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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A 75-kg object traveling 25 m/s collides with and sticks to a 315-kg object initially at rest. What is the final velocity of the two objects?
19 m/s
12 m/s
4.8 m/s
2.9 m/s
The final velocity of the two objects is 4.8m/s.
What does the word "velocity" mean?
The displacement that an object or particle experiences with respect to time is expressed vectorially as velocity. The meter per second (m/s) is the accepted unit of velocity magnitude (also known as speed). Alternately, the magnitude of velocity can be expressed in centimeters per second (cm/s).
The change in velocity between the objects following a collision is known as the relative velocity. When particles collide, momentum and energy are transferred, which results in a change in velocity. It abides under the rule of conservation of energy and momentum.
m1 = 75kg
m2 = 75+315kg = 390kg
v1 = 25m/s
v2 = ?
Initial momentum = m1*v1
Final momentum = m2*v2
Initial momentum = Final momentum
m1v1 = m2v2
75*25 = 390 *v2
v2 = 75*25/390
v2 = 4.8m/s
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two objects are located on an airtrack. the magnitude of the charge on object a is 3 times higher than on object b, and object a also has a 6 times higher mass than object b. which one of the following is true for the magnitudes of the accelerations (not drawn to scale or necessarily in the correct direction)? |aa|
The correct statement is:
"The magnitude of the acceleration of object A is 6 times less than the magnitude of the acceleration of object B"
The magnitude of the acceleration for an object can be calculated using Coulomb's law, which states that the force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. The formula for the force between two charges is:
F = (k * q1 * q2) / r^2
where F is the force, k is the Coulomb constant, q1 and q2 are the charges, and r is the distance between the charges.
Since the acceleration is the force divided by the mass, we can use the formula:
a = F / m
where a is the acceleration, F is the force, and m is the mass.
Given that the charge on object A is 3 times higher than on object B, and object A has a 6 times higher mass than object B, we can determine that:
The force acting on object A is 3 times greater than the force acting on object B (due to the difference in charges)
The mass of object A is 6 times greater than the mass of object B
So, the acceleration of object A is 6 times less than the acceleration of object B.
Therefore, the correct statement is:
"The magnitude of the acceleration of object A is 6 times less than the magnitude of the acceleration of object B"
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question an object of mass 0.5 kg experiences a force that is associated with the potential energy function u(x)
a. The sketch graph of U(x) versus x is in the attachment.
b. The force function that associate with the potential energy function is F(x) = 8.0 (2.0 + x)⁻²
c. The speed of the particle at x = 2 is 2 m/s.
The full question is in the attachment. To create a graph, substitute some values of x into the equation of the function to determine the pair of point coordinates.
a. Graph of U(x) = 4.0/(2.0 + x) versus x making a curve because the function is a fraction function and the curve will not intersect the x-axis.
If x = 0From these coordinates a graph is created in the image.
b. A conservative force is a force that works on an object depends only on the initial and final position of the object and not on the path of the object. The total work from a conservative energy is always the same with the changes in potential energy
W = - ΔU
F × Δx = - ΔU
W = the total work (J)Δx = the distance (m)ΔU = the potential energy (J)The conservative force acting on the object is the derivate of the potential energy function for the objects
F = - dU/dx
U(x) = 4.0/(2.0 + x) = 4.0 (2.0 + x)⁻¹
F = - 4.0 × - 2 (2.0 + x)⁻² × 1
F(x) = 8.0 (2.0 + x)⁻²
c. The kinetic energy Ke = 0.5 mv²
m = the massv = the speedKe = kinetic energyWhen the object is released from rest at the origin to x = 2
The initial speed = v₁ = 0According to law of conservation of energy
Ke₁ + U(0) = Ke₂ + U(2)
0 + 2.0 = Ke₂ + 1.0
Ke₂ = 2.0 - 1.0
Ke₂ = 1.0 J
0.5 mv₂² = 1.0
0.5 × 0.5 × v₂² = 1.0
v₂² = 1.0 ÷ 0.25
v₂² = 4
[tex]v_2 \:=\: \sqrt{4}[/tex]
v₂ = 2 m/s
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What is the average speed of the car during the first hour of the trip? (2 point
O 1 miles/hour
5 miles/hour
40 miles/hour
O 25 miles/hour
Answer:40 miles/hour
the support bearings at a and b allow free turning of the shaft. (figure 1) figure1 of 1 part a determine the resultant internal torque acting on the cross section at points c and d . enter your answers in newton-meters to three significant figures separated by a comma.
