a) The scalar product of A and B is -6.62m2.
b) The vector product of A and B is -8.5k.
Rectangular components of the magnitude of A are:
[tex]\begin{aligned}& A x=3.6 \cos 70 \\& A y=3.6 \sin 70 \\& A=A x^i+A y^j \\& A=3.6 \cos 70 x^i+3.6 \sin 70 x^j \\& A=1.23 x^i+3.38 x^j\end{aligned}[/tex]
Rectangular components of the magnitude of B are:
[tex]\begin{aligned}& B x=-2.4 \cos 30 \\& B y=-2.4 \sin 30 \\& B=B x^i+B y^j \\& B=-2.4 \cos 30 x^i-2.4 \sin 30 x^j \\& B=2.08 x^i-1.20 x^j\end{aligned}[/tex]
a)The scalar product of A.B is
[tex]$$A . B=1.23 *(2.08)+3.38(-1.20)$$$A . B=-6.62 m^2$[/tex]
b)The vector product of A x B is
[tex]\begin{aligned}& A * B=(3.38 * 0+1.20 * 0) i-(1.23 * 0+2.08 * 0) j+(1.23 *-1.20-2.08 * 3.38) k \\& A * B=(-1.476-7.03) k \\& A * B=-8.5 k\end{aligned}[/tex]
What is the scalar product of vectors A and B?The scalar product of two vectors a and b of magnitude |a| and |b| is given as |a||b| cos θ, where θ represents the angle between the vectors a and b taken in the direction of the vectors.
What is a vector product?The Vector Product of two vectors can be defined as the resultant vector perpendicular to both vectors. It is also known as the cross product of two vectors and is often denoted by a x b. The Vector Product of two vectors results in a vector perpendicular to both vectors.
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a gas cools, and the heat transferred in the process is 1550 j. at the same time it is compressed, and the work involved in compression is 640.0 j. calculate the change in internal energy for the gas in joules.
The change in internal energy of a system is equal to the heat transferred plus the work done on the system.
What is internal energy?Internal energy is the energy of a system that is due to its composition and temperature. It is the sum of the kinetic energy and potential energy of all of the components of the system. It is a thermodynamic state function and can be used to calculate other thermodynamic properties such as enthalpy, entropy, and Gibbs free energy.
Given:
Heat transferred = 1550 J
Work done = 640.0 J
Therefore, the change in internal energy of the gas = 1550 J + 640.0 J = 2190 J.
The change in internal energy of a system is equal to the heat transferred to the system plus the work done on the system. In this case, the gas is cooling and being compressed at the same time. The heat transferred to the system is 1550 J and the work done on the system is 640.0 J. The change in internal energy of the gas is equal to the sum of the heat and work, which is 1550 J + 640.0 J = 2190 J.
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The change in internal energy of a system is equal to the heat transferred plus the work done on the system. 2190 J is the change in internal energy for the gas.
What is internal energy?Internal energy is the energy of a system that is due to its composition and temperature. It is the sum of the kinetic energy and potential energy of all of the components of the system. It is a thermodynamic state function and can be used to calculate other thermodynamic properties such as enthalpy, entropy, and Gibbs's free energy.
Given that:
Heat transferred = 1550 J
Work done = 640.0 J
Therefore, the change in internal energy of the gas:
change in internal energy = 1550 J + 640.0 J
change in internal energy = 2190 J.
The change in internal energy of a system is equal to the heat transferred to the system plus the work done on the system. In this case, the gas is cooling and being compressed at the same time. The heat transferred to the system is 1550 J and the work done on the system is 640.0 J. The change in internal energy of the gas is equal to the sum of the heat and work, which is 1550 J + 640.0 J = 2190 J.
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A 58kg soccer player, moving at 3.75m/s north hits another 56kg moving at 4.90m/s collide west and
stick together. what is their speed and direction after collision
Their speed after the collision is 2.5 m/s and their direction is west. The direction after the collision is the direction of the final momentum, in this case, the players are moving in the west direction.
What is the conservation of momentum principle and in what situations it is applied?The conservation of momentum principle states that in a closed system, the total momentum before a collision is equal to the total momentum after the collision. The principle is based on the law of conservation of energy and applies to all types of collisions, whether they are elastic or inelastic. The principle is used to calculate the final velocities and direction of motion of objects after a collision. It is widely used in physics and engineering to understand the motion of objects and predict the outcome of collisions.
