces from the earth to the moon are equal but opposite in direction. Because the gravitational force formula is based on the masses of both objects, the formula applies to both objects.
Therefore, B. The forces are equal and opposite is correct.
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if a 12 V battery is connected to the circuit shown, and R1 and R2 are EACH 2 ohm resistors; what must be the resistance of R4 be if R3 is 4 ohms and the total current is 2 amp?
Answer:
Explanation:
First find the total resistance of the combination circuit:
R = V/I = 12 V / 2 A = 6 Ω
6Ω = R1 + R2 + 1/(1/R3 + 1/R4)
6Ω = 2Ω + 2Ω + 1/(1/4 + 1/R4)
2Ω = 1/(1/4Ω + 1/R4)
2Ω(1/4Ω + 1/R4) = 1
(1/4 + 1/R4) = 1/2
1/R4 = 1/4
R4 = 4Ω
Note: R1 and R2 are in series, so you just add them together. But R3 and R4 are in parallel, so Req = 1/R3 + 1/R4
What is the answer to question which statement correctly describes a characteristic that a scientific measuring tool should have ?
To be accurate, a scientific measuring instrument needs to be able to provide repeatable observations of a quantity.
How can you be scientific?of, pertaining to, or showing the scientific concepts or procedures. conducted scientifically or in accordance with findings of scientific investigation: by practicing or employing comprehensive or orderly procedures. advertising using science.
Who is referred to as scientific?A scientist is a person who methodically acquires data and uses it to form hypotheses, test those assumptions and further knowledge and understanding. Additional characteristics of a scientist include: their methodology, such as their use of statistics.
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Find the average velocity of the cat if she ran +110 meters in 50 seconds. Round to two decimal places, and include both magnitude and direction.
suppose that vehicles taking a particular freeway exit can turn right (r), turn left (l), or go straight (s). consider observing the direction for each of three successive vehicles.
the direction for each of three successive vehicles. A = {RRR,LLL,SSS} , B = {RLS, RSL, LSR, LRS, SRL, SLR} C = {RRS, RRL, RSR, RLR, LRR, SRR}
What is the best definition of direction?Direction is defined as the path that something takes, the path that must be taken to reach a specific place, the way in which something is starting to develop or the way you are facing. An example of direction is when you go right instead of left.
What is direction in a sentence?the course or path on which something is moving or pointing. The army attacked from three different directions. Down the road, he could see a bus coming from the opposite direction. The wind changed direction and started blowing in faces.
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