The internal torque acting at point C is 800 lb-ft clockwise, and at point D is 1500 ft-lb anti-clockwise.
The shaft is bearing at a and b. As the shaft is at rest and not rotating in any direction. So the internal torque must be balancing the external torques acting on the shaft. Near the bearing A, the the external torque acting on the shaft is 1500 lb-ft clockwise, so at point D there must be an anti-clockwise torque. So the torque acting on the D is 1500 ft-lb.
Similarly, near the bearing B the external torque acting on the shaft is 800 lb-ft anti-clockwise, so there must be an equal and external clockwise torque working on point C to balance the 800 anti-clockwise torque. So the internal torque working on point C is 800 lb-ft.
--The given question is incomplete, the complete question is:
"the support bearings at a and b allow free turning of the shaft. (figure 1) figure1 of 1 part a determine the resultant internal torque acting on the cross section at points c and d . enter your answers in newton-meters to three significant figures separated by a comma."
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which of the following is true about the line in relation to the plane ? group of answer choices the line lies on the plane. the line intersects the plane in one point. the line is parallel to the plane.
The line 1-0+t2 in relation to the plane x-2y+z =1 is parallel to the plane as both points satisfy the plane equation.
A plane is a two-dimensional, Euclidean surface which never ends in the mathematics. A plane is a point's (zero dimensions), a line's (one dimensions), and space's (three dimensions) two-dimensional equivalents.
A line is a network of interconnected points that can go on forever in both the directions. Three noncollinear points, two parallel lines, or two intersecting lines can all be used to form a plane. If two points are on the same line, they are said to be collinear.
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which of the following is true about the line 1-0+t2 in relation to the plane x-2y+z =1 ? group of answer choices
the line lies on the plane.
the line intersects the plane in one point.
the line is parallel to the plane.
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find the largest natural number m such that n 3 - n is divisible by m for all n e n. prove your assertion.
Since the sum of the odd term coefficients and the even term coefficients must both be zero, the expression a0+a1k+a2k2++ankn is divisible by 3 for all kN.
What is the greatest integer that can divide each natural number n by n3?Number `n3n is divisible by 6 because there is a multiple of two in a pair of consecutive numbers and a multiple of three in a triplet of consecutive integers.Since the sum of the odd term coefficients and the even term coefficients must both be zero, the expression a0+a1k+a2k2++ankn is divisible by 3 for all kN.Equation n3−n=n(n2−1)=n(n+1)(n−1). There must be at least one even number among these three consecutive integers. Furthermore, 3 must divide one of the integers using the same reasoning. As n3n is divisible by 2 and 3, it follows that it is divisible by 6, too.To learn more about consecutive numbers refer to:
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You’re at the ice-skating rink with a 5kg bowling ball. The two of you (you and the bowling ball) stand motionless in the middle of the rink so that your combined momentum is zero. You then throw the bowling ball and begin to slide backward. If your momentum is then 12 kg • m/s backward, what is speed does the bowling ball have?
The speed of the bowling ball is 2.4 m/s forward.
What is the speed of the bowling ball?
The speed of the bowling ball is calculated by applying the principle of conservation of linear momentum as shown below.
P1 = -P2
where;
P1 is your momentumP2 is the momentum of the bowling ballP1 = -mv
-P1 = mv
where;
m is the mass of the bowling ballv is the speed of the bowling ballThe speed of the bowling ball is calculated as;
v = ( - 12 kgm/s ) / ( 5 kg )
v = -2.4 m/s
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the change in velocity between location d and location f: select an option unanswered the change in momentum between location d and location f: select an option unanswered the average net force between location
The change in the momentum is equal to the product of the mass and the change in the velocity.
what is change in momentum?