The speed and direction of the two soccer players after a collision can be determined using the conservation of momentum principle. This principle states that the total momentum of an isolated system remains constant if no external forces are acting on it.
How can we determine this?To calculate the final velocity and direction of the two soccer players, we can use the following equation:
p1 + p2 = pf
where p1 is the momentum of the first player, p2 is the momentum of the second player, and pf is the final momentum of the two players after the collision.
p1 = 58kg * 3.75m/s = 217.5 kg m/s (north)
p2 = 56kg * 4.90m/s = 273 kg m/s (west)
pf = p1 + p2 = 490.5 kg m/s
To find the velocity after the collision, we divide the final momentum by the total mass:
v = pf / (m1+m2) = 490.5 / (58+56) = 2.5 m/s
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Two bumper cars are driven toward each other. The initial momentum of bumper car 1 is 250. 0 kg and the initial momentum of bumper car 2 is –320. 0 kg. M/s. After the cars collide, the final momentum. Of bumper car 1 is –311 kg. M/s
What is the magnitude of the final momentum of bumper car 2?
Your answer should have three significant figures.
The final momentum of bumper car 2 is -241.0 kgm/s.
The magnitude of the final momentum of bumper car 2 can be found using the conservation of momentum principle, which states that the total momentum of a closed system remains constant before and after a collision.
To calculate the final momentum of bumper car 2, we can use the following equation:
initial momentum of system = final momentum of system
250.0 + (-320.0) = (-311.0) + final momentum of bumper car 2
-70.0 = (-311.0) + final momentum of bumper car 2
final momentum of bumper car 2 = -241.0 kgm/s
The final momentum of bumper car 2 is -241.0 kgm/s.
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a coin with a diameter of 2.21 cm is dropped onto a horizontal surface. the coin starts out with an initial angular speed of 17.5 rad/s and rolls in a straight line without slipping. if the rotation slows with an angular deceleration of 1.66 rad/s2 , how far does the coin roll before coming to rest? answer in units of m. answer in units of m.
Answer:
Approximately [tex]1.02\; {\rm m}[/tex].
Explanation:
Let [tex]\omega_{0}[/tex] denote the initial angular velocity, and let [tex]\omega_{1}[/tex] denote the final angular velocity. It is given that the initial angular velocity is [tex]\omega_{0} = 17.5\; {\rm s^{-1}}[/tex] and [tex]\omega_{1} = 0\; {\rm s^{-1}}[/tex].
Additionally, let [tex]a[/tex] denote the angular acceleration of this coin. It is given that [tex]a = (-1.66)\; {\rm s^{-2}}[/tex] (negative since angular velocity is slowing down.)
Let [tex]\theta[/tex] denote the angular displacement of the coin. Rearrange the rotational SUVAT equation [tex]({\omega_{1}}^{2} - {\omega_{0}}^{2}) = 2\, a\, \theta[/tex] to find the angular displacement [tex]\theta[/tex]:
[tex]\begin{aligned}\theta &= \frac{{\omega_{1}}^{2} - {\omega_{0}}^{2}}{2\, a} \\ &= \frac{(0\; {\rm s^{-1}})- (17.5\; {\rm s^{-1}})}{2\, (1.66\; {\rm s^{-2}})} \\ &\approx 92.25 \; (\text{radians})\end{aligned}[/tex].
It is given that the diameter of the coin is [tex]d = 2.21\; {\rm cm} = 0.021\; {\rm m}[/tex].The radius of the coin would be [tex]r = (d/2) = ((0.021\; {\rm m}) / 2) = 0.0105\; {\rm m}[/tex].
The question is asking for the linear displacement of this coin. Under the assumptions, the linear displacement of this coin would be equal to the product of angular displacement (in radians) and the radius of the coin:
[tex]\begin{aligned}x &= r\, \theta \\ &= (0.0105\; {\rm m})\, (92.25) \\ &\approx 1.02\; {\rm m}\end{aligned}[/tex].
a stone is dropped from the edge of a roof, and hits the ground with a velocity of -125 feet per second. how high (in feet) is the roof?