The change in momentum (Δp ) is defined as the change in the product of an object's mass and velocity. A force is required to change the momentum of an object. This applied force can increase or decrease the momentum or even change the object's direction.The change in momentum = m × (v – u). Here a = [(v - u)t ] is the acceleration, which is the rate of change of velocity. The quantity, k is a constant of proportionality. The SI units of mass and acceleration are kg and m s-2 respectively.Δ p = F net Δ t . F net Δ t F net Δ t is known as impulse and this equation is known as the impulse-momentum theorem. From the equation, we see that the impulse equals the average net external force multiplied by the time this force acts. It is equal to the change in momentum.To learn more about momentum refers to:
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Introduction to forces. Identify the situations that have an unbalanced force. Check all that apply.
The situations that have an unbalanced force are:
A. A baseball speeds up as it falls through the air D. A bumper car hit by another car moves off at an angleE. A balloon flies across the room when the air is released What are the forces about?These situations have an unbalanced force because in all of them an object is either accelerating (speeding up or changing direction) or moving with a force acting on it. In the first one, the baseball is accelerating due to gravity. In the second one, the bumper car is hit by another car and moves off at an angle. In the third one, the balloon flies across the room when the air is released, which is a force acting on it.
On the other hand, a soccer ball at rest on the ground and an ice skater gliding in a straight line at a constant speed, are both examples of balanced forces, as there is no net force acting on the objects and they are not accelerating.
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See full question below
Identify the situations that have an unbalanced force. Check all that apply. A baseball speeds up as it falls through the air. A soccer ball is at rest on the ground. An ice skater glides in a straight line at a constant speed. A bumper car hit by another car moves off at an angle. A balloon flies across the room when the air is released.
How far does the object travel between 5 and 10 s
The distance travelled by the object between 5 and 10 seconds is 25 m.
What is the distance travelled by the object?The area under velocity time graph gives the distance travelled by the object.
The distance travelled by the object between 5 and 10 seconds is calculated from the area of curve within this time range.
Area of the curve between 5 and 10 seconds = Area of triangle
Distance travelled between 5 and 10 seconds = Area of triangle formed between 5 and 10 seconds
Area of triangle = ¹/₂bh
where;
b is the base of the triangleh is the height of the triangleA = ¹/₂ x (10 - 5 ) x ( 10 )
A = 25 m
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Model rocket engines are rated by their thrust force and by the impulse they provide. You can use this information to determine the time interval at which the engines fire. Two rockel engines provide the same impulse. The first engine provides 6 N of thrust for 2 s; the second provides 4 N of thrust. For how long does this second engine fire? A. 1 s B. 2 s C. 3 s D. 4 s
The answer is B. 2 s. The impulse provided by both engines is the same, so they must fire for the same amount of time in order to provide that amount of impulse.
What is engines?Engines are devices that convert energy into mechanical force, usually to power machines and vehicles. Engines come in a variety of forms and sizes, but all are based on the same basic principles of converting thermal energy into mechanical force via combustion.
Since the first engine fires for 2 s and provides 6 N of thrust,
the second engine must also fire for 2 s to provide 4 N of thrust (since 6N/2s = 4N/x, where x = 2s).
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which of the following sketches and choice of coordinate axis best describe the physical situation presented in this problem?
A negative acceleration indicates that you will reduce the velocity's present value, while a positive acceleration indicates that you will increase it.
How can one tell whether an acceleration is positive or negative?According to mathematics, a negative acceleration indicates that you will reduce the velocity's present value, while a positive acceleration indicates that you will increase it.A horizontal line can be seen on the acceleration-time graph in its negative area (negative acceleration).The slope of a line is positive (+) if it slopes uphill from left to right. The slope of a line is negative if it slopes downward from left to right (-). A positive slope in our pizza example indicates that as we add more toppings (x), the overall price of the pizza (y) also rises.To learn more about acceleration refer to:
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according to hfsd, multiplying the number of work-days (people-days) in an iteration by the velocity is necessary because:
Multiplying the number of work-days (people-days) in an iteration by the velocity is necessary in order to calculate the amount of work that can be completed in an iteration.
What is iteration?Iteration is a process in which a sequence of actions or steps is repeated to achieve an intended outcome. It is an efficient programming practice that helps to simplify complex tasks and achieve desired results. Iteration is also known as looping and is an integral part of computer programming. Iteration helps to repeat a set of instructions until a certain condition is met, saving time and effort. It is a powerful tool that can be used to solve complex problems and create efficient algorithms.
The velocity is a measure of how much work can be completed by a team in a given time frame, and thus multiplying it by the number of work-days in an iteration gives an indication of the total amount of work that can be completed in that iteration. This helps teams plan their work and set realistic expectations for what can be accomplished in a given iteration.
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A fisherman notices that his boat is moving up and down periodically, owing to waves on the surface of the water. It takes 3.0 s for
the boat to travel from its highest point to its lowest, a total distance of
0.69 m. The fisherman sees that the wave crests are spaced 8.0 m apart.
(a) How fast are the waves traveling
Longitudinal waves takes the boat 2.5 seconds to move from the highest point to the lowest point and the total distance is 0.62 m. A fisherman confirms that the summit he is 6.0 off.
What is longitudinal waves?In the deep waters far offshore, the slowest wave components with the shortest periods and the smallest wave-to-height intervals can travel at less than 5 miles per hour. The component with the longest period could be moving at 35 miles per hour or more. Longitudinal waves, like sound, travel through a medium at a velocity that depends on the density and elasticity of the material. The speed of sound is 0.33 km/sec (0.2 miles/sec) in air, 1.5 km/sec in water, and 5 km/sec in steel.Longitudinal waves, like sound, travel through a medium at a velocity that depends on the density and elasticity of the material. The speed of sound is 0.33 km/sec (0.2 miles/sec) in air, 1.5 km/sec in water, and 5 km/sec in steel.To learn more about longitudinal waves from the given link:
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classify each of the following substances as an element, compound, or mixture using the dropdown menus in the classification table.
Each sort of atom in an element is unique. The joining of two or more distinct atoms results in a compound. In a mixture, two or more distinct substances are combined but not chemically bonded.
Is CO2 a combination of elements or a compound?With two oxygen atoms and one carbon atom, carbon dioxide, or CO2, is a chemical molecule.Each sort of atom in an element is unique. The joining of two or more distinct atoms results in a compound. In a mixture, two or more distinct substances are combined but not chemically bonded.A crystal-like lattice of the two ions Na+ and Cl- makes up the ionic compound salt, which is composed of two ions. Many sodium chloride molecules can be found in salt water.Carbon, Hydrogen, and Oxygen, which are joined by covalent bonds, make up the organic molecule known as vitamin D. Any chemical species that consists of two or more components is called a compound.To learn more about compound refer to:
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Sally, Max, and William are on a camping trip in the forest. They are riding their bikes through the forest and come across a clearing. In the clearing, there are several trees and a small plane. Sally is curious about the physics of the plane, so she asks Max and William to help her measure the distance from the plane to the nearest tree. They use a measuring tape to find that the distance is 60 meters. They also measure the height of the plane to be 10 meters and the height of the tree to be 20 meters. Using the principles of physics, they calculate the angle at which the plane is flying relative to the tree. What is the angle?
Answer: The angle at which the plane is flying relative to the tree is 19.47 degrees.
Explanation:
To calculate the angle at which the plane is flying relative to the tree, we can use the principle of trigonometry and the Pythagorean theorem. Since we know the distance from the plane to the nearest tree (60 meters), the height of the plane (10 meters), and the height of the tree (20 meters), we can use these measurements to form a right triangle with the plane, the tree, and the ground.
Using the Pythagorean theorem, we can calculate the length of the hypotenuse of the right triangle. The length of the hypotenuse is the distance between the plane and the top of the tree. The hypotenuse is calculated by the square root of (distance^2 + height of the plane^2 + height of the tree^2)
The angle we are trying to calculate is opposite to the height of the tree, therefore we can use the tangent function:
tan(angle) = opposite/adjacent
opposite = height of the tree = 20m
adjacent = distance = 60m
angle = arctan(20/60) = arctan(1/3) = 19.47122063449069 degrees
The angle at which the plane is flying relative to the tree is 19.47 degrees.
consider the prpositions p anmd q where pis you can paddle one canoe down the river and q is you can paddle one kayak down the river
The propositions P and Q are both true. P states that you can paddle one canoe down the river, and Q states that you can paddle one kayak down the river. Both of these activities are possible, making both statements true.
What is propositions?A proposition is a statement or assertion that expresses a judgment or opinion about a particular topic or issue. It is a type of argument used in logic and critical thinking, and is typically expressed in a declarative sentence. Propositions can be either true or false and can be used to support or reject a claim. In philosophy, propositions can also be used to explain and justify a particular belief or set of beliefs. Propositions are often used in academic and scientific discourse to communicate ideas and arguments in a concise and logical manner.