Answer: the acceleration of an object due to earth's gravity is 32 ft/sec2
Explanation:
y = h - gt2/2 = 0; h = gt2/2; v(t) = dy/dt = - gt; t = - v(t)/g; h = g/2·v2(t)/g2 = v2(t)/(2g) = 1252ft2/s2/(2·32ft/s2) =
244.14 ft
HELP PLEASE What is the M.A. (Mechanical Advantage) of a screwdriver with a radius from the center to the outermost edge of the tip of 50.0 mm, and the radius of the handle of 240 mm? Remember that there are 1000.0 mm in 1.0000 m, and while solving the problem show your work of course.
Answer:
The Mechanical Advantage (MA) of a tool is the ratio of the output force to the input force. In the case of a screwdriver, the output force is the force applied to the tip of the screwdriver, and the input force is the force applied to the handle.
To calculate the MA of the screwdriver, we need to use the following formula:
MA = Output Force / Input Force = (Distance from the center to the outermost edge of the tip) / (Distance from the center to the outermost edge of the handle)
The radius from the center to the outermost edge of the tip of the screwdriver is 50.0 mm and the radius of the handle is 240 mm. To find the distance, we need to double the radius.
Distance from the center to the outermost edge of the tip = 2 * 50.0 mm = 100.0 mm
Distance from the center to the outermost edge of the handle = 2 * 240 mm = 480.0 mm
Now we can use the formula to calculate the MA:
MA = 100.0 mm / 480.0 mm = 0.208333
So the MA of the screwdriver is 0.208333. This means that for every 1 N of force applied to the handle, the tip of the screwdriver will exert 0.208333 N of force on the screw.
Explanation:
a force of magnitude acts on a particle during a time interval in which the displacement through a distance of the particle is exactly perpendicular () to the direction of the force. under these conditions the work done by the force will be:
Work done by a force will be the force is in the direction of displacement determined as Force × Displacement in the direction of force.
What does the force on the object do in terms of work?W = Fd is the formula for the amount of work W that a constant force does on an object. It is determined by dividing the force's intensity by the distance the body travels in the force's direction.
What is a distance's displacement?Displacement is simply the distance between an object's starting point and its final location, whereas distance is the length of an object's path. When measured along the shortest path between any two points, displacement is indeed the direct distance between them.
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If they are separated so that they are two meters apart, how will the magnitudes of the electrical force and the gravitational force between the protons be affected?
The ratio of electric force and gravitational force is of the order 10³⁶ between the two protons separated by 2 m apart.
Given that,
Distance between the two protons = 2 m
Gravitational force is given by the formula, Gf = G (mp)²/r²
Electric force is given by the expression, E = (K × e × e)/r²
The ratio of electric force to gravitational force is given by the formula,
Ratio = K (1.6× 10⁻¹⁹)²/r² × r²/G × (1.67 × 10⁻²⁷) = (9 × 10⁹)(1.6× 10⁻¹⁹)²/ (6.67 × 10⁻¹¹)(1.67 × 10⁻²⁷) = 1.23 × 10²⁰ × 10¹⁶ = 1.23 × 10³⁶
Thus, the ratio of electric force and gravitational force is of the order 10³⁶. This means that the value increases drastically.
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Ultrasound waves are used to measure blood- flow speeds. Suppose a device emits sound at 500 kHz, and the speed of sound in human tissue is taken to be 1540 m/s. What is the expected beat frequency if blood is flowing normally in large leg arter- ies at 2.0 cm/ s directly away from the sound source? How can you connect this analogue to the radars for example?
Since the relative velocity of the sound source and the blood flow is zero, the beat frequency is zero.
How to solve this problem?The expected beat frequency can be calculated using the Doppler shift formula, which states that the beat frequency (f) is equal to the difference between the emitted frequency (f0) and the received frequency (f) multiplied by the speed of sound in the medium (c) divided by the relative velocity of the blood flow (v) and the sound source.
f = (f0 - f) * c / (v + c)
Plugging in the given values:
f = (500 kHz - 500 kHz) * 1540 m/s / (2.0 cm/s + 1540 m/s)
f = 0 Hz
Since the relative velocity of the sound source and the blood flow is zero, the beat frequency is zero.
bund waves are similar to radar waves in that they both use sound waves to measure the distance and speed of objects. However, radar uses radio waves instead of sound waves, and it is typically used for detecting objects at a greater distance and at a higher speed than ultrasound.