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You have the option of making a two-point turn, U-turn or going counter-clockwise around the block to reverse your direction. You will likely best minimize your risk by:
a. Making a U-turn
b. Going around the block
c. Making a two-point turn
d. The risk is likely to be the same for all three options given
You will likely best minimize your risk by making a two-point turn.
The greatest strategy to reduce your danger when changing lanes on a two-way street is to do a two-point turn by retreating into a driveway on your right before moving forward into the roadway.
Turnabouts are turning maneuvers in which a driver reverses the direction of a moving vehicle by making a series of motions. A turnabout accomplished by first backing into a driveway or an alley is known as a two-point turnabout. A turnabout can also be accomplished by backing into a roadway after entering an alley or driveway, albeit this method is riskier.
Turning your car around to travel in the opposite direction is known as a turnabout. When deciding to use a turnabout, take the appropriate precautions.
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ou have a lightweight spring whose unstretched length is 4.0 cmcm. first, you attach one end of the spring to the ceiling and hang a 1.4 gg mass from it. this stretches the spring to a length of 5.1 cmcm . you then attach two small plastic beads to the opposite ends of the spring, lay the spring on a frictionless table, and give each plastic bead the same charge. this stretches the spring to a length of 4.6 cmcm . Required:
What is the magnitude of the charge (in nC) on each bead?
The magnitude of the charge on each bead is 7.08nc.
What is the magnitude of charge?Given the following information:
Original length = 4.0 cm converted to m = 0.04 m
1.4 grams to kilograms = 0.0014
5.1 cm to m = 0.051 is the new length.
4.6 cm to m = 0.046 m is the final length.
e = 0.051 - 0.046
= 0.005m in length
Scientific evidence:
Gravitational acceleration = 9.8m/s²
Coulomb's constant is equal to 8.99 x 10⁹ Nm²/C²
We would use Coulomb's law to calculate the magnitude of the charge (in nC) on each bead:
First, we would calculate the spring constant of this lightweight spring
using the following formula:
W = mg = Ke
K = mg/e
K = 0.014 x 9.8 / 0.05
K = 2.744N/m
K, the spring constant, is 2.744N/m.
In terms of electrostatic force:
F = ke
F = 2.77 x 0.05
F = 0.1385
F equals 0.1385 Newton.
Coulomb's electrostatic force law.
The charge in an electric field can be calculated mathematically using the following formula:
q = √F/k x r
We get by substituting the given parameters into the formula;
q = √(0.1385/8.99 x 10⁹) x 0.046
q = √(1.54060 x 10⁻¹²) x 0.046
q = 7.08 x 10⁻⁸
Take note that 1 nC = 1 x 10⁻⁹ C
Charge, q = 7.08nc
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a reactor operates at a power of 103 mw(t) for 1 year. calculate the power from decay heat a. 1 day following shutdown, b. 1 month following shutdown, c. 1 year following shutdown.
So the heat dacy can be calculated using the winger way formula
In one day ,[tex]P_{d}(t)=\\[/tex][tex]6.65\times 10^{-3}[/tex] GW(t), In one month =[tex]P_{d}(t)=\\[/tex][tex]1.946\times 10^{-3}[/tex] GW(t) , in one year , [tex]P_{d}(t)=\\[/tex][tex]2.29\times 10^{-4}[/tex] GW(t)
According to thermodynamics, heat is a type of energy that crosses a thermodynamic systems' boundary due to a temperature differential across the barrier Heat is absent in thermodynamic systems. However, the expression is also regularly used to describe the thermal energy that constitutes a system's internal energy and is reflected in the system's temperature. In all senses of the word, energy is a form of heat.
For the decay we have winger way formula as ,
[tex]P_{d} =0.0622P_{0}[t-0.2-(t_{0}-0.2(t_{0}+t)-0.2][/tex]
[tex]P_{0}=1.5GW(t)[/tex],[tex]t_{0}=31,536,000[/tex]
[tex]P_{d}(t)=\\[/tex]thermal power generation due to beta and gamma rays
[tex]t_{0}=[/tex]time in seconds , of thermal power level before shut down
t= rime , in seconds elapsed since the shutdown
a) In one day ,
Number of seconds ,t=86400s
so , P
[tex]P_{d}(t)=\\[/tex]0.0622 x 1.5 x [86,400-0.2-(31,536,000+86,400)-0.2]
[tex]P_{d}(t)=\\[/tex][tex]6.65\times 10^{-3}[/tex] GW(t)
b ) In one month
Number of seconds ,t=2629800s
[tex]P_{d}(t)=\\[/tex]0.0622 x 1.5 x [2629800-0.2-(31,536,000+2629800)-0.2]
[tex]P_{d}(t)=\\[/tex][tex]1.946\times 10^{-3}[/tex] GW(t)
c) In one year
Number of seconds ,t=2629800s
[tex]P_{d}(t)=\\[/tex]0.0622 x 1.5 x [31,536,000-0.2-(15,768,000+31,536,000)-0.2]
[tex]P_{d}(t)=\\[/tex][tex]2.29\times 10^{-4}[/tex] GW(t)
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during the spin cycle, a clothes washer, with a radius of 1.5 feet, rotates at a rate of four revolutions per second when at maximum speed. if the velocity of the outside wall of the washer follows the function ft/s when starting from rest, determine the time it takes to get the washer to maximum speed. also, find the magnitude of the acceleration of the outside wall the instant before it reaches maximum speed. (7.54 s, 948 ft/s^2)
The magnitude of the acceleration of the outside wall the instant before it reaches maximum speed is 948 ft/s^2.
What is acceleration?Acceleration is the rate of change of velocity over time. It is the increase in speed or the decrease in the time taken to cover a particular distance.
The equation describing the velocity of the outside wall of the washer is a linear one, given by the equation:
v(t) = at
where a is the acceleration of the wall and t is the time.
We know that the velocity of the wall when it reaches maximum speed is 4 revolutions per second. We can convert this to linear velocity by multiplying it by the circumference of the washer, 2πr, where r is the radius of the washer (1.5 feet). This gives us a final velocity of 9π ft/s
We can now solve for the acceleration of the wall. We know the final velocity and we can set the initial velocity to 0 due to the fact that the washer is starting from rest. So we can solve for the acceleration using the equation:
a = v(t) / t
Plugging in our values, we get:
a = 9π ft/s / t
Now we can solve for the time it takes to get the washer to maximum speed. We know that the final velocity is 9π ft/s and the acceleration is a. So we can solve for the time by rearranging the equation to get:
t = v(t) / a
Plugging in our values, we get:
t = 9π ft/s / a
Solving for t, we get:
t = 9π ft/s / 948 ft/s^2
Simplifying, we get:
t = 7.54 s
Therefore, it takes 7.54 seconds for the washer to reach its maximum speed. The magnitude of the acceleration of the outside wall the instant before it reaches maximum speed is 948 ft/s^2.
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A certain lightning bolt moves 22.7 C of charge. How many fundamental units of charge is this? Your answer will be in the form of: N x 1019 and you need to indicate the number N, do not include the unit.
Hint: e = 1.6 x 10-19 C.
The fundamental units of charge is 14.18 C for moving 22.7C of charge.
An object's ability to feel an attractive or repulsive force toward another is determined by its electric charge, also known as charge for short. The coulomb is the primary measure of charge (C). There are two forms of charge: protons exhibit positive charge, while electrons exhibit negative charge (exhibited by electrons). The electric forces between charged particles are described by Coulomb's law; if the charges shift, the electromagnetic force becomes more complex.
fundamental charge=[tex]\frac{q}{e}[/tex]
Now, n=[tex]\frac{22.7}{1.6\times10^{-19} }[/tex]
n=[tex]1.418\times10^{20}[/tex]
and according to question,
the value of fundamental unit charge is 14.18.
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a simply supported beam has a concentrated moment ma applied at the left support and a concentrated force f applied at the free end of the overhang on the right. using superposition, determine the deflection equations in the regions ab and bc.
To determine the deflection equations in the regions AB and BC of the simply supported beam using superposition, we first need to find the deflection equations for the beam under each load separately and then add them together.
Deflection due to the concentrated moment M_A at the left support:
The deflection equation for this case can be found using the equation:
δ(x) = (M_A * x²) / (6 * E * I)
Where δ(x) is the deflection at a distance x from the left support, M_A is the concentrated moment at the left support, E is the modulus of elasticity, and I is the moment of inertia.