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What is the slope of a Resistance vs Length graph (including units)?
The slope of a Resistance vs Length graph is equivalent to
m = ρ/A. Its unit will be mho m⁻².
What is resistance with reference to a electric wire?Resistance is a measure of the opposition to current flow in an electrical circuit.Resistance is measured in ohms. It is symbolized by the Greek letter omega (Ω). An electric current flows when electrons move through a conductor, such as a metal wire. The moving electrons can collide with the ions in the metal. This makes it more difficult for the current to flow, and causes resistance.Given is the graph between resistance and the length of the wire.
We can write the resistance of a wire as -
R = (mL/ne²Aτ)
In this formula, the term -
(m/ne²τ)
represents a constant value called resistivity {ρ}. So, we can write -
R = ρL/A
where the metallic wire is of length {L}, cross - sectional area {A} and resistivity {ρ}.
Now, we can write the slope of resistance {R} and the length of the wire {L} as the ratio of {R} and {L}. So, we can write -
R/L = m
On comparing, we get -
m = ρ/A
Therefore, the slope of a Resistance vs Length graph is equivalent to
m = ρ/A. Its unit will be mho m⁻².
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Of the blocks listed below, which combination of materials will have the highest resistance to sliding?block Weight FrictionA 150lb 30lbB 20N 5NC 1,800lb 60lb
The higher the weight, the greater the static friction force, and the higher the resistance to sliding. Therefore, the combination with the highest resistance to sliding is C) 1,800lb 60lb.
What is static friction force?Static friction force is the force that resists two objects from moving relative to each other. It is the force that is generated when two objects are in contact with each other and in a stationary state. This force is also referred to as the static coefficient of friction. It is a force that is always present between two surfaces when they are in contact. The magnitude of this force is dependent upon the nature of the surfaces and the amount of force applied to the surfaces. The magnitude of static friction force is usually greater than the kinetic friction force. Therefore, it is necessary to overcome static friction in order to initiate movement between two objects.
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Complete Question:
Of the blocks listed below, which combination of materials will have the highest resistance to sliding?block Weight Friction
A) 150lb 30lb
B) 20N 5N
C) 1,800lb 60lb.
D) non of these
If you jounce up and down on a bathroom scale, what varies on the scale reading is
A) mg.
B) the normal force.
C) both of these
D) neither of these
If you jounce up and down on a bathroom scale, what varies on the scale reading is the normal force that is option b is the correct answer.
Why does standing still allow for the best weight reading?The support force acting on you will only accurately reflect your weight when you are in equilibrium. So it is equivalent to the gravity force acting on you.
Would a bathroom scale's gauge have more compression?The bathroom scale's springs are more squeezed as the elevator is moving upwards and display a higher weight reading as a result. The bathroom scale's springs are less compressed and display a lower weight reading when the lift is accelerating downhill.
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2. A body in motion has velocity of 5i +2j-3k and it is acted upon by a constant force of 4i +3j-2k compute the instantaneous power and the angle between the force and velocity
In order to calculate the instantaneous power, we can use the dot product of the force vector and the velocity vector. The dot product is defined as:
F·V = (4i + 3j - 2k)·(5i + 2j - 3k) = (45) + (32) + (-2*-3) = 20 + 6 - 6 = 20
So the instantaneous power is 20.
To calculate the angle between the force and velocity vectors, we can use the formula:
cos(θ) = (F·V) / (||F|| * ||V||)
where θ is the angle between the vectors, F is the force vector, V is the velocity vector, and ||F|| and ||V|| are the magnitudes of the force and velocity vectors.
First, we need to find the magnitudes:
||F|| = sqrt(4^2 + 3^2 + (-2)^2) = 5
||V|| = sqrt(5^2 + 2^2 + (-3)^2) = sqrt(29)
So we can now calculate the angle:
cos(θ) = (20) / (5 * sqrt(29))
We can get the angle by using the inverse cosine function (arccos)
angle = arccos(cos(θ))
Note that the angle is in radians, if you want to get the angle in degrees, you can use the conversion factor of 180/π.