Deflection due to the concentrated force F at the free end of the overhang on the right:
The deflection equation for this case can be found using the equation:
δ(x) = (F * (L - x)³) / (3 * E * I)
Where δ(x) is the deflection at a distance x from the right support, F is the concentrated force at the free end of the overhang, L is the length of the beam, E is the modulus of elasticity, and I is the moment of inertia.
SuperpositionBy the principle of superposition, the total deflection at any point is the sum of the deflections caused by each load.
Therefore,
δ(x) = (M_A * x²) / (6 * E * I) + (F * (L - x)³) / (3 * E * I)
Where x is the distance from the left support (AB) and
δ(x) is the total deflection in AB
And,
δ(x) = (F * (L-x)³) / (3 * E * I)
Where x is the distance from the right support (BC) and
δ(x) is the total deflection in BC
Note: The concentrated moment M_A has no effect on deflection in BC as it is on the left side of the support.
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A loaded ore car has a mass of 950 kg and rolls on rails with negligible friction. IT starts from rest and is pulled up a mine shaft by a cable connected to a winch. The shaft is inclined at 30.0o above the horizontal The car accelerates uniformly to a speed of 2.20 m/s in 12.0 s and then continues at constant speed. What power must the winch motor provides when the car is moving at constant speed?
10.628 kW of power must the winch motor provides when the car is moving at constant speed at the slope of 30.0o at a speed of 2.20m/s for 12 s to keep of moving.
The maximum Force, with the maximum speed of the motor, gives maximum power Now we know
a = (vf-vi)/t = (2.20 - 0)/12 => 0.1853 m/s^2
The maximum force is when the car is accelerating so,
f = fa+fg
F = ma+ ma * sign 30o => 4831.035 N ( As shown in the Image attached how the perpendicular vector that is a signθ is taken)
So the force will be 4831.035 N
Hence the maximum power p = fxV
4831.035 * 2.20
P =10626.27 w
which results in 10626.27/1000 kW
So 10.628 Kw is the maximum power required for the slop of 30o.
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a conducting bar moves to the left at a constant speed v on two conducting rails joined at the left as shown. as a result of the bar moving through a constant magnetic field, a current i is induced in the indicated direction. which one of the following directions is that of the magnetic field?
As a result of the bar moving through a constant magnetic field, a current i is induced in the indicated direction. The field is pointing downwards as a result of this.
Option E is correct.
How does a magnetic field work?A moving electric charge or an electric current can produce a magnetic field, which is a physical phenomenon. It is a field of force that is hard to see that surrounds an object and has the power to attract or repel other magnets. Tesla or Gauss units are used to measure magnetic field strength. Magnetic resonance imaging (MRI), electricity generation, and navigation are just a few examples of the many applications for magnetic fields.
The magnetic field is oriented out of the plane of the page and is perpendicular to the plane of the conducting rails. The field is pointing downwards as a result of this. If a compass needle were placed in the field, its north-seeking pole would point in the same direction as the current that was induced in the rails because of the field's direction.
Question incomplete:a conducting bar moves to the left at a constant speed v on two conducting rails joined at the left as shown. as a result of the bar moving through a constant magnetic field, a current i is induced in the indicated direction. which one of the following directions is that of the magnetic field?
A. towards the right
B. towards the left
C.parallel along the axis
D. into the page
E. out the page
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A pendulum that consists of a 2kg mass swings a maximum vertical displacement of 10 cm above its rest position. At its lowest point, the KE of the mass is equal to
F. 0.196 J
G. 1.96 J
H. 19.6 J
J. 196 J
K. 1960 J
The kinetic energy at the lowest point is 1.96 Joule. The result is obtained by using the concept of Conservation of mechanical energy.
What is the conservation of mechanical energy?The Conservation of mechanical energy states that the total mechanical energy of a system is conserved. It can be expressed as
E initial = E final
KE₁ + U₁ = KE₂ + U₂
½mv₁ + mgh₁ = ½mv₂ + mgh₂
Where
E = mechanical energyKE = kinetic energyU = potential energym = mass of an objectv = speed of objecth = height of objectThe index 1 and 2 shows at point 1 (initial) and 2 (final).