A woman of m= 63 kg stands on the ice. The contact area between her skate and the ice is A = 0.0065 m2a) express the force that the person exerts on the ice, F, in terms of m and g. you do not need to include the force of the column air above herb) calculate the numerical value of F in Nc) express the pressure on the ice from the person P in terms of F and Ad) calculate tthe numerical value of P in Pa.
Force exerted on the eye will be equal to PA, the value of the force applied will be 630 Newton the pressure on the ice from the person will be FA and the numerical value of the pressure will be 96923 Pa.
The mass of the woman is given to be taken 3 kg and the women is standing over a skate and the contact area between her skate and the ice is given to be 0.0065m².
According to the standard relation the pressure the applied force and the area of contact are related to each other as,
P = F/A
They applied force will be equal to the weight of the women and that will be equal to,
F = MG
F = 63×10
F = 630N
Putting the values,
P = 630/0.0065
P = 96923 Pa
So, the pressure that will be felt by the surface of the ice will be 96923 pascals.
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Consider the circuit shown in (Figure 1). Assume 1 =0.92 A. Part A What is the value of resistor R? Express your answer with the appropriate units. % R = Value Figure 1 of 1 Submit Previous Answers Request Answer 2.00 A Incorrect; Try Again; 2 attempts remaining Provide Feedback 10 15 Q
The maximum Current is 19.57 ohm, as mentioned inside the paragraph preceding.
What is a definition of a circuit simple?A circuit in electronics is a totally circular path that electricity passes through. A current source, wires, and a load are the components of a basic circuit. Any ongoing channel for the conveyance of energy, info, or a signal is referred to as a "circuit" in a wide sense.
Voltage across the left 10 ohm resistance is V = IR = 0.92A * 10 ohm = 9.2 V
Thus this is the voltage across the 15 ohm and R
Therefore the current in the 15 ohm = 9.2/15 = 0.61 A
Kirchoff's current law states that current in = current out
So, from the 10 ohm & 15 ohm resistors, 2A is entering, while 0.92 + 0.61 are exiting.
Let current from R resistance is I₁
So, 2A = 0.92 + 0.61 + I₁
I₁ = 0.47A
For Resistance R,
V = I₁R
R = V/I₁ = 9.2/0.47
R = 19.57 ohm
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An electric car of mass 1000kg uses twenty five 12v batteries connected together to create a p.d. of 300V. The car accelerates from rest to a speed of 30ms^-1 in 12 seconds.
a) what is the final kinetic energy of the car?
b) what is the power of the car?
c) How much electrical current flows from the battery?
What assumptions have you made in calculating a) to c)?
Answer:
Explanation:
a) The final kinetic energy of the car is equal to the work done in accelerating the car from rest to a speed of 30ms^-1. Therefore, the final kinetic energy of the car is equal to:
KE = ½ mv^2 = ½(1000kg)(30ms^-1)^2 = 450,000 J
b) The power of the car can be calculated by dividing the work done by the time taken for the acceleration. Therefore, the power of the car is equal to:
Power = Work/Time = 450,000 J/12s = 37,500 W
c) The electrical current flowing from the battery can be calculated by dividing the power by the voltage of the battery. Therefore, the electrical current flowing from the battery is equal to:
Current = Power/Voltage = 37,500 W/300V = 125 A
Assumptions:
1. The car is assumed to be moving in a straight line with no friction.
2. The batteries are assumed to be wired correctly and in good condition.
3. The car is assumed to have a constant acceleration over the 12s period.
4. The voltage of the battery is assumed to remain constant over the 12s period.
Problem 5: A car and a dump truck are involved in an accident and crash into each other.
Assuming the only force acting is the force of collision, which one experiences the most force during the crash - the car or the dump truck? Multiple Choice 1) It depends on which one is moving faster. 2) The dump truck. 3) The car. 4) It depends on the angle of their collision 5) They experience the same size force.
5) They experience the same size force. Both car and dump truck will experience the force of same magnitude. But, change in acceleration is greater for smaller car.
What is collision?Collision is when two or more objects collide with each other, either directly or indirectly. In physics, collision is defined as the interaction between two or more bodies, where the total kinetic energy of the two bodies before the collision is greater than the total kinetic energy of the two bodies after the collision.