A pendulum that consists of
m = 2 kgh max = 10 cm (0.1 m) above its rest position.At its lowest point, find kinetic energy!
The lowest point is at the mean position where h = 0.
Let's say, point 1 is at the highest point and point 2 is at the lowest point.
E initial = E final
½mv₁ + mgh₁ = ½mv₂ + mgh₂
At the highest, the speed is zero. h max means highest position. It would be
½m(0) + mgh₁ = ½mv₂ + mg(0)
mgh₁ = ½mv₂
U₁ = KE₂
The kinetic energy is
KE₂ = mgh₁
KE₂ = 2 (9.8) (0.1)
KE₂ = 1.96 Joule
Hence, the kinetic energy at the lowest point is 1.96 Joule.
The correct option is (G).
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1. Two balls with masses of 2.0kg and 60kg traveling at 12ms and 4.0 m/s, respectively. They have a
head-on inelastic collision (not perfectly). The 2.0kg moves in the opposite direction with a speed of 8.0
m/s.
a. Find the speed of the 6.0kg ball after the collision.
B. Find the KE for each ball before and after the collision
C. Find the amount of KE that is lost during the collision.
a) The speed of the 60 Kg ball is 4.1 m/s
b) The KE before and after collision is 144 J and 64 J respectively
c) The KE lost is 80 J
What is the momentum?We know that when we talk about the momentum, our minds would go to the collision of the objects that we have in this case which are the balls in the question.
a) Momentum before collision = Momentum after Collison
(2 * 12) + (4 * 60) = (8 * 2) + (60 * v)
v is the velocity of the 60Kg ball
24 + 240 = 16 + 60v
v = 4.1 m/s
b) KE before collision
1) 0.5 * 2 * (12)^2 = 144 J
2) 0.5 * 60 * 4^2 = 480 J
KE after collision;
1) 0.5 * 2 * 8^2 = 64 J
2) 0.5 * 60 * (4.1)^2 = 504.3 J
c) The KE lost in the collision is; 144 J - 64 J = 80 J
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pls answer it
thanks
(a) The change in the length of the bar is 0.012 m.
(b) The new length of the bar is 10.012 m.
What is the change in length of the bar?The change in the length of the bar is calculated by applying the following formula.
ΔL = αLΔθ
where;
α is the linear expansivityL is the original length of the barΔθ is the change in lengthΔL = ( 24 x 10⁻⁶ x 10) x ( 40 - -10)
ΔL = ( 24 x 10⁻⁶ x 10) x ( 50)
ΔL = 0.012 m
The new length of the bar is calculated as follows;
L₁ = L + ΔL
L₁ = 10 m + 0.012 m
L₁ = 10.012 m
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work and Tes...
As shown in the drawing, a positively charged particle B has
charge q = +6.1 x 104 C. The particle lies between particles C
and A whose charges, respectively, are qA= - 10 x 10 -4 ℃ and qc
+17.3 x 104 C. The distance between A and B is 0.73 m and
the distance between C and B is 1.09 m. What is the magnitude
of the net force on particle B due to the other two particles?
Please round your answer to the nearest whole number (integer).
Take k as 9.0 x 10⁹ Nm²/C².
=
A
B
Equation: In general,
F = k12. Use this equation twice,
7-2
one for A and B, another for C and B.
The magnitude of the n.et force on particle B due to the other two particles is 8 x 10¹⁹ N
What is the net force on particle B due to the other two particles?The net force on particle B due to the other two particles is calculated by applying the formula for electric force.
F = ( kq₁q₂) / r²
where;
K is Coulomb's constantq₁ is first chargeq₂ is second charger is the distance between the chargesElectric force between A and B;
F(AB) = ( 9 x 10⁹ x 10 x 10⁻⁴ x 6.1 x 10⁴ ) / ( 0.73² )
F (AB) = 1.03 x 10¹² N
Electric force between B and C;
F(BC) = ( 9 x 10⁹ x 17.3 x 10⁴ x 6.1 x 10⁴ ) / ( 1.09² )
F (BC) = 8 x 10¹⁹ N
The net force on particle B is calculated as;
F (net) = - F (AB) - F (BC)
F (net) = - 1.03 x 10¹² N - 8 x 10¹⁹ N
F (net) = - 8 x 10¹⁹ N
F (net) = 8 x 10¹⁹ N towards A
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