Collisions can involve two or more objects and can be elastic or inelastic. Elastic collisions involve objects that bounce off of each other and inelastic collisions involve objects that stick together after the collision. Collisions can also involve two or more particles, where the particles interact and exchange energy, momentum and angular momentum.
Both car and dump truck will experience the force of same magnitude. But, change in acceleration is greater for smaller car.
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An airplane passenger carries a 215-n suitcase up the stairs, a
displacement of 4.20 m vertically and 4.60 m horizontally.
a) how much work does the passenger do on the suitcase?
b) the same carries the same suitcase back down the same set of stairs. how much work does the passenger do on the suitcase to carry it down the stairs?
b) Work = force x displacement = 215 N x (-4.60 m) = -992.5 J. the same carries the same suitcase back down the same set of stairs. how much work does the passenger do on the suitcase to carry it down the stairs.
what is work ?
Work is an activity that involves physical or mental effort undertaken in order to achieve a result. It is usually done in exchange for money, but can also be done out of necessity or for pleasure. Work is often seen as an important part of life and it can come in many different forms, ranging from manual labour to professional and creative work.
Work can be rewarding and provide a sense of purpose and achievement for those who engage in it. It can also be a source of stress, especially when it is not well-suited to an individual’s skills or needs. The type of work an individual does can vary depending on their skills, interests, and resources. Working can help to build relationships, develop skills, and provide financial security.
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A car of mass 1500 kg, travelling at a steady speed, has a kinetic energy of 200 kj. what is the speed of the car?
The speed of the car is 16.32 m/s, when the mass of the car is 1500kg and the kinetic energy is 200kj.
What is kinetic energy?The energy of motion is known as kinetic energy, and it is manifested in the motion of objects and subatomic particles. Every particle and moving object contains kinetic energy. When something moves, such as when someone walks, a baseball soars, a piece of food falls off a table, or a charged particle moves in an electric field, kinetic energy is clearly visible. The kinetic energy of stationary objects is zero.
The potential energy of objects that aren't moving (the other main type of energy). Potential energy becomes kinetic energy when an object is propelled into motion by a force, such as gravity. For instance, a stretched rubber band stores elastic potential energy, which, upon release, is converted into kinetic energy.
The formula for kinetic energy is
K.E. = 1/2m × v²
200(1000j) = 1/2(1500) × v²
200000 = 750 × v²
v² = 200000/750
v² = 266. 6
v = √266. 6
v = 16.32 m/s
Thus, the speed of the car is 16.32 m/s
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Calculate the gallons of gasoline needed to drive an equivalent distance of 7 trips between the Earth and its moon (1 trip = 239,000 miles). You will only type in the number for your result in scientific notation here (no units).
The the number of gallons needed for the trip will be 83.72 gallons.
What is scientific notation?Scientific notation is a method of displaying very large or very small numbers in a more simplified format. We know that entire numbers can be extended indefinitely, but such large numbers cannot be written on a piece of paper. Furthermore, the numbers in the millions place after the decimal required to be represented in a simpler format.
As a result, representing a few integers in their expanded form is challenging. As a result, we employ scientific notation. In this case, the gallons needed to travel is 1 gallon per 20000 miles.
The equivalent distance of 7 trips between the Earth and its moon will be:.
= 7 × 239,000 miles
= 1674400 miles
Since 1 gallon per 20000 miles,the number of gallons needed will be:
= 1674400 / 20000
= 83.72 gallons.
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Complete questions
The gallons needed to travel is 1 gallon per 20000 miles. Calculate the gallons of gasoline needed to drive an equivalent distance of 7 trips between the Earth and its moon (1 trip = 239,000 miles). You will only type in the number for your result in scientific notation here (no units).
For the three vectors shown in (figure 1), A + B + C = 1ȷ^. What is vector B ?
(i) Write B in component form
(ii) Write B as a magnitude and a direction
a. -4i^ + 3 j^; 5.0, 37°
b. 4i^ - 3j^; 3.5, 53°
c. -4i^ - 3j^; 4.5, 65°
d. 4i^ + 3j^; 5.0, 53°
a. -4i^ + 3 j^; 5.0, 37° is vector B, its magnitude and direction.
What does the word "vector" mean?A vector is a quantity or occurrence with the discrete characteristics of magnitude and direction. Additionally, the phrase signifies how such a quantity is represented mathematically or geometrically. Examples of vectors in nature include weight, force, electromagnetic fields, momentum, and velocity.
Based on the figure = > A = 4i^
c= -2 j^
A + B + C = 1ȷ^
=> B= 1ȷ^ - 4i^ -(-2 j^)
=> - 4i^ + 3 j^
|B| = sqrt(4^2+3^2) => 5
Direction = tan Ф = 4/3 => 37°
How do you calculate XYZ's magnitude?|v| =(x2 + y2) is the formula to calculate the magnitude of a vector (in two dimensions) v = (x, y). The Pythagorean theorem serves as the basis for this formula.|V| = (x2 + y2 + z2) is the formula to calculate the magnitude of a vector (in three-dimensional space) V = (x, y, z).Learn more about vector here:
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i need help plssssssss
The object with the greatest inertia is 8 kg bowling ball.
option A is the correct answer.
What is Newton's first law of motion?Newton's first law of motion states that a body at rest or uniform motion in a straight line will continue in that form unless it is acted upon by an external force.
Newton's first law of motion is also called the law of inertia because it depends on the mass of the object.
The inertia of a body or an object is the measure of the reluctance of the body or object to start moving when it is at rest or to to stop moving when it is in motion.
The inertia of an object depends on the mass of the object, thus the greater the mass of an object the greater the inertia of the object and vice versa.
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Arianna lives in a neighborhood where gang members hang out to sell drugs. Shootings occur on a regular basis, usually caused by gang members targeting each other; but sometimes the shootings affect bystanders. When she is 15, Arianna begins to date a 17-year-old gang member, although her parents disapprove. She often sneaks out of her home late at night to meet him in the street.
Identify three of Arianna’s risk factors for an injury from gun violence. Identify whether each risk factor is behavioral, environmental, or genetic. Is each risk factor modifiable or nonmodifiable?
The risk factors which are associated with dating a gang member include severe issues such as drug addiction and disorders like depression and anxiety. This could be avoided by maintaining a healthy relationship with the parents and partners.
What are risk factors of dating a gang member?The risk factors which are associated with dating a gang member include many problems and disorders. Problems could be major such as drug addiction, trafficking, etc. The constant problems could lead to depression and anxiety in an individual which could be life-threatening if remains untreated for a long time.
The ways in which these risk factors could be minimized and Arianna could be saved from dating a gang member include cumulative protection across domains, cumulative protection in the family domain, educational aspirations and self-esteem in the individual domain, and parental supervision and parent/partner status in the family domain.
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What frequency does a photon of wavelength 4.5×[tex]10^{-4}[/tex]m have?
A.1.35×[tex]10^{5}[/tex] Hz
B.2.98×[tex]10^{-37}[/tex] Hz
C.1.47×[tex]10^{-30}[/tex] Hz
D.6.67×[tex]10^{11}[/tex] Hz
Answer:
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what would happen to the volume of a gas if the kelvin temperature is doubled while the pressure is halved
The volume of the gas will be four times the initial volume, if the kelvin temperature of the of the gas is doubled and the pressure is halved.
Let the initial temperature of the gas = T₁
Let the final temperature of the gas = T₂ = 2T₁
Initial pressure of the gas = P₁
Final pressure of the gas = P₂ = P₁/2
The initial volume = V₁
Final volume of the gas = V₂
We know (P₁V₁)/T₁ = (P₂V₂)/T₂
V₂ = (P₁V₁T₂)/(T₁P₂)
V₂ = (P₁V₁× 2×T₁)/(T₁P₁/2)
V₂ = (P₁V₁× 2×T₁×2)/(T₁P₁)
V₂ = 4V₁
Hence the final volume will be four times the initial volume.
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Which cools at the faster rate, a pot of boiling/hot water left at room temperature? Or a same-size pot of lukewarm water left at room temperature?
Please explain why though? I know it is the boiling water, but why? Shouldn't it be the lukewarm water?
Answer:
The pot of boiling/hot water will cool at a faster rate than the same-size pot of lukewarm water left at room temperature. This is because the boiling/hot water has more energy than the lukewarm water and is thus more likely to transfer energy to its surroundings. When energy is transferred, the temperature of the pot of boiling/hot water will decrease, while the temperature of the lukewarm water will remain relatively unchanged. This transfer of energy is called conduction, and it is the process by which heat is transferred from one object to another.
Explanation:
see above
a particle has a mass of 4.00 x 10-27 kg and has a kinetic energy of 7.60 mev. what is the speed of this particle?
The speed of this particle v = 1.16 x 106 m/s
what is speed?
Speed is a measure of how quickly an object is moving. It is usually measured in units of distance traveled per unit of time, such as miles per hour (mph) or kilometers per hour (kph).
Given:
Mass (m) = 4.00 x 10-27 kg
Kinetic Energy (Ek) = 7.60 meV
Solution:
Mass-Energy Equivalence:
Ek = (1/2)mv2
Substituting the given values:
7.60 meV = (1/2)(4.00 x 10-27 kg)v2
Rearranging to isolate the variable:
v2 = (7.60 meV)(2/4.00 x 10-27 kg)
Taking the square root:
v = (√(7.60 meV)(2/4.00 x 10-27 kg))
v = 1.16 x 106 m/s
Therefore, The speed of this particle v = 1.16 x 106 m/s
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In this experiment, optical density is measured using a _______.
spectrophotometer
thermocycler
microscope
caliper
Using a spectrophotometer, optical density is determined in the experiment.
Describe optical density.The optical density of a transparent material is a measure of how quickly light passes through the material. The degree to which any optically dense medium bends transmitted light rays toward or away from the norm is known as its optical density.
High optical density: What does that mean?The slower the wave moves through the material, the higher the optical density. By examining the material's refractive index, one can establish its optical density. How much slower a light wave would flow through the medium in comparison to how quickly it would go through vacuum is represented by the dimensionless refractive index value.
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procedure calculate the density of the aluminum block using measurements taken with the ruler and triple-beam balance 1. measure and record the dimensions and mass of the aluminum block and record values below. include uncertainties. 2. calculate the density of the block and its uncertainty. 3. calculate the percent error between your calculated density value and the expected value of 2.699g/cm3
Dimensions: Length = 12.45cm +/- 0.05cm, Width = 5.65cm +/- 0.05cm, Height = 2.85cm +/- 0.05cm,Mass = 221.3g +/- 0.1g,Calculation of Density:Volume of Block = Length x Width x Height= 12.45cm x 5.65cm x 2.85cm,= 214.25 cm3 +/- 0.25 cm3,Density = Mass / Volume,= 221.3g / 214.25 cm3,= 1.03 g/cm3 +/- 0.01g/cm3,Calculation of Percent Error:Percent Error = (Calculated Value - Expected Value) / Expected Value x 100,= (1.03 g/cm3 - 2.699g/cm3) / 2.699g/cm3 x 100,= -61.90%.
What is the Calculation ?
Calculation is a process of solving a problem by performing a series of mathematical operations or calculations. It involves the use of numerical data, formulas and equations to arrive at a desired result or answer. Calculations can be done manually or by using computers. Calculations are used in a variety of fields such as engineering, finance, physics and economics. Calculation is a way of problem-solving that is used to gain insight into a problem or to arrive at a solution. It involves a systematic approach to arriving at an answer or solution to a problem.
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a cluster of galaxies is observed to have a recessional velocity of 60,000 km/s. find the distance to the cluster, assuming a hubble constant of 72 km/s per mpc (1 mpc
On the basis of a hubble constant approximately 72 km/s per mpc, D is equal to 833.33 to the cluster.
The Hubble constant is what?In cosmology, the Hubble characteristic is a constant of proportionality that describes the relationship between it velocities of far-off objects and their lengths. It conveys the rate of the universe's expansion. most latest accurate measurements of distant objects' motions and distances.
Does Hubble's Constant exceed the speed of light?The region whereby the galaxies are moving away from each other faster than the speed of light is known as the Hubble sphere, after Edwin Hubble who found the universe was expanding back in the 1920s. Because they light is more red than it should be, they are almost all moving away from us, which is how we know.
Hubble constant = Mpc
= 60,000 / 72
D = 833.33
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